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NONLINEAR CONTINUUM
MECHANICS FOR FINITE
ELASTICITY-PLASTICITY
NONLINEAR
CONTINUUM
MECHANICS FOR
FINITE ELASTICITY-
PLASTICITY
Multiplicative Decomposition With
Subloading Surface Model
KOICHI HASHIGUCHI
Technical Adviser, MSC Software Ltd.
(Emeritus Professor of Kyushu University),
Tokyo, Japan
Elsevier
Radarweg 29, PO Box 211, 1000 AE Amsterdam, Netherlands
The Boulevard, Langford Lane, Kidlington, Oxford OX5 1GB, United Kingdom
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Publisher: Matthew Deans

Acquisitions Editor: Dennis McGonagle
Editorial Project Manager: Joshua Mearns
Production Project Manager: Sojan P. Pazhayattil
Cover Designer: Greg Harris
Typeset by MPS Limited, Chennai, India
Contents
Preface xi
1. Mathematical fundamentals 1
1.1 Matrix algebra 1
1.1.1 Summation convention 1
1.1.2 Kronecker’s delta and alternating symbol 2
1.1.3 Matrix notation and determinant 2
1.2 Vector 6
1.2.1 Definition of vector 7
1.2.2 Operations of vector 7
1.3 Definition of tensor 15
1.4 Tensor operations 18
1.4.1 Properties of second-order tensor 18
1.4.2 Tensor components 19
1.4.3 Transposed tensor 20
1.4.4 Inverse tensor 21
1.4.5 Orthogonal tensor 22
1.4.6 Tensor decompositions 24
1.4.7 Axial vector 25
1.4.8 Determinant 27
1.4.9 Simultaneous equation for vector components 30
1.5 Representations of tensors 31
1.5.1 Notations in tensor operations 31
1.5.2 Operational tensors 32
1.5.3 Isotropic tensors 34
1.6 Eigenvalues and eigenvectors 35
1.6.1 Eigenvalues and eigenvectors of second-order tensor 35
1.6.2 Spectral representation and elementary tensor functions 37
1.6.3 Cayley Hamilton theorem 38
1.6.4 Scalar triple products with invariants 39
1.6.5 Second-order tensor functions 39
1.6.6 Positive-definite tensor and polar decomposition 40
1.6.7 Representation theorem of isotropic tensor-valued tensor function 42
1.7 Differential formulae 43
1.7.1 Partial derivatives of tensor functions 43
1.7.2 Time-derivatives in Lagrangian and Eulerian descriptions 48
1.7.3 Derivatives of tensor field 49
1.7.4 Gauss’ divergence theorem 51
1.7.5 Material-time derivative of volume integration 52
v
vi CONTENTS
1.8 Variations of geometrical elements 53

1.8.1 Deformation gradient and variations of line, surface and volume
elements 53
1.8.2 Velocity gradient and rates of line, surface and volume elements 56
2. Curvilinear coordinate system 61

2.1 Primary and reciprocal base vectors 61
2.2 Metric tensor and base vector algebra 65
2.3 Tensor representations 68
3. Tensor operations in convected coordinate system 77

3.1 Advantages of description in embedded coordinate system 77
3.2 Convected base vectors 79
3.3 Deformation gradient tensor 80
3.4 Pull-back and push-forward operations 83
3.5 Convected time-derivative 88
3.5.1 General convected derivative 89
3.5.2 Corotational rate 92
3.5.3 Objectivity of convected rate 95
4. Deformation/rotation (rate) tensors 101

4.1 Deformation tensors 101
4.2 Strain tensors 106
4.2.1 Green and Almansi strain tensors 106
4.2.2 General strain tensors 109
4.2.3 Logarithmic strain tensor 113
4.3 Volumetric and isochoric parts of deformation gradient tensor 114
4.4 Strain rate and spin tensors 117
4.4.1 Strain rate and spin tensors based on velocity gradient tensor 117
4.4.2 Strain rate tensor based on general strain tensor 120
5. Conservation laws and stress tensors 123

5.1 Conservation laws 123
5.1.1 Conservation law of physical quantity 123
5.1.2 Conservation law of mass 124
5.1.3 Conservation law of linear momentum 125
5.1.4 Conservation law of angular momentum 126
5.2 Cauchy stress tensor 127
5.2.1 Definition of Cauchy stress tensor 127
5.2.2 Symmetry of Cauchy stress tensor 130
5.3 Balance laws in current configuration 132
5.3.1 Translational equilibrium 133
5.3.2 Rotational equilibrium: symmetry of Cauchy stress tensor 133
5.3.3 Virtual work principle 134
CONTENTS vii
5.3.4 Conservation law of energy 135

5.4 Work-conjugacy 135
5.4.1 Kirchhoff stress tensor and work-conjugacy 136
5.4.2 Work-conjugate pairs 137
5.4.3 Physical meanings of stress tensors 138
5.4.4 Relations of stress tensors 141
5.4.5 Relations of stress tensors to traction vectors 142
5.5 Balance laws in reference configuration 145
5.5.1 Translational equilibrium 145
5.5.2 Virtual work principle 146
5.5.3 Conservation law of energy 146
5.6 Simple shear 147
6. Hyperelastic equations 151

6.1 Basic hyperelastic equations 151
6.2 Hyperelastic constitutive equations of metals 155
6.2.1 St. Venant Kirchhoff elasticity 155
6.2.2 Modified St. Venant Kirchhoff elasticity 156
6.2.3 Neo-Hookean elasticity 157
6.2.4 Modified neo-Hookean elasticity (1) 157
6.3 Hyperelastic equations of rubbers 159
6.4 Hyperelastic equations of soils 160
6.5 Hyperelasticity in infinitesimal strain 161
7. Development of elastoplastic and viscoplastic constitutive

equations 163
7.1 Basis of elastoplastic constitutive equations 163
7.1.1 Fundamental requirements for elastoplasticity 164
7.1.2 Requirements for elastoplastic constitutive equation 166
7.2 Historical development of elastoplastic constitutive equations 168
7.2.1 Infinitesimal hyperelastic-based plasticity 168
7.2.2 Hypoelastic-based plasticity 178
7.2.3 Multiplicative hyperelastic-based plasticity 181
7.3 Subloading surface model 182
7.4 Cyclic plasticity models 188
7.4.1 Cyclic kinematic hardening models with yield surface 188
7.4.2 Ad hoc Chaboche model and Ohno-Wang model excluding yield
surface 191
7.4.3 Extended subloading surface model 192
7.5 Formulation of (extended) subloading surface model 195
7.5.1 Normal-yield and subloading surfaces 195
7.5.2 Evolution rule of elastic-core 198
viii CONTENTS
7.5.3 Plastic strain rate 205

7.5.4 Strain rate versus stress rate relations 206
7.5.5 Calculation of normal-yield ratio 207
7.5.6 Improvement of inverse and reloading responses 208
7.5.7 Cyclic stagnation of isotropic hardening 209
7.6 Implicit time-integration: return-mapping 213
7.6.1 Return-mapping formulation 213
7.6.2 Loading criterion 221
7.6.3 Initial value of normal-yield ratio in plastic corrector step 224
7.6.4 Consistent tangent modulus tensor 227
7.7 Subloading-overstress model 229
7.7.1 Constitutive equation 230
7.7.2 Defects of past overstress model 238
7.7.3 On irrationality of creep model 240
7.7.4 Implicit stress integration 243
7.7.5 Temperature dependence of isotropic hardening function 249
7.8 Fundamental characteristics of subloading surface model 249
7.8.1 Distinguished abilities of subloading surface model 250
7.8.2 Bounding surface model with radial-mapping: Misuse of subloading
surface model 252
8. Multiplicative decomposition of deformation gradient tensor 255

8.1 Elastic-plastic decomposition of deformation measure 256
8.1.1 Necessity of multiplicative decomposition of deformation gradient
tensor 256
8.1.2 Isoclinic concept 259
8.1.3 Uniqueness of multiplicative decomposition 262
8.1.4 Embedded base vectors in intermediate configuration 263
8.2 Deformation tensors 264
8.2.1 Elastic and plastic right Cauchy-Green deformation tensor 264
8.2.2 Strain rate and spin tensors 265
8.3 On limitation of hypoelastic-based plasticity 269
8.4 Multiplicative decomposition for kinematic hardening 271
9. Subloading-multiplicative hyperelastic-based plastic and

viscoplastic constitutive equations 273
9.1 Stress measures 273
9.2 Hyperelastic constitutive equations 275
9.3 Conventional elastoplastic model 277
9.3.1 Flow rules for plastic strain rate and plastic spin 277
9.3.2 Confirmation for uniqueness of multiplicative decomposition 281
9.4 Continuity and smoothness conditions 283
9.5 Initial subloading surface model 284
9.6 Multiplicative extended subloading surface model 286
9.6.1 Multiplicative decomposition of plastic deformation gradient for
elastic-core 286
CONTENTS ix
9.6.2 Normal-yield, subloading and elastic-core surfaces 289

9.6.3 Plastic flow rules 291
9.7 Material functions of metals and soils 296
9.7.1 Metals 296
9.7.2 Soils 300
9.8 Calculation procedure 306
9.9 Implicit calculation by return-mapping 309
9.9.1 Return-mapping 309
9.9.3 Initial value of normal-yield ratio in plastic corrector step 314
9.10 Cyclic stagnation of isotropic hardening 317
9.11 Multiplicative subloading-overstress model 320
9.11.1 Constitutive equation 320
9.11.2 Calculation procedure 326
9.11.3 Implicit calculation by return-mapping 328
9.12 On multiplicative hyperelastic-based plastic equation in current
configuration 330
10. Subloading-friction model: finite sliding theory 335

10.1 History of friction models 335
10.2 Sliding displacement and contact traction vectors 336
10.3 Hyperelastic sliding displacement 339
10.4 Normal-sliding and subloading-sliding surfaces 340
10.5 Evolution rule of friction coefficient 341
10.6 Evolution rule of sliding normal-yield ratio 342
10.7 Plastic sliding velocity 344
10.8 Calculation procedure 348
10.9 Return-mapping 349
10.9.1 Return-mapping formulation 349
10.10 Subloading-overstress friction model 356
10.11 Implicit stress integration 362
10.12 On crucially important applications of subloading-friction model 363
10.12.1 Loosening of screw 363
10.12.2 Deterministic prediction of earthquake occurrence 364
11. Comments on formulations for irreversible mechanical

phenomena 365
11.1 Utilization of subloading surface model 365
11.1.1 Mechanical phenomena described by subloading surface model 365
11.1.2 Standard installation to commercial software 367
11.2 Disuses of rate-independent elastoplastic constitutive equations 368
11.3 Impertinence of formulation of plastic flow rule based on second law of
thermodynamics 369
x CONTENTS
Appendix 1: Proofs for formula of scalar triple products

with invariants 371
Appendix 2: Convective stress rate tensors 373
Appendix 3: Cauchy elastic and hypoelastic equations 377
Bibliography 379
Index 393
Preface
The elastoplasticity theory is now faced to the epoch-making devel-

opment that the exact description of the finite irreversible (plastic or vis-
coplastic) deformation/sliding behavior under the monotonic/cyclic
loading in the general rate of deformation/sliding from the static to the
impact loading is attained as the subloading multiplicative hyperelas-
tic based plasticity and viscoplasticity. This is the first book on this the-
ory, comprehensively describing the underlying concepts and the
formulations for the subloading surface model and for the multiplicative
decomposition of deformation gradient tensor into the elastic and the plastic
(or viscoplastic) parts and their combination.
The precise description of the plastic strain rate induced by the rate
of stress inside the yield surface is inevitable for the prediction of cyclic
loading behavior, which is crucial for the accurate mechanical design of
solids and structures in engineering. A lot of works have been executed
and various unconventional plastic constitutive (cyclic plasticity) models,
named by Drucker (1998), have been proposed aiming at describing the
plastic strain rate caused by the rate of stress inside the yield surface
after 1960s when the demands of mechanical designs of solids and
structures for the mechanical vibration and the seismic vibrations have
been highly raised responding to the high development of machine
industries and the frequent occurrences of earthquakes, e.g. Chile (1960)
and Niigata (Japan) (1964). Among various unconventional models the
multi surface model (Mroz, 1967; Iwan, 1967), the two surface model
(Dafalias and Popov, 1975; Krieg, 1975; Yoshida and Uemori, 2002), and
the superposed-kinematic hardening model (Chaboche et al., 1979;
Ohno and Wang, 1993) are well known. However, they assume a sur-
face enclosing a purely elastic domain and are based on the premise
that the plastic strain rate develops with the translation of the small
yield surface so that they are called the cyclic kinematic hardening model.
Therefore they possess various defects, for example, (1) the abrupt tran-
sition from the elastic to the plastic state violating the continuity and
the smoothness conditions (Hashiguchi, 1993a,b, 1997, 2000), (2) the
incorporation of the offset value of the plastic strain at yield, which is
accompanied with the unreality and the arbitrariness, (3) the incapabil-
ity of cyclic loading behavior for the stress amplitude less than the small
xi
xii Preface
surface enclosing an elastic domain, (4) the incapability of the nonpro-

portional loading behavior, (5) the incapability of extension to the rate-
dependency at high rate of deformation up to the impact loading behav-
ior, (6) the limitation to the description of deformation behavior in
metals, and (7) the necessity of the additional cumbersome operation to
pull back the stress to the yield surface or the small surface enclosing an
elastic domain. In particular, it is quite pitiful from the scientific point
of view that the superposed cyclic plasticity model, i.e. the Chaboche
model and the Ohno-Wang model are diffused widely, which are the
most primitive ad hoc cyclic plasticity models ignoring the historical
development of the plasticity but regressing to the easy going way by
the empirical method as will be explained in Section 7.4.
Now, it should be noted that the plastic strain rate is not induced
abruptly but develops gradually as the stress approaches the yield sur-
face. In fact, the mutual slips of material particles, for example, crystal
particles in metals and soil particles in sands and clays leading to the
plastic deformation is not induced simultaneously but induced gradu-
ally from parts in which mutual slips can be induced easily, exhibiting
the smooth transition from the elastic to the plastic transition. The sub-
loading surface model (Hashiguchi, 1978, 1980, 1989, 2017a; Hashiguchi
and Ueno, 1997) is free from the existence of the stress region enclosing
the purely elastic domain, while the existence has been postulated in
the other elastoplasticity models. The subloading surface, which passes
through the current stress and is similar to the yield surface, is assumed
inside the yield surface, and then it is postulated that the plastic strain
rate is not induced suddenly at the moment when the stress reaches the
yield surface but it develops as the stress approaches the yield surface,
that is, as the subloading surface expands. Therefore the smooth transi-
tion from the elastic to the plastic state, that is, the smooth elastic-plastic
transition leading to the continuous variation of the tangent stiffness
modulus tensor is described in this model. The subloading surface
model has been applied to the descriptions of the elastoplastic deforma-
tion behaviors of various solids, for example, metals, soils, concrete, etc.
Further, it has been extended to describe the viscoplastic deformation
by incorporating the concept of the overstress. The subloading surface
model would be regarded to be the governing law of the irreversible
mechanical phenomena of solids.
The subloading surface model has been incorporated into the com-
mercial software “Marc” in MSC Software Corporation as the standard
installation by the name “Hashiguchi model,” which can be used by all
Marc users (contractors) since October, 2017. Therefore it is explained in
the Marc user manual (MSC Software Corporation, 2017) in brief.
Further, the function for the automatic determination of material para-
meters was installed into the Marc as the standard function in June
Preface xiii
2019. Furthermore, the subloading-friction model will also be incorpo-

rated into the Marc as the standard installation until the end of 2020.
The mechanisms of the elastic deformation and the plastic deforma-
tion in the solids consisting of material particles are physically different
from each other such that the former is induced by the deformation of
material particles themselves (e.g., crystal particles in metals and soil
particles in sands and clays) but the latter is induced by the mutual
slips between the material particles. Further, note that all the deforma-
tion measures, for example, the infinitesimal and the finite-strain tensors
and the strain rate tensor (skew-symmetric part of velocity gradient ten-
sor) are defined by the deformation gradient tensor. Therefore the exact
description of finite elastoplastic deformation requires the exact decom-
position of the deformation gradient tensor into the elastic and the plas-
tic parts. Furthermore, note that the deformation gradient tensor is
defined by the ratio (note: not difference) of the current infinitesimal
line element vector to the initial one. Then, the multiplicative decompo-
sition of the deformation gradient tensor has been introduced for the
exact description of finite elastoplastic deformation by the leading scho-
lars (Kroner, 1960; Lee and Liu, 1967; Lee, 1969; Mandel, 1971, 1972,
1973a; Kratochvil, 1973). However, it now passed already more than a
half century after the proposition of the multiplicative decomposition of
deformation gradient tensor. In the meantime, unfortunately the
hypoelastic-based plasticity has been studied enthusiastically by numer-
ous workers represented by Rodney Hill and James R. Rice after the
proposition of the hypoelasticity by Truesdell (1955), which is not based
on the multiplicative decomposition so that it is limited to the infinitesi-
mal elastic deformation and accompanied with the cumbersome time-
integration procedure of the corotational rates of the stress and tensor-
valued internal variables. In addition, the concept of the multiplicative
decomposition has not been delineated properly even in the
notable books referring to this concept (cf. Lubliner, 1990; Simo, 1998;
Simo and Hughes, 1998; Lubarda, 2002; Haupt, 2002; Nemat-Nasser,
2004; Asaro and Lubarda, 2006; Bonet and Wood, 2008; de Sauza Neto
et al., 2008; Gurtin et al., 2010; Hashiguchi and Yamakawa, 2012;
Belytshko et al., 2014, etc.).
The multiplicative hyperelastic based plasticity has been studied
centrally by Simo and his colleagues (e.g., Simo, 1985, 1988a,b, 1992;
Simo and Ortiz, 1985) in the last century, in which the logarithmic strain
has been used mainly leading to the coaxiality of stress and strain rate
so that it has been limited to the isotropy. It has been developed actively
from the beginning of this century by Lion (2000), Menzel and
Steinmann (2003a,b), Wallin et al. (2003), Dettmer and Reese (2004),
Menzel et al. (2005), Wallin and Ristinmaa (2005), Gurtin and Anand
(2005), Sansour et al. (2006, 2007), Vladimirov et al. (2008, 2010),
xiv Preface
Henann and Anand (2009), Brepols et al. (2014), etc., in which constitu-
tive relations are formulated in the intermediate configuration imagined
fictitiously by the unloading to the stress-free state along the hyperelas-
tic relation, based on the isoclinic concept (Mandel, 1971). However, the
plastic flow rule with the generality unlimited to the elastic isotropy
remains unsolved and only the conventional plasticity model, named by
Drucker (1998), with the yield surface enclosing the elastic domain have
been incorporated so that only the monotonic loading behavior of elasti-
cally isotropic materials is concerned in them.
The subloading multiplicative hyperelastic based plastic model has
been formulated by the author recently (Hashiguchi, 2018c), which is
capable of describing the finite elastoplastic deformation/rotation rigor-
ously under the monotonic/cyclic loading process. Further, it has been
extended to the subloading-multiplicative hyperelastic-based viscoplas-
ticity recently, which is capable of describing the rate-dependent elasto-
plastic deformation behavior at the general rate from the static to the
impact loading. It is to be the best opportunity to review the multiplica-
tive hyperelastic based plasticity comprehensively and explain the
detailed formulation of the subloading multiplicative hyperelas-
tic based plastic model systematically. This is the first book on the sub-
loading multiplicative hyperelastic based plasticity and viscoplasticity
for the description of the general irreversible deformation/sliding
behavior.
The subloading surface model and the multiplicative hyperelas-
tic based plasticity are explained comprehensively providing the
detailed physical interpretations for all relevant concepts and the deriv-
ing processes of all equations. Further, the incorporation of the subload-
ing surface model to the multiplicative hyperelastic plastic relation is
described in detail. Further, it is extended to the description of the vis-
coplastic deformation by incorporating the concept of overstress, which
is capable of describing the general rate of deformation ranging from
the quasistatic to the impact loading behaviors (Hashiguchi, 2016a,
2017a). In addition, the exact hyperelastic based plastic and viscoplastic
constitutive equation of friction (Hashiguchi, 2018c) is formulated rigor-
ously, while the hypoelastic-based plastic constitutive equation of fric-
tion has been formulated formerly (Hashiguchi et al., 2005; Hashiguchi
and Ozaki, 2008; Hashiguchi, 2013a).
The aim of this book is to give a comprehensive explanation of the
finite elastoplasticity theory and viscoplasticity under the monotonic
and the cyclic loading processes. The incorporation of the Lagrangian
tensors is required originally in the formulation of finite elastoplasticity
and viscoplasticity, since the deformation of the material involved in
the reference configuration, which is invariant through the deformation,
is physically relevant. Therefore the necessity and the meanings of the
Preface xv
Lagrangian tensors and the transformations rules between the Eulerian

and the Lagrangian tensors, that is, the pull-back and push-forward
operations are explained concisely. Various Lagrangian stress tensors
are derived based on the requirement of the work-conjugacy from the
Cauchy stress tensor in the current configuration. To this end, the
descriptions of physical quantities and relations in the embedded (con-
vected) coordinate system, which turns into the curvilinear coordinate
system under the deformation of material, are required, since their
physical meanings can be captured clearly by observing them in the
coordinate system that not only moves but also deforms and rotates
with material itself. In other words, the essentials of continuum mechan-
ics cannot be captured without the incorporation of the general curvilin-
ear coordinate system, to which the embedded coordinate system
changes, although the explanation only in the rectangular coordinate
system is given in a lot of books entitled “continuum mechanics.”
The author expects that the readers of this book will capture the fun-
damentals in the finite-strain elastoplasticity theory and they will con-
tribute to the development of mechanical designs of machinery and
structures in the field of engineering practice by applying the theories
addressed in this book. A reader is apt to give up reading through a
book if one encounters a matter that is uneasy to understand by insuffi-
cient explanation. For this reason, the detailed explanations of physical
concepts in elastoplasticity are delineated, and the derivations/transfor-
mation processes of all equations are given with detailed proofs but
without abbreviation.
The author wishes to express cordial thanks to his colleagues at
Kyushu University, who have discussed and collaborated over several
decades: Prof. M. Ueno (currently Emeritus Professor at University of
the Ryukyus) in particular, and Dr. T. Okayasu (currently Associate
Professor at Kyushu University), Dr. S. Tsutsumi (currently Associate
Professor at Osaka University), Dr. T. Ozaki of Kyushu Electric Eng.
Consult. Inc., Dr. S. Ozaki (currently Associate Professor at Yokohama
National University), and Dr. T. Mase of Tokyo Electric Power Services
Co., Ltd. (currently Professor of Tezukayama Gakuin Univ.)
Furthermore, the author is thankful to Dr. K. Okamura, Dr. N.
Suzuki, and Dr. R. Higuchi, Nippon Steel & Sumitomo Metal
Corporation, Dr. M. Oka and Mr. T. Anjiki, Yanmar Co. Ltd., for the col-
laborations on constitutive relations of metals and the numerical calcu-
lations. In particular, the numerical calculations performed by Mr. T.
Anjiki was quite effective for the improvement of the subloading-
overstress model. The author is also grateful to Mr. T. Kato (President)
and Dr. M. Tateishi (Fellow), MSC Software, Ltd., Japan for the standard
implementation of the Hashiguchi (subloading surface) model to the
commercial FEM (Finite Element Method) software Marc.
xvi Preface
The heartfelt gratitude of the author is dedicated to Prof. Yuki

Yamakawa of Tohoku University, for various advices and close colla-
borations with detailed discussions on elastoplasticity theory, particu-
larly on the finite-strain theory and the numerical method. In addition,
the author acknowledges the great gratitude to Prof. Yamakawa for crit-
ical reading of the original manuscript and then suggesting various pre-
cious elaborations.
The author expresses his sincere gratitude to Prof. Genki Yagawa,
Emeritus Professor, The University of Tokyo, for encouraging always
the author with undeserved high appreciation of research contributions,
and thus the author was stimulated to the publication of this book.
The author is convinced that this book will contribute substantially to
the steady developments of solid mechanics and the manufacturing and
constructing industries through the readers. Finally, the author would
like to acknowledge the enthusiastic supports by the editor Mr. Dennis
Mcgonagle, the editorial project manager Mr. Joshua Mearns, and the
project manager: Mr. Sojan P. Pazhayattil, Elsevier, for the generous cor-
porations on the publication of this book.
Koichi Hashiguchi
June 2020
C H A P T E R
1
Mathematical fundamentals
The mathematical fundamentals are addressed in this chapter, which

are required to understand sufficiently the elastoplasticity theory
described in the subsequent chapters. First, the basics of vector and ten-
sor algebra are explained and then the differential formula and the var-
iations of the geometrical elements are described comprehensively.
Readers are tempted to skip to study these mathematical fundamentals
but they are explained concisely by showing the derivation processes
for almost all equations. Component descriptions of vectors and tensors
in this chapter are limited in the normalized rectangular coordinate system,
that is, rectangular coordinate system with unit base vectors, while the
terms orthogonal, orthonormal, and Cartesian are often used instead of
rectangular. However, these tensor relations hold even in the general
curvilinear coordinate system of the Euclidian space described in the
subsequent chapters.
1.1 Matrix algebra
The basic matrix algebra with some conventions and symbols appear-
ing in the continuum mechanics are described in this section.
1.1.1 Summation convention

The Cartesian summation convention is first introduced in which
repeated suffix in a term is summed over numbers that the suffix can
take, for example,
Nonlinear Continuum Mechanics for Finite Elasticity-Plasticity

DOI: https://doi.org/10.1016/B978-0-12-819428-7.00001-8 1 © 2020 Elsevier Inc. All rights reserved.
2 1. Mathematical fundamentals
8
>
> X 3
>
> u v 5 ur vr 5 u1 v1 1 u2 v2 1 u3 v3 ;
>
>
r r
>
> r51
>
< X3
Trr 5 Trr 5 T11 1 T22 1 T33 (1.1)
>
>
>
> r51
>
> X 3
>
>
> Tir vr 5
: Tir vr 5 Ti1 v1 1 Ti2 v2 1 Ti3 v3 ;
r51
A letter of the repeated suffix is arbitrary and thus it is called the

dummy index as known from
ur vr 5 us vs ; T rr 5 Tss ; Tir vr 5 Tis vs : (1.2)
This rule is also called Einstein’s summation convention. A repeated index

obeys this convention unless otherwise specified by the additional
remark “(no sum)” after an equation.
1.1.2 Kronecker’s delta and alternating symbol

The Kronecker’s delta δij ði; j 5 1; 2; 3Þ is defined as follows:

1: i 5 j
δij 5 (1.3)
0 : i 6¼ j
fulfilling
δir δrj 5 δij 5 δji ; δii 5 3 (1.4)
Further, the alternating (or permutation) symbol or Eddington’s epsilon

εijk is defined as follows:
8
< 1: even permutation of ijk from 123 ð123; 231; 312Þ
>
εijk 5 2 1: odd permutation of ijk from 123 ð213; 321; 132Þ (1.5)
>
:
0: others
fulfilling the following relation for the product.

εijk εijk 5 3! (1.6)
1.1.3 Matrix notation and determinant

Let the quantity T possessing nine (3 3 3) components Tij be
expressed in the arrangement

1.1 Matrix algebra 3
2 3
T11 T12 T13
T 5 ½Tij 5 4 T21 T22 T23 5 (1.7)
T31 T32 T33
which is called a matrix notation. The matrix I possessing the compo-

nents of the Kronecker’s delta is given by
2 3
1 0 0
I 5 ½δij 5 4 0 1 0 5 (1.8)
0 0 1
The quantity v possessing three (3 3 1) components is expressed as

2 3
v1
v 5 ½vi 5 4 v2 5 5 v1 v2 v2 (1.9)
v3
The multiplications of the quantity v and the matrix B by the matrix

A are denoted as Av and AB and defined as
ðAvÞi 5 Air vr 5 vr Air 5 ðvAT Þi (1.10)
ðABÞij 5 Air Brj 6¼ Bir Arj 5 ðBAÞij (1.11)
where ð ÞT stands for the transpose of the row and the column in the
matrix.
The quantity defined by the following equation is called the determi-
nant of T and is shown by the symbol det T, that is,

T11 T12 T13

detT 5 εijk T1i T2j T3k 5 εijk Ti1 Tj2 Tk3 5 T21 T22 T23 (1.12)
T31 T32 T33
with
detTT 5 detT; detðsTÞ 5 s3 detðTÞ (1.13)
Here, the number of permutations that the suffixes i, j, and k in εijk can
take is 3!. Therefore Eq. (1.12) can be written as
1
detT 5 εijk εpqr Tip Tjq Tkr (1.14)
3!
Eq. (1.14) is rewritten as
1 1 1
detT 5 Trs ðcof TÞrs ; detT 5 T: ðcof TÞ 5 trðTðcofTÞT Þ (1.15)
3 3 3

4 1. Mathematical fundamentals
or
detT 5 T1s ðcofTÞ1s 5 T2s ðcofTÞ2s 5 T3s ðcofTÞ3s
(1.16)
5 Tr1 ðcofTÞr1 5 Tr1 ðcofTÞr1 5 Tr2 ðcofTÞr2 5 Tr3 ðcofTÞr3
where
1
ðcofTÞip εijk εpqr Tjq Tkr (1.17)
2!
noting

1 1 1 1
εijk εpqr Tip Tjq Tkr 5 Tip εijk εpqr Tjq Tkr 5 Tip ðcofTÞip
3! 3 2! 3
ðcofTÞij is called the cofactor for the i-column and the j-row. The cofactor
is obtained through multiplying the minor determinant lacking the
ith row and jth column components by the sign ð21Þi1j .
The following lemmas for the properties of the determinant hold.
Lemma 1.1: If the first and the second rows are same, that is, T2j 5 T1j
for instance, we have εijk T1i T1j T3k 5 εjik T1j T1i T3k 5 2 εijk T1i T1j T3k .
Therefore we have the lemma “the determinant having same lines or
rows is zero.” Therefore the following relation is obtained from
Eq. (1.16) that
Tis Δjs 5 Tri Δrj 5 δij detT (1.18)
Lemma 1.2: If the first and the second lines are exchanged, that is, 122
for instance, we have εijk T2i T1j T3k 5 εjik T1i T2j T3k 5 2 εijk T1i T2j T3k .
Therefore we have the lemma “the determinant changes only its sign by
exchanging lines (or rows).”
By multiplying εijk to both sides in Eq. (1.12), we have
εijk detT 5 εijk εpqr T1p T2q T3r 5 εpqr Tip Tjq Tkr (1.19)
The transformation from the second side to the third side in

Eq. (1.19) is resulted from the abovementioned Lemmas 1.1 and 1.2.
Here, note that the expression of the determinant in Eq. (1.14) is derived
also by multiplying εijk to both sides in Eq. (1.19) and noting Eq. (1.6).
The additive decomposition of the components T2j into T2j 5 A2j 1 B2j
leads to
εijk T1i ðA2j 1 B2j ÞT2k 5 εijk T1i A2j T2k 1 εijk T1i B2j T2k (1.20)

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and at four o’clock the next day all was still. During the next ten
days clouds of black smoke continued to pour out, but all trusted
that the worst had passed, when, on the 14th, at half-past twelve or
almost exactly at midnight, a “frightful, unearthly thundering” began
again, and the shocks became heavier and more frequent until half-
past three (before it would have been light if the sky had been
clear), when the last house in the whole place had been laid in ruins.
The earth split open with a cracking that could be distinctly heard
above the awful thundering of the mountain. Out of the fissures jets
of hot water rose for a moment, and then the earth closed again, to
open in another place. An educated gentleman, who, from his great
wealth, generosity, and liberality, is justly known as the “Prince of
the Moluccas,” assured me that when two men were about one
thousand yards apart, one would see the other rise until his feet
seemed as high as the head of the observer, then immediately he
would sink and the observer rise until he seemed as much above his
fellow as he had been below him before. The published accounts
entirely agree with this statement. For fifteen hours the solid ground
thus rolled like the sea, but the heaviest wave did not occur till ten
o’clock on the 15th of February. Fort Orange, which had withstood
all the shocks of two hundred and thirty years, was partly thrown
down, and wholly buried under a mass of pumice-stone and the
débris of the forests above it. The people, as soon as this last day of
destruction commenced, betook themselves to their boats, for, while
the land was heaving like a troubled ocean, the sea continued quiet;
no great wave came in to complete the work of destruction on the
shore. It seemed, indeed, as if the laws that govern these two great
elements had been suddenly exchanged, and the fixed land had
become the mobile sea. The whole loss caused by this devastating
phenomenon was estimated at four hundred thousand Mexican
dollars; and yet, after all this experience, so great was the
attachment of both foreigners and natives to this particular spot,
that they would not select some one less dangerous on the
neighboring shores, but all returned and once more began to build
their houses for another earthquake to lay in the dust, proving that
the common remark in regard to them is literally true, that “they are
less afraid of fire than the Hollanders are of water.” The present city,
however, judging by the area of the ruins, is not more than two-
thirds the size of the former one. Its total population is about 9,000.
Of these, 100 are Europeans, 300 mestizoes, 200 Arabs, 400
Chinese, and the others natives of this and the adjoining islands. It
is divided into two parts, the southern or European quarter, known
by the peculiar name Malayu, and north of this the Chinese and Arab
quarter. Near the latter is Fort Orange, which was built in 1607, as
early as the settlement of Jamestown. In 1824 this fort was
pronounced by the governor-general the best in all the Netherlands
India. Beyond the fort is “the palace” of the Sultan of Ternate, and
north of this is the native village. The palace is a small residence,
built in the European style, and stands on a terrace, facing a wide,
beautiful lawn, that descends to the sea. Near it is a flag-staff, which
leans over as if soon to fall, a fit emblem of the decaying power of
its owner, whose ancestors were once so mighty as to make the
Dutch regard them with fear as well as with respect.
According to Valentyn, who gathered his information from the
native records, there were formerly in Gilolo a number of
independent states, each with its “kolano” or chief. In about a. d.
1250, two hundred and seventy years before any European sailed in
these seas, a great migration took place to the neighboring islands,
and a village named Tabona was formed on the top of this
mountain, which has been an active volcano ever since it was known
to Europeans. In a. d. 1322, many Javanese and Arabs came here to
buy cloves. This is the first historical record we have of the spice-
trade. The inhabitants of Obi and Bachian now united to counteract
the growing power of the prince of Ternate, but this union effected
little, for, in a. d. 1350, Molomateya, who was then reigning at
Ternate, learned from the Arabs how to build vessels, and, having
prepared a fleet, conquered the Sula Islands. The Arabs and
Javanese meantime made great exertions to convert these people to
Mohammedanism, and in a. d. 1460,[44] a little more than two
centuries after it had been introduced into Java, Mahum, the prince
of Ternate, became a Mohammedan “through the influence of the
Javanese.” About this time Malays and Chinese came from Banda to
purchase cloves, which they sold to Indian traders at Malacca. In
1512 Francisco Serano, whose vessel struck on the Turtle Islands,
when returning with D’Abreu from Amboina and Banda, induced the
natives to assist him in getting his ship afloat while the rest of the
fleet were returning to Malacca, and to pilot him to Ternate; and
thus he was the first European who reached the great centre of the
clove-trade. In 1521 the fleet of Magellan anchored off Tidore, an
island separated from Ternate by only a narrow strait.
Ferdinand Magellan, who organized this fleet, was a Portuguese
nobleman. He sailed, however, under the patronage of Charles V. of
Spain. On the 20th of September, 1519, he left the port of St. Lucas
with “five small ships of from sixty to one hundred and thirty tons,”
his object being to find a western passage to the Indies, particularly
the Spice Islands. Coasting southward along the shores of Brazil, he
found the strait which still continues to bear his name. This he
passed through with three ships, one having been wrecked, and one
having turned back. For one hundred and sixteen days he continued
sailing in a northwest direction, over (as it seemed to them) an
endless ocean. Their food became exhausted, but they yet kept on
the same course until at last their eyes were blessed with the sight
of land. Pigafetta, a member of this expedition, thus pictures their
sufferings: “On Wednesday, the 28th day of November, 1520, we
issued from the strait, engulfing ourselves in the ocean, in which,
without comfort or consolation of any kind, we sailed for three
months and twenty days. We ate biscuit which was biscuit no longer,
but a wormy powder, for the worms had eaten the substance, what
remained being fetid with the urine of rats and mice. The dearth was
such that we were compelled to eat the leathers with which the
yards of the ships were protected from the friction of the ropes. This
leather, too, having been long exposed to the sun, rain, and wind,
had become so hard that it was necessary to soften it by immersion
in the sea for four or five days, after which it was broiled on the
embers and eaten. We had to sustain ourselves by eating sawdust,
and a rat was in such request that one was sold for half a ducat.”
The first islands Magellan saw were those he named the Ladrones
or “Islands of Thieves.”[45] From those he came to the Philippines,
and on one of these (Mactan, near Zebu) he was murdered by the
natives, as was also Barbosa, a gentleman of Lisbon, who had
previously visited and described India, and from whose writings we
have frequently had occasion to quote. From Zebu, Magellan’s
companions sailed to the northern part of Borneo and Tidore.
Thence they continued southward, touching at Bachian and Timur, in
1522, and finally arrived safely back in Spain, having completed the
first circumnavigation of our globe. This great voyage was
accomplished nearly a century before the Pilgrims landed on our
New-England shores. Soon after the Portuguese had established
themselves at Ternate, they began to teach the natives their Catholic
creed, and in 1535 the native king, who had accepted that religion
and been christened at Goa, returned to Ternate and began his
reign. Other native princes then proposed to the Portuguese to
become Catholics, if they would take them under their protection,
and thus Catholicism began to spread rapidly, but the same year all
the native converts were destroyed by Mohammedans, headed by
Cantalino, who was styled “the Moluccan Vesper.” In 1546, Francis
Xavier,[46] a Catholic priest, visited Ternate. He afterward went back
to Malacca and proceeded to China and Japan, and returning from
the latter country died on an island off Macao, near Canton. The
Dutch first came to Ternate under Admiral Houtman, in 1578. In
1605, under Stephen van der Hagen, they stormed and took
Ternate, and thus drove the Portuguese out of the Moluccas, and the
island, since that date, has continued in their hands, the English not
being able to capture it during the early part of this century, when
they took Amboina and the neighboring islands. They now continued
their strenuous attempts to dislodge the Spaniards from their
stronghold on Tidore, until the besieged, finding themselves
constantly in danger, deserted the whole Moluccas to the Dutch in
1664.
As the Portuguese and Spaniards had been anxious to convert the
natives to Catholicism, so the Dutch were anxious to convert them to
Protestantism, but they did not, however, labor in the same manner
as the former. Pigafetta informs us that in eight days “all the
inhabitants of this island” (Zebu, one of the Philippines) “were
baptized, and also some of the other neighboring islands. In one of
the latter we set fire to a village” (because the inhabitants would
neither obey the king of Zebu nor Magellan). “Here we planted a
wooden cross, as the people were Gentiles. Had they been Moors”
(Arabs), “we should have erected a stone column, in token of their
hardness of heart, for the Moors were more difficult of conversion
than the Gentiles.” In three days after this conversion, these very
natives murdered Magellan, and in twelve days more they waylaid
and butchered twenty-four of his companions. The natives were first
instructed in Protestant doctrines by teachers in 1621, and in 1623
the first Protestant clergyman came into the Moluccas. This faith has
made little progress, however, and, except the inhabitants of
Haruku, Saparua, and Nusalaut, and small communities at the chief
places of Amboina and Ternate, the whole native population east of
Celebes is either Mohammedan or heathen.
The islands on which the clove-tree grew spontaneously, and the
ones originally known as “the Moluccas,” are Ternate, Tidore, Motir,
Makian, and Bachian, which are situated in a row off the west coast
of the southern half of Gilolo. Of this group Tidore and Bachian, only,
belong to the prince of Ternate, and the Dutch East India Company,
in order to make the monopoly they already enjoyed more perfect,
offered this prince a yearly sum of seventeen thousand four hundred
guilders, nearly seven thousand dollars, for the privilege of
destroying all the clove and nutmeg trees they could find in his wide
territory; for besides these five islands and other smaller ones near
them, and also the adjoining coast of Gilolo, where the clove-tree
was indigenous, it had been introduced by the natives themselves
into Ceram, Buru, and Amboina, before the arrival of the
Portuguese. This offer the prince accepted in 1652, perhaps because
he could not refuse longer. From that date his power began to
decline, and in 1848 he was unable to make the people of the little
island of Makian acknowledge his sovereignty, which once extended
from north of Gilolo to Buton and Muna south of Celebes, a distance
of six hundred geographical miles. His empire also included the
western coast of Celebes; and the islands that lie between it and
Bachian, Buru, and a large part of Ceram, and one-half the area of
Gilolo, were within its limits. For a long time expeditions were fitted
out every year by the Dutch, to search each island anew, and
destroy all the trees which had sprung up from seed planted by
birds. Another such piece of selfishness it would be difficult to find in
all history. The result of this agreement and this policy has been
that, for a considerable number of years, the income of the
government in the Moluccas and Bandas, taken together, has not
been nearly equal to its expenses in these islands; and it is now
evident to all that very much has been lost by this ungenerous and
exclusive mode of trade.
On landing at this village I found a pleasant residence with a good
English lady, the second it had been my good fortune to meet since I
left Java. After living so long among a people speaking another
language, it is a privilege indeed to hear one’s native tongue spoken
without a foreign accent, and to converse with a person whose
religion, education, and views of life accord with one’s own. On
these outer borders of civilization, Americans and Englishmen are—
as we ought to be everywhere—members of the same family.
The same afternoon, as it was clear, I rode with an officer up the
mountain to a summer-house, two thousand four hundred feet
above the sea. From this high position we had a fine view over the
wide bay of Dodinga, formed by the opposite re treating coast of
Gilolo. High mountains are seen to rise in the interior, and several of
these are said to be volcanoes, either active or extinct. In the
northern part of the island, opposite the island of Morti, the Resident
informed me that there was a crater which, according to the
accounts given him by the officials who had visited it, must be nearly
as large as the famous one in the Tenger Mountains on Java. On
Morti itself is Mount Tolo, which suffered a severe eruption in the
previous century. Before that time Morti was said to be well peopled,
but now only the natives of the adjoining coast of Gilolo, who are
most notorious pirates, stay there from time to time.
A large number of the natives of Gilolo were then here at Ternate.
Though frequently called “Alfura,” they are strictly of the Malay type,
and have not the dark skin and frizzly hair of the Alfura of Ceram
and Buru, though representatives of that people may exist in other
parts of Gilolo. Of the whole population of Gilolo, which is supposed
to be about twenty-seven thousand, all but five thousand are under
the Sultan of Ternate. During the war in Java, from 1825 to 1830,
the sultan sent a considerable force of his subjects to assist the
Dutch, and those who were then at Ternate had been ordered to
come over to hold themselves in readiness to aid in suppressing the
revolt in Ceram, for the Dutch believe in the motto “cut diamond
with diamond.” These natives appear to be quite as mild as most
Malays, but the foreigners here say that they fought so persistently
while in Java, that soon they were styled “the bloodhounds of
Gilolo.” A small number of Papuans are also seen in the village. They
were mostly brought here from Papua by the fleet that collects the
yearly tribute for the Sultan of Tidore. While I was at Amboina a
very unfavorable account of them was given by a native captain of
Macassar, who had been taken prisoner near this place. According to
his report to the government, when he returned, all his crew was
seized and eaten one after another, and the only thing that saved
him from a like fate was that he read parts of the Koran. This led
them to believe him a priest, and finally induced them to allow him
to depart on the next vessel that came to their shores. East of
Geelvink Bay two Dutch expeditions have found that the whole
population, men, women, and children, always go absolutely naked.
On our right, as we looked toward the east from our lofty position,
the steep, conical peak of Tidore was seen rising about six thousand
feet above the sea. It is one of the sharpest peaks in all this part of
the archipelago. As it has no crater either at the summit or on its
sides, there is no vent by which the gases beneath it can find a
ready escape. They must therefore remain confined until they have
accumulated sufficient power to hurl high into the air the whole
mass of ashes, sand, and rock which presses them down. This is
exactly what happened at Makian. Professor Reinwardt, who
examined this peak in 1821, declared that it would be blown up in
twenty years, and, strange to say, it was nineteen years afterward
that the terrific eruption of Makian, already described, occurred. As
the islands Ternate, Tidore, Motir, and Makian, are only cones
standing on the same great fissure in the earth’s crust, Professor
Reinwardt’s prediction was fulfilled almost to the very letter.
The village of Tidore is situated on its southern side, and is the
residence of the sultan, whose territory is no less extensive than that
of the Sultan of Ternate. It includes Tidore, Mari, the two eastern
peninsulas of Gilolo, Gebi, Misol, Salwatti, Battanta, and the adjacent
islands, the western and northern shores of the western peninsula of
New Guinea, and the islands in Geelvink Bay. The population of
Tidore and Mari is about seven thousand five hundred. The former
cultivate the flanks of the mountain up to a height of about three
thousand feet. Above this line is a dense wood, but the pointed
summit is quite bare. The income of this sultan consists in his share
of the produce obtained on Gilolo, in the sago, massoi-bark, tortoise-
shell, tripang, and paradise-birds, which are yearly brought from
Papua, and the islands between it and Celebes, and in twelve
thousand eight hundred guilders (over five thousand dollars) paid
him by the Dutch Government, in accordance with the promise made
by the East India Company, when they destroyed the spice-trees in
his territory. The extension of the empire of Tidore eastward was
probably effected by Malays, who migrated in that direction; for it is
stated in regard to Misol that the Papuans, who are now driven back
into the interior, occupied the whole island when it was first visited
by Europeans. This tendency to push on toward the coast is the
more interesting, because it is generally supposed that, ages and
ages ago, the ancestors of the present Polynesian race passed out
from this part of the Malay Archipelago into Micronesia, and thence
into the wide area they now occupy. From the northern end of
Gilolo, and the adjacent island of Morti (which is really but a part of
the northern peninsula), the voyage to Lord North’s Island, and
thence to the Pelew group, would not be more difficult to accomplish
than the piratical expeditions which even the Papuans, an inferior
race, are known to have made since the Dutch possessed the
Moluccas.
The taxes on paradise-birds[47] and other articles, levied on Papua
and the islands near it, are obtained by a fleet which is sent out
each year from the port of Tidore, and which, according to the
official reports of the Dutch, carries out the sultan’s orders in such a
manner that it is little better than a great marauding expedition.
But while we have been engaged in viewing the scene before us,
and recalling its history, the hours have been gliding by, and we are
admonished to hasten down the mountain by the approaching night.
When we reached the village, I was shown a remarkable case of
birth-mark on a young child, whose father owned the summer-house
we had just visited high up on the mountain. A short time previous
to the birth of the child, the family were living there. One night a
heavy earthquake occurred, and a brilliant cloud was seen rising out
of the top of the mountain. Immediately they began to prepare to
hasten down, and the mother, being greatly frightened, attempted to
run before, but fell heavily on her right arm, bruising it severely in
one place. Soon afterward the child was born, and on its right arm,
and exactly in the same relative position as where the mother had
received the injury from her fall, was found a red spot, or mark,
which all agreed had exactly the outline of the bright cloud seen by
them on the mountain-top.
The chief articles of export from this place are those brought from
the islands to the east, namely, tortoise-shell, tripang, paradise-
birds, massoi-bark, and wax. Up to 1837, paradise-birds formed a
very important article of export from Ternate. In 1836 over 10,000
guilders’ worth were exported, chiefly to China. In 1844 over 10,000
guilders’ worth of massoi-bark was exported from this small
emporium. It comes from the interior of New Guinea, and is sent to
Java, where its aromatic oil is used by the natives in rheumatic
diseases. Until 1844, from 14,000 to nearly 70,000 guilders’ worth of
tortoise-shell was annually exported, chiefly to China; but since that
time it has frequently not exceeded 4,000. The chief imports are
rice, salt, and cotton goods. A merchant who sends a small vessel
each year to Misol, and along the northern coast of Papua, kindly
offered me an opportunity to take passage on her; but as it would
be about six months before she would come back to Surabaya, in
Java, I was in doubt whether I ought to go further east, especially
as Mr. Wallace had obtained little at Dorey, the only port on the
north coast, and besides, it has the unfavorable reputation of being
one of the most sickly places in the whole archipelago. The two
missionaries stationed at that place are now here, having been
obliged to return on account of repeated and severe attacks of fever.
I was told that the residents of Dorey are only free from this disease
when they have a running sore on some part of the body. While I
was thus doubting whither to direct my course, the man-of-war
stationed to watch for pirates in the Molucca Passage, between this
island and the northern end of Celebes, came into port. She would
return immediately to Kema, a port on the eastern shore of the
northern peninsula of Celebes, and her commander kindly offered to
take me over to the “Minahassa,” as the Dutch call the northern
extremity of that island. I had long heard this spoken of as decidedly
the most charming part of the archipelago, and probably the most
beautiful spot in the world. But a moment was needed, therefore, to
decide whether I would go to the sickly coast of Papua, or visit that
beautiful land, and I accepted the commander’s invitation with many
thanks. I had been on this island four days, and we had had four
earthquakes. Indeed, the mountain seemed preparing for another
grand eruption, and I was not loath to leave its shores. So great is
the danger of its inhabitants being entombed alive by night in the
ruins of their own dwellings, that all the foreigners have a small
sleeping-house in the rear of the one occupied by day. The walls of
the larger one are usually of brick or stone, but those of the
sleeping-house are always made of gaba-gaba, the dried midribs of
large palm-leaves, which, when placed on end, will support a
considerable weight, and yet are almost as light as cork. The roof is
of atap, a thatching of dry palm-leaves, and the whole structure is
therefore so light that no one would be seriously injured should it fall
on its sleeping occupants. Such continual, torturing solicitude
changes this place, fitted, by its fine climate, luxuriant vegetation,
and beautiful scenery, for a paradise, into a perfect purgatory.
On the morning of the 12th of December we steamed out of the
roads for Kema. Soon we passed near the southeast end of Ternate,
and the commander pointed out to me a small lake only separated
from the sea by a narrow wall, and informed me that when the
Portuguese held the island they attempted to cut a canal through
the wall or dike, and use this lake as a dock—certainly a very
feasible plan; but for some reason, probably because they were so
continually at war with their rivals, the Spaniards, they did not carry
it out. This lake is said to be deep enough to float the largest ships,
and is, I believe, nothing more than an old, extinct crater. On our
larboard hand now was Mitarra, a steep volcanic cone as high as the
Gunong Api at Banda, but appearing much smaller from being, as it
were, beneath the lofty peak of Tidore. It also is of volcanic
formation. We now came out into the Molucca Passage, and were
steering west, and I could feel that at least my face was turned
homeward, a thought sufficient to give any one a deep thrill of
pleasure who had wandered so far.
The wind being ahead, and our vessel steaming slowly, we did not
expect to see the opposite shore until the next day, much to my
satisfaction, for it gave me a good opportunity to learn from the
officers many particulars about the pirates in these seas. Piracy has
probably existed among these islands ever since they were first
peopled. It was undoubtedly plunder, and not trade, that stimulated
the natives to attempt the first expedition that was ever made over
these waters. Piracy is described in the earliest Malay romances, and
spoken of by these natives, not as a failing of their ancestors, but as
an occasion for glorying in their brave deeds. Such has also been the
case in the most enlightened parts of the earth, when civilization
and Christianity had made no further progress in those regions than
it has here among the Malays. It has also been prevalent along the
northern shores of Europe and the British Isles. The only reason that
it was not a common practice among our Indians was because they
had not made sufficient progress in the arts to construct large boats,
and were obliged to confine their plundering expeditions to rivers
and lakes, and could not sail on the stormy ocean.
Pirates have been as numerous on the coasts of China for
centuries as they are now. Sometimes they have come to the
Philippines and the northern parts of Borneo, but rarely or never
among these islands. When the Europeans first came to the East,
pirates abounded in every part of the archipelago, particularly in the
Straits of Malacca, in the Sulu archipelago, between Borneo and
Mindanao, and especially on the southern shores of the latter island.
The establishment of a large port at Singapore by the English, and a
settlement on Rhio by the Dutch, have quite scattered them from
the former region, but they continue to infest the Sulu Sea and the
southern part of the Philippines. They come down here in the middle
of the western monsoon, that is, in January and February, and
return in the beginning of the eastern monsoon, so as to have fair
wind both ways, and be here during the calms that prevail in these
seas in the changing of the monsoons, when the large number of
oars they use enables them to attack their prey as they please. They
appear to come mostly from the shores of Lanun Bay, on the south
coast of Mindanao. From Dampier we learn that in 1686 they were
an inland people. “The Hilanoones,” he says, “live in the heart of the
country” (Mindanao). “They have little or no commerce by sea, yet
they have praus that row with twelve or fourteen oars apiece. They
enjoy the benefit of the gold-mines, and, with their gold, buy foreign
commodities of the Mindanao people.” They are now the most daring
pirates in these seas. Last year the man-of-war on this station had
the good fortune to surprise five boats, one of them carrying as
many as sixty men. At first they attempted to escape by means of
their oars, but her shot and shell soon began to tear them to pieces.
They then pulled in toward the shore and jumped overboard, but, by
this time, they had come near a village, and the natives at once all
turned out with their spears, the only weapons they had, and
scoured the woods for these murderers until, as far as could be
ascertained, not one of them was left alive. They seldom attack a
European vessel, but, when they do and succeed, they take revenge
for the severe punishment their countrymen receive from the Dutch
war-ships, and not one white man is left to tell the tale of capture
and massacre. The vessels that they prey on chiefly are the small
schooners commanded by mestizoes and manned by Malays, which
carry on most of the trade between the Dutch ports in these islands.
One of those vessels was taken and destroyed by these murderers
last year while sailing down the coast from Kema. The whites and
mestizoes are always murdered, and the Malay crews are kept as
slaves. While I was at Kema two Malays appeared at the house of
the officer with whom I was residing, and said they were natives of
a small village on the bay of Gorontalo; and that, while they were
fishing, they had been captured by a fleet of pirates, who soon after
set out on their homeward voyage; and, while the fleet was passing
Sangir, a small island between the northern end of Celebes and
Mindanao, they succeeded in escaping by jumping overboard and
swimming a long distance to the shore. They had now reached
Kema, on their voyage toward Gorontalo, and they came to the
officer to apply for food, clothing, and some means of reaching their
homes once more. Such cases are specially provided for by the
Dutch Government, and their request was immediately granted. A
few years ago these pirates sent a challenge to the Dutch fleet at
Batavia to come and meet them in the Strait of Macassar, and
several officers assured me that five ships were sent. When they
arrived there no pirates were to be seen, but to this day all believe
the challenge was a bona fide one, and that the only reason that the
pirates were not ready to carry out their part was because more
men-of-war appeared than they had anticipated. A short time after I
arrived back at Batavia, a fleet of these plunderers was destroyed in
that very strait. One chief, who was taken on the opposite coast of
Borneo a few years ago, acknowledged that he had previously
commanded two expeditions to the Macassar Strait, and that,
though the Dutch war-ships had destroyed his fleet both times, he
had been able to escape by swimming to the shore. At Kema I saw
one of the five praus that were taken in that vicinity last year. It was
an open boat about fifty feet long, twelve wide, and four deep.
There were places for five oars on each side. At the bow and stern
was a kind of deck or platform, and in the middle of each a small
vertical post, on which was placed a long swivel, throwing a pound-
ball. They do not, however, depend on these small cannon, but
always get alongside a vessel as soon as possible, and then board
her at the same moment on all sides in overpowering numbers. It is
almost impossible to catch them unless it is done by surprise, and
this they carefully guard against by means of spies on the shore. Our
captain informed me that several times when he has suddenly
appeared on some part of the adjacent coasts, fires have been
instantly lighted on the tops of the neighboring hills, evidently as
signals to pirates in the immediate vicinity. As soon as they receive
this alarm they hide away in the shallow creeks and bays among the
mangrove-trees, so that a war-vessel might steam past them again
and again without discovering the slightest indication of where they
are concealed. To the Dutch almost exclusively belongs the honor of
having rendered the navigation of these seas so comparatively safe
as it now is. The English have assisted in the western part of the
archipelago, but the Spaniards, from whose territory these
marauders now come, have effected little toward removing this pest
from the Philippines, where it is as rife as it was two hundred years
ago.
CHAPTER X.
THE NORTHERN PENINSULA OF CELEBES.
On the morning of the 13th of December Mount Klabat, a conical

volcanic mountain attaining an elevation of six thousand five
hundred feet, appeared on the horizon; and soon after, north of
Klabat, was seen Mount Sudara, “The Sisters,” a twin cone whose
highest peak is about four thousand four hundred feet above the
sea. North of this again is Batu angus, two thousand three hundred
feet in height. Its name in Malay means “the hot rock,” but it is really
a large volcano, whose top has been blown off and a great crater
thus formed; and this shows the fearful fate that awaits each of the
other two cones, as soon as the gases pent up beneath their mighty
masses have acquired the necessary power. We now approached
Limbi, a high, uninhabited island with abrupt shores extending in a
northwest and southeast direction, and soon after came to anchor in
the road off Kema, the coast here curving inward so as to form a
small bay. This is the port used now in the western monsoon. During
the eastern monsoon, steamers and ships go round the northern
end of Celebes to Menado, in the Strait of Macassar. Kema is a
village of two thousand inhabitants. Its streets are very broad, and
cross each other at right angles. The houses are well built, and
placed on piles twelve or eighteen inches in diameter and six feet
high—a remnant of the old custom of placing their huts on high
posts to avoid attacks of enemies, which was practised by these
people previous to the arrival of Europeans. It is certainly a good
custom, not only because all such unwelcome intruders as the large
snakes, which are very numerous here, are thus avoided, but also to
keep the house dry and cool, by allowing a free circulation of air
beneath. Each house has a small plot of ground, and this is
separated from that of its neighbor by hedges, which also border the
streets, and give the whole village a charming air compared to the
irregular, unsightly appearance of those I had been visiting. Most of
the streets are also lined with shade-trees, and in the gardens,
behind the hedges, are rows of orange-trees, some of their branches
bearing flowers, some green fruit, and some drooping under the
abundance of their golden-yellow loads.
The controleur here kindly received me into his house. He was just
going to Limbi, an island five or six miles north of Kema, to try to
take some living babirusa for the governor-general’s garden at
Buitenzorg, back of Batavia. That was exactly such an excursion as
suited my fancy, and I was very willing to accept his invitation to join
him before I began a journey I had been planning over to Menado,
and thence up into the interior. While we were preparing for our
excursion, another gentleman, Mr. K., decided to join us.
December 20th.—A bright, clear day, and just suitable for starting
on our hunt. We have a ship’s long-boat and a small prau, both
containing about twenty natives, and a large pack of dogs to start up
the game. The controleur is the captain of our boat, and an old, gray
Malay, who has been a seaman and a whaler for most of his days, is
the coxswain of the other, and pilot for both. For ballast we have a
full load of rice, our two boats carrying only half the whole party, the
other portion—twenty-five natives and half as many dogs—went
yesterday, under the charge of the second native chief of the village,
who rejoices in the euphonious title of Hukom kadua, but the Dutch
call him the “Second Head.” From Kema up to the strait, between
Limbi and Celebes, we had a light air off the shore. A thin cloud, like
a veil of gauze, gathered on the heads of the twin-peaks known as
“The Sisters,” and fell down in rich graceful folds over their green
shoulders. From the crests of all these peaks, down to the high-
water line on the shore, is one dense, unbroken forest. There dwells
the sapi utung or “wild ox,” probably not indigenous, but descended
from the tame sapi introduced from Java and Madura. The natives
describe them as being exceedingly fierce, both the cows and the
bulls. Here that peculiar antelope, the Anoa depressicornis, H. Smith,
abounds. In these same dense, undisturbed forests the babirusa
(Babirusa alfurus, Less.) is found in large numbers; and a species of
Sus, much like the lean hog that lives in the forests of our Southern
States, is very abundant. As soon as we entered the strait we found
a strong current against us, and landed on the south side in a small
bay to take our lunch. Again we rowed and beat until we came to
the narrowest part of the strait, where high, perpendicular walls of
rock rise on either hand. The tide which sets toward the east, that is
before the wind, now changed, and away we shot between the
overhanging crags with the speed of an arrow. Outside of these
narrows the shores open on both sides, so that almost at once we
were exposed to the full strength of the stormy monsoon. The
strong tide running against the wind rolled up a high, irregular sea;
in fact, the ocean seemed to boil. “Have you any idea that we can
land on that exposed shore in the midst of such a surf?” I asked the
controleur. “Well, it is getting dreadfully rough,” was his indefinite
reply. The old Malay pilot, who had kept his boat ahead, now stood
up, and seeing the combing waves, into which the strong current
was rapidly driving us, shouted out to the controleur, “Dra bisa
Tuan!” “It is impossible, sir! It is impossible, sir!” Instantly we tacked
and stood over toward the Celebes side, and, under the guidance of
the old whaler, soon entered a small, well-sheltered bay. Near its
middle part the island of Limbi is very narrow, and across that place
had been stretched a series of strong nets made of rope a quarter of
an inch in diameter, the meshes being about six inches square. Our
plan was to commence driving at the northern end of the island and
force the wild babirusas into this trap; but it was already quite dark,
and the place where the hukom had landed was a long way to
windward, and we therefore concluded to camp here to-night. For a
tent we cut poles from the neighboring bunches of bamboo and
covered them with the boat’s sail and an old tarpaulin. Our friend K.,
who was extremely careful not to boast of being a good sailor,
became exceedingly frightened while we were in the midst of the
combing waves, and asked me, half a dozen times during the
evening, if the tide would not rise so high as to wash us off this
steep shore before morning, but I tried to quiet his nerves by
assuring him that such a thing could not happen unless the earth
should sink, a very possible thing now that I come to think of it, for
that very beach was composed of black volcanic sand, and we were
almost beneath a cone, which rose on the flanks of Batu angus, and
had been formed so recently that even the luxuriant vegetation of
these tropics had not yet had time to gain a footing on its dark
sides. In order to get a partial shelter from the heavy showers we
expected before morning, we pitched our camp beneath the sturdy
branches of an old tree. There we slept while the wind, in heavy
gusts, sighed through the dense foliage over our heads, and at our
feet rose the heavy, pulsating roar of the ocean-surf.
December 21st.—After passing a comfortable night,
notwithstanding the fears of our companion that we should awake
before morning, and find ourselves in the midst of the sea, we again
attempted to reach the northern end of Limbi, but, as soon as we
got out of the bay, we struck into such a heavy sea that our men
could not take us to windward, and were therefore obliged to put
back once more. This time, to vary the scenery, we passed through
the narrows, and encamped on a charming little beach on the island
side of the strait, between two high, precipitous crags. Our first care
was, of course, to construct a tent, a work soon finished by our large
crew. At 11 a. m. we all felt a heavy earthquake-shock, which lasted,
apparently, thirty seconds; but these are frequent phenomena in this
part of Celebes. On the 25th of last month, not four weeks ago,
there was a very heavy earthquake over the whole Minahassa. At
Kema we could still see great rents in the ground, three or four
inches wide, which could be traced for several rods. The shock was
so severe that nearly every article of glass or earthen-ware in the
controleur’s house was broken into fragments. Indeed, as I look up
now toward the west, I do not wonder the earth heaves beneath us
like a troubled sea; for there rises the old volcano known in olden
times as Mount Tonkoko. It has a great yawning crater, six hundred
feet deep, out of which are rising thick, white clouds of gas. On the
northwest side a deep ravine cuts through its flanks, and opens out
into the crater. Farther down this same side is the new cone,
beneath which we pitched our camp last night. In 1806 a great
eruption began in this old volcano, and ashes, sand, and pumice-
stone were thrown out in great quantities. At Ayar-madidi the ashes
were fine and of a gray color, and covered the ground with a layer
an inch thick. For two days the heavens were darkened by the great
quantity of these light materials floating in the air. So many stones
were ejected, that at a distance of nearly three miles a new cone
was formed, from which a long tongue of land stretched itself into
the sea. This point the natives called Batu angus, “the Hot Rock,”
and since that time the whole volcano has been known by that
name. Some of the pumice-stones were said to have been as large
as the native huts, but so changed into a kind of foam by the action
of heat, that they readily floated on the sea.
Soon after sunset I went out to fish in a small canoe with the
controleur and his old pilot. The place we chose was under a high,
perpendicular precipice that rose up out of the dark water like an
artificial wall. Here we remained while the rocks grew higher and
higher and more and more overhanging as the daylight faded, and
the approaching night blended the sharp outlines and increased the
magnitude of every object around us. Near by was a deep ravine,
and from its farthermost recesses rolled out the reverberating,
moaning cries of monkeys, who all night long keep up a piteous
calling, each answering his fellow in the same mournful tones.
Our lines were just about as large as a mackerel-line. The hooks
each native makes for himself, from brass wire, and about a fathom
of wire is attached to each hook before the line is fastened to it, in
order to prevent the fish from severing the cord with their sharp
teeth. For bait, small fish are taken. In fishing at anchor, no leads
are used, but, instead of them, a kind of sling of palm-leaf is
fastened to each hook. This sling contains a small stone, so fixed
that it will carry down the line, but drop out as soon as it touches
the bottom. After we had obtained a good supply of fine fish, we
slowly passed along the high, well-sheltered shore, while the heavy
wind sighed through the lofty branches over our heads. Now a
gleam of light comes over the dark water, just beyond that high
bluff; we are near the camp, and in a few moments stand again on
the beach. This day is done, and yet the storm continues, but we
hope we may be more favored to-morrow.
December 22d.—Last night I soon fell asleep after such vigorous
use of the paddle, though the storm wailed, and my couch was any
thing but a bed of down. At midnight a troubled dream disturbed my
brain. An indefinite horror thrilled along my veins as I fancied for a
moment that I was whirling round such a deep yawning maelstrom
as Poe has pictured, and then literally “a change came o’er the spirit
of my dream,” but scarcely a change for the better, for I was fixed in
the midst of a water-spout, and, in my struggles to escape, awoke
and found a great stream of water pouring down on me from the
tarpaulin that formed the roof of our tent. A heavy shower had come
on, and the water was all running into a depression in the sail over
me, in which, of course, there was a hole, so that the whole formed
one big tunnel. Of course, both K. and the controleur enjoyed my
discomfiture greatly, but I consoled myself with the thought that
long before daylight they would find themselves in the same plight;
and the next morning, apparently, the thing that was farthest from
their thoughts was to inquire of me in regard to the water-spout.
That portion of the party that had left Kema in advance of us had
taken little rice. The controleur, therefore, thought we must make a
third attempt to reach the northern end of the island,
notwithstanding K.’s earnest entreaties to be only taken back to
Kema once more. We had not reached the narrows, however, before
we met the hukom with all his men and dogs. They had found the
surf so high that the only way most of his men had been able to
reach their boats, was to run down the steep rocks and plunge head
foremost into the combing waves. We now landed a few natives to
scour the woods, and finally come to the southern end of the island,
while we went round in the boats. In order to make their way
through the dense forest, instead of putting on more clothing as a
protection against the sticks and stones and thorny vines, they
stripped off what little they wore, except a narrow band over the
loins. At the southern end of the island was a small, deep bay, and
here we encamped for the third time. Soon the natives came in, but
they had secured only two wild hogs. I preserved the skull of one, a
female, in which the canine teeth were not as long as those of a
male. The hukom declared that in the babirusa only the males have
the long curved teeth, which the Malays have fancied resemble the
antlers of a deer. While waiting for us, he had been hunting in the
vicinity of his camp, and had taken one female by driving her to the
end of a high point. As soon as she saw there was no chance for her
to escape, she leaped down the precipice and was killed by the fall.
Such suicide, he says, is frequently resorted to by that animal when
it finds it can retreat no farther. The wild hogs plunge into the water
to avoid the dogs, and the natives then pursue them in boats and kill
them with spears. As soon as the hunters return to camp, they cut
up the hogs, and smoke the pieces over a smouldering fire. The
dogs now skulk about to seize a piece if possible, and while the
natives are crouching round the fire transforming the lean pork into
tough bacon, you are frequently startled by a sharp yelping as some
one finds his portion disappearing beneath the jaws of one of these
hungry brutes, and a liberal chastisement is at once administered to
the thief with the first stick or club at hand.
December 23d.—Last night there was another heavy shower. The
water poured down in torrents through our thatching of palm-leaves,
for we had already found that both the boat’s sail and the old
tarpaulin afforded little protection here where the water appears to
fall in broad sheets. Late in the evening the controleur came back
from fishing. We could hear the Malays that were pulling his boat
singing in an unusually loud and merry style, and all gathered on the
beach to see what wonderful monster of the deep they had secured.
It proved to be a fish as large as a horse-mackerel, and weighing
fully two hundred pounds, which the controleur had succeeded in
taking with a small line by chancing to get it alongside the boat and
securing it by gaffs. As our stock of rice was getting low, we decided
to return, though I could scarcely feel satisfied, for I had hoped to
get a complete skeleton of the rare babirusa; however, the
controleur more than made up the loss by giving me half a dozen
skulls of the equally rare antelope of this region. We now crossed
over to the Celebes side to a village of four or five huts, to be
sheltered from the heavy rains that have drenched us every night
but one since we left Kema. A few natives have moved here from
Kema because they take many fish off this part of the coast, and
there is a small stream emptying into the sea in the vicinity. They
live almost wholly by fishing, and have cleared only a small place
near their houses for a garden of Indian corn. This evening they
have shown me one of the monsters of these forests. It was an
enormous python. Its head has been taken off, but by careful
measurement I find it must have been at least fifteen feet long. It
was killed here the day before yesterday by one of the natives living
in the house where we are now sheltered from the rain. Missing his
dog, he chanced to go to the brook where they get water, and there
he found this monstrous reptile trying to swallow his favorite. As
quietly as possible he stole back to the village and gave the alarm,
and at once all went out and succeeded in cutting off its head before
it could disgorge its prey and attack them. The natives are now
taking off the skin to make rude moccasins, which they frequently
use when hunting in the woods, or more especially when travelling
through the tall, sharp-edged prairie-grass. They all agree that this
tough, scaly skin is much more durable for such a purpose than the
best kind of leather. Our old boatman tells me that he once killed
one of those great reptiles on Limbi, while it was trying to swallow a
wild pig. All the natives assert that this monster sometimes attacks
the wild ox, sapi utung, though none of them have ever seen such a
dreadful combat. The controleur states to me that when he was
stationed at Bachian, near the southern end of Gilolo, he was once
out hunting deer, at a place called Patola, with a large party of
natives. They had succeeded in starting up several, and he himself
saw one of them pass under a tree and at the same instant a great
snake came down from one of the lower limbs and caught the flying
deer with his jaws. Unfolding his tail from the limb, he instantly
wound round his victim, crushing its bones as if they were straw. An
alarm was given, and the natives gathered with their spears and
killed the great reptile on the spot. It was not as large round as this
one, but longer. Many of our men tell me that they once assisted in
killing a larger snake than this at the bathing-place back of Kema. It
had seized a hog, whose squealing soon gave all the inhabitants a
warning of what had happened. They also say (and this remarkable
story has since been repeated to me by several other persons at
Kema) that a few years ago a native boy went out as usual to work
in his ladang, or garden, some distance from the village. At night he
did not return, and the next morning a native chanced to pass the
garden and saw one of these great monsters trying to swallow the
boy head first, having already crushed the bones of its victim. He at
once returned to the village, and a large party of natives went out
and found the snake and its prey exactly as had been reported, and
immediately killed it with such weapons as they had, and gave the
body of their young friend a decent burial. While they were telling
me these stories I thought of the danger to which I must often have
been unconsciously exposed while wandering mile after mile through
the jungles on Buru, never suspecting that, before I left the
archipelago, I myself should be forced into a dreadful combat with
one of these monsters, and in such a place that one or the other
must die on the spot.
The next day we returned to Kema, and I began my journey over
the peninsula to Menado, and thence up to the plateau in the
interior.
December 26th.—At 9 a. m. started on horseback, the only mode
of travelling in the Minahassa, for Menado, the largest village in this
peninsula of Celebes, and the place where the Resident of this
region is located. I went there first, in order to see the Resident and
obtain letters to the officials of the interior. The distance from Kema
to Menado is about twenty miles. The road is made only for carts,
but nearly all the way it is lined with shade-trees, and in several
places, for long distances, they meet overhead so as to form a
continuous covered way, thus affording to those who travel to and
fro an admirable shelter from the hot sunshine and heavy showers.
Among these trees were many crows, Corvus enka, not shy as they
always are in our country, but so tame that I frequently rode within
ten yards of where they were sitting without causing them to move.
Numbers of a bright-yellow bird, about as large as our robin, were
seen among the branches, and on the ground another somewhat
larger than a blackbird, Dicrurus, with a long, lyre-shaped tail, and a
plumage of shining blue-black. These birds rarely or never hear the
report of a gun, and therefore have not learned to look on man as a
universal destroyer, and the tameness they manifest is perfectly
charming. Even the black crow, with its hoarse caw, becomes an
attractive bird when you find he no longer tries to shun your
company, but makes all the overtures he can to be social.
The road runs along the southern flanks of Mount Klabat, and is
slowly ascending from Kema to Ayar-madidi, which is about half-way
across, and then slowly descends again to the western shore of the
peninsula. On my right hand was a deep valley, and fine scenery was
occasionally revealed through the foliage of the trees that covered
the way. On the opposite side of the valley were many small
projecting ridges that have been formed by denuding torrents, and
extend down to the level of the stream that flows out from the lake
of Tondano to the ocean at Kema.
By noon I came to the village of Ayar-madidi, “Hot Water,” a name
it receives from a neighboring spring, which in former times was hot.
As it comes out of Mount Klabat, it was probably heated by the
volcanic action that raised that great mountain, which is only an
extinct volcano. As the volcanic action decreased, the heat passed
off, until now, the water is as cool as that of any other stream in the
vicinity. Even as late as the 12th of November, 1848, this water was
described as “cooking hot.” According to Valentyn, in the year 1683,
a great eruption took place in a mountain near Menado, which he
calls “Kemaas,” and all the surrounding country was laid waste.
“Kemaas” Dr. Junghuhn has supposed to be Klabat, but he never
visited this region, and the conical summit of Klabat shows its
destruction by heavy eruptions has not yet begun. It is far more
probable that Kemaas was the mountain now known as Sudara,
whose two peaks are only the fragments of the upper part of the
cone that were left standing when the eruptive force blew off the
other parts, or so weakened their foundations, that they have long
since fallen, and the materials of which they were composed have
been brought down, and spread out by the rains over the flanks of
the mountain. Natives, who have been to the top of Klabat, inform
me that there is a small lake on the northwest side. Its basin is, no
doubt, that part of the old crater which has not yet been filled so as
to make the whole elevation a perfect cone. If this, lake was of any
considerable size, then, as occurred on Mount Papandayang, in Java,
mud and hot water will certainly pour down the sides of this
mountain, if it is again convulsed by the mighty forces that are now
slumbering beneath it. Ayar-madidi is a large kampong, or négri, as
the Malays sometimes call their villages. It is beautifully situated on
the southern flanks of Mount Klabat. Its streets all cross each other
at right angles, and are well shaded. So far as we are aware, the
Malays and Javanese had no word for village previous to the arrival
of the Telingas, and it has been conjectured, from this fact, that they
were scattered everywhere over their particular territories exactly as
we have seen is the custom of the aborigines of Buru, the Alfura,
who have been beyond the influence of both Hindus and Arabs, and
even of those natives who have adopted any foreign religion or
custom. Ayar-madidi is a prettier village than Kema. Indeed, the
more I travelled in the Minahassa, the more I admired the
kampongs, they are so incomparably superior to those of every
other part of the archipelago in the regularity of their streets and the
beautiful hedges with which they are lined, and, above all, in the
neatness and evidence of thrift that everywhere appear.
The chief native of this village is also the chief of the district,
which contains several villages. His title in the native language is
Hukom Biza, or “Great Chief,” though he prefers to be addressed by
the Dutch title of major. The native official next in rank is the chief of
one of the smaller villages, as at Kema. His title is Hukom Kadua. At
smaller villages than Kema the chief is called Hukom Tua, or “Old
Hukom,” and beneath him is the Hukom Kachil, or Little Hukom.
These officers are nominally elected by the natives, but the choice is
generally confined to the sons of the deceased.
The Majors and Second Heads receive a percentage on all the
coffee raised and delivered to the government. This amounts to
about twenty thousand guilders per year for the seventeen districts
in the whole Minahassa. Besides this income, the Major receives one
guilder, and the Second Head half a guilder from each family in their
respective districts and sub-districts, and the Hukom Tua five days’
labor from each able-bodied man yearly.
The natives themselves are divided by the Dutch into burgers or
“free citizens,” and inlanders or “natives,” who are obliged to work a
certain number of days in the coffee-gardens belonging to the
government. The total population of the Minahassa in this year
(1866), as furnished me by the Resident from the official documents,
is 104,418,[48] and the marked degree of variation in the population
of this country, where the natives have never been a maritime
people, is worth more than a passing notice, because it shows in
some degree the beneficial effect of a stable government, and how
the natives are sometimes swept away by disease. In 1800,
according to Valentyn, the population was 24,000, though he gives
the number of able men at only 3,990. In 1825 it was 73,000; in
1842, 93,332; in 1853, 99,588. In 1854 a great mortality appeared,
and the population was diminished to 92,546, no less than 12,821
persons, or about one-seventh of the population, having died in a
single year. In the district of Amurang the loss was as high as 22½
per cent. The principal diseases are fevers and dysentery. The
population of the Minahassa, as compared to its area, 14,000 English
square miles, is by no means large. The island of Madura, which is
of about the same extent, has more than five times as large a
population; and the residency of Surabaya, also of about the same
extent, contains more than ten times as many people. The natives
directed me to the major’s residence, which I found to be a small
but neat and well-painted house, built in European style. It is
situated in the middle of a large, oblong lawn, that is surrounded
with a row of trees much like our locust-trees, and which are now in
full bloom. Near the gate are a guard-house and long series of
stables. Dismounting here, I walked up to the broad piazza, where
the major sat smoking his pipe in the Dutch style, and discussing in
the Dutch language the state of the weather, the crops, and such
things as interested the Dutchmen of those lands. His manners were
polished, and he received me in a most stately way. His friends were
going to Menado, so that I should have companions the rest of the
way. Our dinner was in European style, which seemed the more
remarkable to me because it differed so much from the way I had
been entertained by the rajahs of the Moluccas. In our dining-room
was a fine-series of pictures representing scenes in that most
charming tale, “Paul and Virginia.” We were just at the foot of Mount
Klabat, but we could not see its summit on account of thick rain-
clouds that covered its sides, and now and then rolled down and
poured out heavy showers over the village. As one of these floated
away to the east, the sun came out brightly and changed the falling
drops into a remarkably broad and brilliant rainbow, which seemed
suspended from the cloud, and floated along with it in a most
magical manner.
Here I saw for the first time the plant from which “manilla hemp”
is manufactured. It is a species of banana, Musa textilis, and grows
to a height of twelve or fifteen feet. It appears to be indigenous, and
can be raised here from the seed. The fibres are taken from the
large, succulent leaves. Though it resembles the banana so closely
that at first most people would mistake it for that plant, its fruit is
small, disagreeable to the taste, and not edible. Several residents
have made strenuous efforts to extend its cultivation, but the result
has shown that the natives can be more profitably employed in
raising coffee. The rain-clouds having cleared away, we all started
for Menado. The horse that had been kindly furnished me by an
officer was not fast nor sure-footed; and, finally, as we were going
down a gentle declivity at a quick canter, he fell headlong. As I am,
at least, a much better sailor than horseman, I went off over his
head with a most surprising momentum, my feet, unfortunately,
passing so far into the stirrups that I could not extricate either of
them. This so frightened the horse that he reared and plunged
fearfully, but I had no idea of being dragged off like Mazeppa, and
held on to the reins until my feet were once more clear, when, with
one leap, I was again in the saddle, and ready for further experience
in this mode of travelling. Though I was aware my position was
somewhat dangerous, I could not help feeling amused at the alarm
manifested by my companions. They all seemed delighted to know
that I had escaped with only such inconvenience as one clad in a
summer suit of white would necessarily experience in coming down
in such an unceremonious manner into the midst of a muddy
stream. Late in the evening we came to the Resident’s house, where
a cordial welcome awaited me, and I had the pleasure to find myself
once more in the midst of a pleasant family after so long and lonely
an exile.
The next morning I walked through the village. Its total population
is only about 2,500, of which 300 are Europeans and mestizoes;
about 600 Chinamen, and 1,200 natives, half of whom are Christians
and the other half Mohammedans. The Resident’s house is
surrounded by large grounds, abounding in the choicest of tropical
plants. Not far from it is the market, a house without walls, the roof
resting on pillars of wood and masonry. This is the universal style of
the markets in all parts of the archipelago. Here various kinds of
fruits, gambier, betel-nuts, and siri are sold by the natives, and salt,
cotton fabrics, and cutlery, by Chinese. The salt used here is not
imported from Java, as that used on the other islands I have visited,
but is made by the natives themselves in the following manner:
Littoral-plants are gathered and burned. The ashes are then placed
in a bamboo, which is filled with water. After this has remained for
some time, the water is strained off and evaporated. The residuum
is a dark, impure salt, but the natives prefer it to any that can be
imported. This custom seems to have been introduced lately, for in
1841 the government sold three hundred and twelve thousand
pounds of imported salt, but in 1853 only two thousand. From the
village of Menado I walked northward parallel to the bay, and,
crossing the little stream Menado, came to the village of the Bantiks,
a peculiar people, numbering about two thousand five hundred, who
refuse to become Mohammedans or Christians, and continue to
retain the heathen belief of their forefathers. Many of them are taller
than the other people I saw in the Minahassa. Their houses are not
placed on higher posts than those of other natives, but they are
frequently long, and occupied by several families—a custom which
appears to have been general throughout the archipelago in ancient
times, and is still practised at Dorey, on the north coast of New
Guinea, and again by the people of the Tenger Mountains in Java,
who pride themselves on retaining the customs of their ancestors.
The view has been advanced that the Bantiks are descendants of
Chinamen, who established themselves here when they first came to
the Moluccas to purchase spices. This may have been the case, but
their features, though somewhat different from the other natives,
did not appear to me to be so unlike them as to necessitate such a
theory. As they have kept themselves more away from the influence
of all foreigners than most Malays, they give us a good idea of what
the aborigines of this region were before the arrival of the
Portuguese.
About three miles round the northern side bay, we came to
Temumpa, where all the lepers of this residency are obliged to live,
banished forever from all communication with other natives, except
such of their friends as come to see them. The little village consists
of twelve small houses, regularly arranged on either side of a street.
They were all neatly whitewashed, and each has a small plot of
ground, where its unfortunate occupants can busy themselves, and
forget their incurable sufferings and their banishment. A native who
lives near by has charge of them, and my opinion was very decided
that they were well cared for by the government. As we passed from
house to house, the officer called them out, and I gave each a small
piece of silver, for which they appeared very grateful. There are now
nineteen here afflicted with this loathsome malady. The part that
appears to be the first attacked is the nose, the next is the hands,
and the last the feet, though in some it only appears in one of these
organs. In one case the nose had wholly disappeared—even the
partition between the nostrils—so that I could look directly into the
chamber over the mouth. At the same time the muscles on one side
of the face were so contracted that the features presented a most
sickening sight. In another case, the nose and all the upper lip were
gone, and even the outer part of the upper jaw, so that the front
teeth only stuck fast on one side, and were completely exposed to
view throughout their entire length. These, however, were the older
cases, in which the disease had made greater progress. Many had
lost their fingers and toes. One little girl had her ankles and feet so
swollen that her ankle-bones could not be seen, and yet I could not
but notice how cheerful she appeared. Two men had the disease in
their feet, which had swollen until they were three times their proper
size, and all broken open and fissured in the most shocking manner.
No one who has not seen such lepers as these can have any idea of
what forms human flesh can assume, and life yet remain in the
body. Suffering from such an incurable, loathsome malady is literally
a living death. I found it so sickening, even to look at them, that I
was glad when I came to the last house. Here I was shown a young
child, a few weeks old. No marks of the disease could be detected,
unless it might be that it was very much lighter colored than either
of its parents. The father was one of the worst cases I saw, but the
disease had not appeared in the mother, except as a great swelling
in the ankles. This child must certainly die a leper, and probably will
never leave the village where it was born. For this reason, if for no
other, the government certainly acts wisely in compelling all who
have this disease to come and live here together, where, at all
events, it cannot be widely spread. When it does not appear in a
very malignant form in the parents, it has been known to fail to
appear in the children, but to appear again in the grandchildren.
Governor Arriens told me of such a case in Java. It was evident that
the man was a leper, though only a considerable swelling could be
detected on one ear, yet he was able to prove that neither of his
parents was a leper, but, on further inquiry, the governor found that
the man’s grandfather was a leper. This disease is regarded here as
an endemic, that is, chiefly confined to the Minahassa and the
Moluccas. Much discussion has arisen whether leprosy is contagious.
The doctor with whom I resided while at Buru had been previously
stationed at Amboina, and while there a soldier who was born in

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Nonlinear Continuum Mechanics for Finite

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Free-surface flow: environmental fluid mechanics

Proper orthogonal decomposition methods for partial

Plasticity of Metallic Materials 1st Edition Oana

Brain Plasticity and Learning: Implications for

Mechanics of Hydraulic Fracturing: Experiment, Model,

Transport and Surface Phenomena 1st Edition Kamil

Tissue Elasticity Imaging S. Kaisar Alam

Elasticity: theory, applications, and numerics Fourth

Publisher: Matthew Deans

1.8 Variations of geometrical elements 53

2. Curvilinear coordinate system 61

3. Tensor operations in convected coordinate system 77

4. Deformation/rotation (rate) tensors 101

5. Conservation laws and stress tensors 123

5.3.4 Conservation law of energy 135

6. Hyperelastic equations 151

7. Development of elastoplastic and viscoplastic constitutive

7.5.3 Plastic strain rate 205

8. Multiplicative decomposition of deformation gradient tensor 255

9. Subloading-multiplicative hyperelastic-based plastic and

9.6.2 Normal-yield, subloading and elastic-core surfaces 289

10. Subloading-friction model: finite sliding theory 335

11. Comments on formulations for irreversible mechanical

Appendix 1: Proofs for formula of scalar triple products

The elastoplasticity theory is now faced to the epoch-making devel-

surface enclosing an elastic domain, (4) the incapability of the nonpro-

2019. Furthermore, the subloading-friction model will also be incorpo-

Lagrangian tensors and the transformations rules between the Eulerian

The heartfelt gratitude of the author is dedicated to Prof. Yuki

The mathematical fundamentals are addressed in this chapter, which

1.1 Matrix algebra

1.1.1 Summation convention

Nonlinear Continuum Mechanics for Finite Elasticity-Plasticity

A letter of the repeated suffix is arbitrary and thus it is called the

This rule is also called Einstein’s summation convention. A repeated index

1.1.2 Kronecker’s delta and alternating symbol

Further, the alternating (or permutation) symbol or Eddington’s epsilon

fulfilling the following relation for the product.

1.1.3 Matrix notation and determinant

Nonlinear Continuum Mechanics for Finite Elasticity-Plasticity

which is called a matrix notation. The matrix I possessing the compo-

The quantity v possessing three (3 3 1) components is expressed as

The multiplications of the quantity v and the matrix B by the matrix

Nonlinear Continuum Mechanics for Finite Elasticity-Plasticity

The transformation from the second side to the third side in

Nonlinear Continuum Mechanics for Finite Elasticity-Plasticity

On the morning of the 13th of December Mount Klabat, a conical

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