Me 185 F18
Me 185 F18
Me 185 F18
Topics:
I. Mathematical preliminaries:
1. Linear spaces.
2. Vectors and tensors in Euclidean spaces.
3. Tensor algebra and calculus.
II. Kinematics of deformation:
1. Bodies, configurations, motions.
2. Mass and density.
3. Deformation gradient and its polar decompositions; rotation and stretch; strain measures.
4. Velocity gradient, stretching and vorticity tensors.
5. Rigid-body motions.
6. Reynolds’ transport theorems.
III. Physical principles:
1. Mass conservation.
2. Definition of forces.
3. Balance of linear momentum and moment of momentum.
4. Traction vector and stress tensor. Local (differential) equations of motion.
5. Alternative stress measures.
6. Change of frame and transformations under superposed rigid-body motions.
7. Balance of energy.
IV. Constitutive theory:
1. Invariance requirements and other restrictions on constitutive equations.
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2. Viscid and inviscid fluids.
3. Elastic solids. Linearization of elasticity theory and associated kinematics.
Suggested reading:
1. C. Truesdell and R.A. Toupin. The classical field theories. In: S. Flügge, ed., Handbuch der
Physik III/1, pp. 226-793. Springer-Verlag, Berlin, 1960. [QC22.H26 v.3.1]
2. C. Truesdell and W. Noll. The non-linear field theories of mechanics. In: S. Flügge, ed., Handbuch
der Physik III/3, Springer-Verlag, Berlin, 1965. [QC22.H26 v.3.3]
4. G.E. Mase. Schaum’s Outline on Theory and Problems of Continuum Mechanics. McGraw-Hill,
N.Y., 1970 [QA808.2.M36]
6. M.E. Gurtin. An Introduction to Continuum Mechanics. Academic Press, N.Y., 1981. [QA3.M286]
7. C.A. Truesdell. A First Course in Rational Continuum Mechanics. Academic Press, Boston, 2nd
edn., 1991. [QA3.P8 v.71]