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Peridynamic modeling and simulation of thermo-mechanical fracture in inhomogeneous ice

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Abstract

It is challenging to build a physically accurate sea ice model, which is highly sensitive to temperature and many uncertain factors, such as its nonuniform and inhomogeneous microstructure. In this work, we adopt a peridynamics approach to develop an inhomogeneous sea ice model and applied it to simulate crack propagation in a thermo-mechanical field of ice sheet. To develop an inhomogeneous ice model, we treat the critical stretch of inhomogeneous ice material as a random variable that obeys the Weibull distribution. A coupled thermo-mechanical peridynamics approach is adopted to simulate ice crack propagation, and a key component of this approach is adopted the temperature-dependent critical stretch. Thus, we can model the temperature-dependent crack propagation. Moreover, the wing crack growth problem is simulated to demonstrate the accuracy of the proposed inhomogeneous peridynamics ice model, whose simulation results agree well with the experimental data. Furthermore, the influence of the initial crack length, temperature, and bubbles in ice were also studied to understand the microcrack formation mechanism in ice. The results of this work show that the proposed peridynamic ice model not only provides an efficient tool to simulate the complex deformation pattern in ice failure process in a coupled thermo-mechanical field, but also reveals the mechanical mechanism of fracture in ice.

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Abbreviations

\({{{\varvec{\xi }}}_{\text {AB}}}\) :

The bond vector of material point \({{\mathbf {x}}_{\text {A}}}\) and \({{\mathbf {x}}_{\text {B}}}\) in reference configuration

\({{{\varvec{\eta }}}_{\text {AB}}}\) :

The relative displacement vector of material point \({{\mathbf {x}}_{\text {A}}}\) and \({{\mathbf {x}}_{\text {B}}}\) in current configuration

\({{c}_{v}}\) :

The specific heat capacity

\({{h}_{s}}\) :

The heat generate rate

\(\varTheta ({{\mathbf {x}}_{\text {A}}},t)\) :

The temperature at material point \({{\mathbf {x}}_{\text {A}}}\)

\({{\theta }_{\text {AB}}}\) :

The temperature difference between material point \({{\mathbf {x}}_{\text {A}}}\) and \({{\mathbf {x}}_{\text {B}}}\)

\({{H}_{{{x}_{\text {A}}}}}\) :

The horizon of particle \({{\mathbf {x}}_{\text {A}}}\)

\(\mathbf {f}({\varvec{\xi }},{\varvec{\eta }},t)\) :

The body force density function

\({{f}_{h}}\) :

The heat flow density function

\({{\mu }_{h}}\) :

The bond history function

\({{\phi }_{h}}\) :

The failure function index

s :

The bond stretch

\({s}_{0}^{{}}\) :

The critical bond stretch

c :

The micro-modulus

\({{f}_{h}}({{\varTheta }_{\text {B}}}-{{\varTheta }_{\text {A}}},{{\mathbf {x}}_{\text {B}}}-{{\mathbf {x}}_{\text {A}}},t)\) :

The thermal bond force density

\(\kappa ({{\mathbf {x}}_{\text {A}}},{{\mathbf {x}}_{\text {B}}})\) :

The micro-conductivity of the thermal bond

\(K({{\mathbf {x}}_{\text {A}}},{{\mathbf {x}}_{\text {B}}})\) :

The thermal conductivity of the material

\({{G}_{0}}\) :

The energy release rate

\({{K}_{I}}\) :

The fracture toughness

\({s}_{{}}^{\text {TH}}\) :

Thermo-mechanical bond stretch

\({s}_{0}^{\text {TH}}\) :

Thermo-mechanical bond critical stretch

\({s}_{i}^{\text {TH}}\) :

The critical stretch variable

\(\overline{{s}_{i}}^{\text {TH}}\) :

The average critical stretch

m :

The shape parameter

\(f\left( {s}_{i}^{\text {TH}},\overline{{s}_{i}}^{\text {TH}},m\right)\) :

The probability density distribution function

\(F\left( {s}_{i}^{\text {TH}},\overline{{s}_{i}}^{\text {TH}},m\right)\) :

The probability distribution function

p :

The porosity of ice

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Acknowledgements

YS and YL were supported by the National Natural Science Foundation of China (Grant No. 51979049).

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Authors and Affiliations

  1. College of Ocean Science and Engineering, Shanghai Maritime University, Shanghai, 200135, China

    Ying Song & Yunbo Li

  2. Department of Civil and Environmental Engineering, University of California, Berkeley, USA

    Shaofan Li

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  1. Ying Song
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  2. Shaofan Li
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  3. Yunbo Li
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Contributions

YS: conceptualization, software, and writing; SL: methodology, supervision, and writing; YL: resources, analysis, and writing.

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Correspondence to Shaofan Li.

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Song, Y., Li, S. & Li, Y. Peridynamic modeling and simulation of thermo-mechanical fracture in inhomogeneous ice. Engineering with Computers 39, 575–606 (2023). https://doi.org/10.1007/s00366-022-01616-7

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