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Modeling and simulation of non-isothermal rate-dependent damage processes in inhomogeneous materials using the phase-field approach

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Abstract

We present a continuum model that incorporates rate-dependent damage and fracture, a material order-parameter field and temperature within a phase-field approach. The models covers partial damage as well as the formation of macro-cracks. For the material order parameter we assume a Cahn Larché-type dynamics, which makes the model in particular applicable to binary alloys. We give thermodynamically consistent evolution equations resulting from a unified variational approach. Diverse coupling mechanisms can be covered within the model, such as heat dissipation, thermal-expansion-induced failure and crack deflection due to inhomogeneities. With help of an adaptive finite element code we conduct numerical experiments of different complexity in order to study the possibilities and limitations of the presented model. We furthermore include anisotropic linear elasticity in our model and investigate the effect on the crack pattern.

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Notes

  1. Small Greek letters are used for spatial indexing. We use the summation convention for coordinates unless otherwise stated.

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Acknowledgements

The authors would like to acknowledge the Einstein Foundation Berlin, who partially supported this work in the framework of the MATHEON.

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Authors and Affiliations

  1. Weierstrass Institute for Applied Analysis and Stochastics, Leibniz Institute in Forschungsverbund Berlin e. V., Mohrenstrasse 39, 10117, Berlin, Germany

    Markus Radszuweit & Christiane Kraus

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  1. Markus Radszuweit
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  2. Christiane Kraus
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Correspondence to Markus Radszuweit.

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Radszuweit, M., Kraus, C. Modeling and simulation of non-isothermal rate-dependent damage processes in inhomogeneous materials using the phase-field approach. Comput Mech 60, 163–179 (2017). https://doi.org/10.1007/s00466-017-1393-4

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