Phase-inherent linear visco-elasticity model for infinitesimal deformations in the multiphase-field context
Open Access
- 2 December 2020
- journal article
- Published by Springer Science and Business Media LLC in Advanced Modeling and Simulation in Engineering Sciences
- Vol. 7 (1), 1-32
- https://doi.org/10.1186/s40323-020-00178-x
Abstract
A linear visco-elasticity ansatz for the multiphase-field method is introduced in the form of a Maxwell-Wiechert model. The implementation follows the idea of solving the mechanical jump conditions in the diffuse interface regions, hence the continuous traction condition and Hadamard’s compatibility condition, respectively. This makes strains and stresses available in their phase-inherent form (e.g. $$\varepsilon ^{\alpha }_{ij}$$ ε ij α , $$\varepsilon ^{\beta }_{ij}$$ ε ij β ), which conveniently allows to model material behaviour for each phase separately on the basis of these quantities. In the case of the Maxwell-Wiechert model this means the introduction of phase-inherent viscous strains. After giving details about the implementation, the results of the model presented are compared to a conventional Voigt/Taylor approach for the linear visco-elasticity model and both are evaluated against analytical and sharp-interface solutions in different simulation setups.
Keywords
Funding Information
- Deutsche Forschungsgemeinschaft (GRK 2078, NE822/31-1: Gottfried-Wilhelm-Leibniz prize)
- Deutsche Forschungsgemeinschaft (EXC 2154: PoLiS)
- Helmholtz-Gemeinschaft (Energy Efficiency, Materials and Resources)
- Deutsche Forschungsgemeinschaft (Future Fields)
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