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. $$\varepsilon ^{\alpha }_{ij}$$ , $$\varepsilon ^{\beta }_{ij}$$ ), 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.

中文翻译：

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多相场环境中无穷小变形的相干线性粘弹性模型

以Maxwell-Wiechert模型的形式介绍了用于多相场方法的线性粘弹性Ansatz。该实现遵循解决扩散界面区域中的机械跳跃条件的思想，因此分别解决了连续牵引条件和Hadamard的相容性条件。这使得应变和应力以其固有的相位形式可用（例如$$ \ varepsilon ^ {\ alpha} _ {ij} $$，$$ \ varepsilon ^ {\ beta} _ {ij} $$），这方便地允许根据这些数量分别为每个阶段的材料行为建模。在Maxwell-Wiechert模型的情况下，这意味着引入了相位固有的粘性应变。在提供有关实现的详细信息之后，