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首页> 外文期刊>Journal of the Mechanics and Physics of Solids >Variational coarse-graining procedure for dynamic homogenization
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Variational coarse-graining procedure for dynamic homogenization

机译：动态均质化的变分粗粒度过程

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摘要

We present a variational coarse-graining framework for heterogeneous media in the spirit of FE~2 methods, that allows for a seamless transition from the traditional static scenario to dynamic loading conditions, while being applicable to general material behavior as well as to discrete or continuous representations of the material and its deformation, e.g., finite element discretizations or atomistic systems. The method automatically delivers the macroscopic equations of motion together with the generalization of Hill's averaging relations to the dynamic setting. These include the expression of the macroscopic stresses and linear momentum as a function of the microscopic fields. We further demonstrate with a proof of concept example, that the proposed theoretical framework can be used to perform multiscale numerical simulations. The results are compared with standard single-scale finite element simulations, showcasing the capability of the method to capture the dispersive nature of the medium in the range of frequencies permitted by the multiscale strategy.
机译：我们本着FE〜2方法的精神提出了一种异构介质的变分粗粒度框架，该框架允许从传统的静态场景到动态加载条件的无缝过渡，同时适用于一般的材料行为以及离散或连续的行为材料及其变形的表示形式，例如有限元离散化或原子系统。该方法自动提供宏观运动方程，以及希尔对动态设置的平均关系的概括。这些包括宏观应力和线性动量的表达，作为微观场的函数。我们通过概念验证示例进一步证明，所提出的理论框架可用于执行多尺度数值模拟。将结果与标准的单尺度有限元模拟进行比较，显示了该方法在多尺度策略允许的频率范围内捕获介质的色散特性的能力。

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