We present a variational framework for the computational homogenization of chemo-mechanical processes of soft porous materials. The multiscale variational framework is based on a minimization principle with deformation map and solvent flux acting as independent variables. At the microscopic scale we assume the existence of periodic representative volume elements (RVEs) that are linked to the macroscopic scale via first-order scale transition. In this context, the macroscopic problem is considered to be homogeneous in nature and is thus solved at a single macroscopic material point. The microscopic problem is however assumed to be heterogeneous in nature and thus calls for spatial discretization of the underlying RVE. Here, we employ Raviart–Thomas finite elements and thus arrive at a conforming finite-element formulation of the problem. We present a sequence of numerical examples to demonstrate the capabilities of the multiscale formulation and to discuss a number of fundamental effects.

中文翻译：

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基于变分最小化原理的瞬态化学机械过程的计算均质化

我们提出了一种变体框架，用于软多孔材料的化学机械过程的计算均质化。多尺度变分框架基于最小化原理，其中变形图和溶剂通量充当自变量。在微观尺度上，我们假设存在周期性代表性的体积元素（RVE），这些元素通过一阶尺度转换与宏观尺度联系在一起。在这种情况下，宏观问题在本质上被认为是同质的，因此可以在单个宏观物质点上得到解决。然而，微观问题被认为本质上是异质的，因此需要底层RVE的空间离散化。在这里，我们使用Raviart–Thomas有限元，从而得出问题的一致有限元表述。