The governing equations and numerical solution strategy to solve porohyperelastic problems as multiscale multiphysics media are provided in this contribution. The problem starts from formulating and non-dimensionalising a Fluid-Solid Interaction (FSI) problem using Arbitrary Lagrangian-Eulerian (ALE) technique at the pore level. The resultant ALE-FSI coupled systems of PDEs are expanded and analysed using the asymptotic homogenisation technique which yields three partially novel systems of PDEs, one governing the macroscopic/effective problem supplied by two microscale problems (fluid and solid). The latter two provide the microscopic response fields whose average value is required in real-time/online form to determine the macroscale response. This is possible efficiently by training an Artificial Neural Network (ANN) as a surrogate for the Direct Numerical Solution (DNS) of the microscale solid problem. The present methodology allows for solving finite strain (multiscale) porohyperelastic problems accurately using the direct derivative of the strain energy, for the first time. Furthermore, a simple real-time output density check is introduced to achieve an optimal and reliable training dataset from DNS. A Representative Volume Element (RVE) is adopted which is followed by performing a microscale (RVE) sensitivity analysis and a multiscale confined consolidation simulation showing the importance of employing the present method when dealing with finite strain poroelastic/porohyperelastic problems.

翻译：摘要：本文提出了求解多尺度多物理介质中多孔超弹性问题的控制方程及数值求解策略。该问题从使用任意拉格朗日-欧拉（ALE）技术在孔隙尺度上构建并无量纲化流固耦合（FSI）问题开始。利用渐近均匀化方法对由此得到的ALE-FSI耦合偏微分方程系统进行展开与分析，得到三个部分新颖的偏微分方程系统：一个控制宏观/等效问题，并由两个微观尺度问题（流体与固体）提供补充。后两者提供微观响应场，其平均值需以实时/在线形式获取，以确定宏观响应。通过训练人工神经网络（ANN）作为微观固体问题直接数值求解（DNS）的替代模型，可高效实现上述目标。本方法首次能够利用应变能的直接导数精确求解有限应变（多尺度）多孔超弹性问题。此外，引入了一种简单的实时输出密度检查方法，以从DNS中获取最优且可靠的训练数据集。研究采用代表性体积单元（RVE），并依次进行了微观尺度（RVE）敏感性分析及多尺度受限固结模拟，结果表明了本方法在处理有限应变多孔弹性/多孔超弹性问题中的重要性。