The governing equations and numerical solution strategy to solve porohyperelstic 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 to solve finite strain (multiscale) porohyperelastic problems accurately using 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:通过提供多级多物理介质,解决多级多光学问题的管理方程式和数字解决方案战略在此贡献中提供。问题起源于在孔级使用任意拉格朗加亚-尤利安(ALE)技术在孔级开发和非维化液-液体相互作用(FSII)问题。由此产生的APDE 的ALE-FSI组合系统扩大并分析,使用无孔不入的同质化技术,产生三套局部的PDES系统,其中一种系统管理两个微规模问题(液态和固体)提供的宏观/有效问题。后两种系统则提供以实时/线性形式要求其平均价值的显微孔反应字段,以确定宏观反应。通过培训人工神经网络(ANNE)作为微规模固体问题直接神经溶解的代谢。目前的方法可以用伸缩缩(多级)微孔弹性(多度)的显性弹性弹性弹性弹性弹性/有效弹性问题,通过实时/直径的缩缩缩缩度分析,从实时/直径分析,从最精确的磁度分析到最精确的磁度分析,以最精确的磁级的磁级的磁度进行磁度分析。