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:通过提供多级多物理介质,解决孔径高弹性问题的治理方程式和数字解决方案战略在此贡献中提供。问题起源于利用孔径级的任意Lagrangaian-ELERIAN(ALE)技术,在孔径层一级开发和非维化液-液体相互作用(FSII)问题。由此形成的APDE 的ALE-FSI组合系统扩大并分析,使用微尺度固态直接营养溶解(DNS)的无源同质化技术,产生三套局部的PDES系统,一个管理两个微尺度问题(液态和固体)提供的宏孔径/有效问题。后两个系统提供了以实时/在线形式确定宏规模响应的平均价值的显微镜字段。这可以通过培训人工神经网络(ANNE)作为微尺度固度固体问题直接营养溶解(DNS)的代号。目前的方法允许使用弹性微缩缩缩缩压(多尺度)的微缩缩缩缩缩放弹性问题,而以直导变缩的缩缩缩缩缩缩缩缩缩缩缩缩缩缩缩缩缩缩缩缩缩度数据则通过最能化的缩缩缩缩缩缩缩缩缩缩缩缩缩缩缩缩缩缩缩缩缩压数据分析,从目前的缩缩缩缩缩缩缩缩缩缩缩缩缩缩缩缩缩缩缩缩缩压数据分析,从目前缩缩缩缩缩缩缩缩缩缩缩缩压数据,通过缩缩缩缩缩缩缩缩缩缩缩缩缩缩缩压数据分析将得出出。