ANN-aided incremental multiscale-remodelling-based finite strain poroelasticity

Abstract

Mechanical modelling of poroelastic media under finite strain is usually carried out via phenomenological models neglecting complex micro-macro scales interdependency. One reason is that the mathematical two-scale analysis is only straightforward assuming infinitesimal strain theory. Exploiting the potential of ANNs for fast and reliable upscaling and localisation procedures, we propose an incremental numerical approach that considers rearrangement of the cell properties based on its current deformation, which leads to the remodelling of the macroscopic model after each time increment. This computational framework is valid for finite strain and large deformation problems while it ensures infinitesimal strain increments within time steps. The full effects of the interdependency between the properties and response of macro and micro scales are considered for the first time providing more accurate predictive analysis of fluid-saturated porous media which is studied via a numerical consolidation example. Furthermore, the (nonlinear) deviation from Darcy’s law is captured in fluid filtration numerical analyses. Finally, the brain tissue mechanical response under uniaxial cyclic test is simulated and studied.

Homogenized Balance Equations for Nonlinear Poroelastic Composites

“…Developing suitable computational schemes is a current active area of research. A recent example of a proposed method that could be potentially used to solve the types of problems arising in this work is found in [45]. It is important to note that the potential results of any simulations should be validated by experimental data, which could be related to biological tissues.…”

“…Despite the complexity, there are some potential emerging techniques that may mean it would be possible to solve this model numerically in the future. A recent example of a proposed method that could be potentially used to solve the types of problems arising in this work is found in [45]. This work investigated the potential of using Artificial Neural Networks (ANNs) for quick, accurate upscaling and localisation of problems.…”

“…This method is applicable to finite strain and large deformation problems, whilst there will only be infinitesimal deformation within each incremental time step. Reference [45] investigated the full effects of the coupling between the macroscale and microscale for the first time in the analysis of fluid-saturated porous media. We believe that by following an approach similar to the one set out in [45], we could obtain a solution to our model numerically.…”

“…Reference [45] investigated the full effects of the coupling between the macroscale and microscale for the first time in the analysis of fluid-saturated porous media. We believe that by following an approach similar to the one set out in [45], we could obtain a solution to our model numerically.…”

Finite strain poro-hyperelasticity: an asymptotic multi-scale ALE-FSI approach supported by ANNs

“…However, if we can obtain the average displacement tensor differently there is no need for solving for the full displacement field as part of the effective system of PDEs. This can be achieved with considerable speed-up by exploiting the predictive power of ANNs in the context of computational mechanics [20][21][22][23].…”