Modelling large-deforming fluid-saturated porous media using an Eulerian incremental formulation

TL;DR

This paper develops an Eulerian incremental formulation for modeling large-deforming fluid-saturated porous media, integrating hyperelasticity, Darcy flow, and finite element methods, validated through numerical simulations.

Contribution

It introduces a novel Eulerian incremental approach with a linearization scheme based on two-scale homogenization for large deformation poroelastic media.

Findings

Validated numerical model in SfePy code.

Effective linearization scheme for large deformation.

Successful application to isotropic hyperelastic media.

Abstract

The paper deals with modelling fluid saturated porous media subject to large deformation. An Eulerian incremental formulation is derived using the problem imposed in the spatial configuration in terms of the equilibrium equation and the mass conservation. Perturbation of the hyperelastic porous medium is described by the Biot model which involves poroelastic coefficients and the permeability governing the Darcy flow. Using the material derivative with respect to a convection velocity field we obtain the rate formulation which allows for linearization of the residuum function. For a given time discretization with backward finite difference approximation of the time derivatives, two incremental problems are obtained which constitute the predictor and corrector steps of the implicit time-integration scheme. Conforming mixed finite element approximation in space is used. Validation of the numerical model implemented in the SfePy code is reported for an isotropic medium with a hyperelastic solid phase. The proposed linearization scheme is motivated by the two-scale homogenization which will provide the local material poroelastic coefficients involved in the incremental formulation.