Fixed stress splitting approach for contact problems in a porous medium

TL;DR

This paper introduces a fixed stress splitting iterative scheme for solving coupled poromechanics contact problems, extending existing methods to include contact mechanics with proven convergence.

Contribution

The paper develops a fully discrete fixed stress splitting scheme for poromechanics with contact, combining finite elements and backward Euler, and proves its contraction property.

Findings

The scheme effectively decouples flow and mechanics equations.

The fixed stress split scheme is shown to be a contraction.

Numerical stability and convergence are established.

Abstract

We consider a poromechanics model including frictionless contact mechanics. The resulting model consists of the Biot equations with contact boundary conditions leading to a variational inequality modelling mechanical deformations coupled to a linear parabolic flow equation. We propose a fully discrete iterative scheme for solving this model. This scheme decoupled the flow and mechanics equations and extends the fixed-stress splitting scheme for the Biot equations. We use finite elements in space and a backward Euler discretization in time. We show that the fixed stress split scheme is a contraction.