Fixed stress splitting approach for contact problems in a porous medium

Tameem Almani; Kundan Kumar

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arXiv · 2407.13459

Fixed stress splitting approach for contact problems in a porous medium

Tameem Almani·Kundan Kumar

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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.

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Tameem Almani, Kundan Kumar. 2024-07-18. Fixed stress splitting approach for contact problems in a porous medium. https://arxiv.org/abs/2407.13459

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