A Galerkin least-square stabilisation technique for hyperelastic biphasic soft tissue

TL;DR

This paper introduces a Galerkin least-square stabilization method for hyperelastic biphasic soft tissue models, effectively reducing pressure oscillations in slow-draining 3D finite element simulations without extensive mesh refinement.

Contribution

It proposes a novel stabilization framework that enhances numerical stability and accuracy in biphasic tissue modeling, addressing pressure oscillations in tetrahedral Taylor-Hood elements.

Findings

Significantly reduces pressure oscillations in 3D simulations.

Improves robustness of finite element analysis for biphasic tissues.

Demonstrates effectiveness on a complex numerical example.

Abstract

An hyperelastic biphasic model is presented. For slow-draining problems (permeability less than 1\times10-2 mm4 N-1 s-1), numerical instabilities in the form of non-physical oscillations in the pressure field are observed in 3D problems using tetrahedral Taylor-Hood finite elements. As an alternative to considerable mesh refinement, a Galerkin least-square stabilization framework is proposed. This technique drastically reduces the pressure discrepancies and prevents these oscillations from propagating towards the centre of the medium. The performance and robustness of this technique are demonstrated on a 3D numerical example.