A Galerkin least-square stabilisation technique for hyperelastic biphasic soft tissue
For researchers simulating soft tissue mechanics, this work provides a stabilization method to avoid costly mesh refinement in slow-draining biphasic problems.
The paper addresses numerical instabilities (non-physical pressure oscillations) in 3D hyperelastic biphasic soft tissue simulations using tetrahedral Taylor-Hood elements for slow-draining problems. A Galerkin least-square stabilization technique is proposed, which drastically reduces pressure discrepancies and prevents oscillation propagation, demonstrated on a 3D numerical example.
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.