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

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