A linearised consistent mixed displacement-pressure formulation for hyperelasticity

TL;DR

This paper introduces a new mixed displacement-pressure formulation for hyperelasticity that is consistent across compressible and incompressible regimes, offering a simplified and efficient alternative to existing three-field methods.

Contribution

The paper presents a novel two-field mixed displacement-pressure formulation that is applicable to both compressible and incompressible hyperelastic materials, simplifying existing models.

Findings

Applicable to nearly and truly incompressible cases

Proven to be a simplified alternative to three-field formulations

Validated through analytical derivation and numerical results

Abstract

We propose a novel mixed displacement-pressure formulation based on an energy functional that takes into account the relation between the pressure and the volumetric energy function. We demonstrate that the proposed two-field mixed displacement-pressure formulation is not only applicable for nearly and truly incompressible cases but also is consistent in the compressible regime. Furthermore, we prove with analytical derivation and numerical results that the proposed two-field formulation is a simplified and efficient alternative for the three-field displacement-pressure-Jacobian formulation for hyperelastic materials whose strain energy density functions are decomposed into deviatoric and volumetric parts.