A linearized consistent mixed displacement-pressure formulation for hyperelasticity

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.

Keywords:

• Bézier elements
• finite element analysis
• hyperelasticity
• incompressibility
• mixed formulation

Acknowledgments

The first author acknowledges the support of the Supercomputing Wales project, which is part-funded by the European Regional Development Fund (ERDF) via the Welsh Government. The authors are indebted to an anonymous reviewer for the useful insights into the idea of complementary energy functions presented in Appendix.