A linearized consistent mixed displacement-pressure formulation for hyperelasticity

Kadapa, Chennakesava; Hossain, Mokarram

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.

• Journal Article Type: Article
• Acceptance Date: Apr 27, 2020
• Online Publication Date: May 20, 2020
• Publication Date: Jan 14, 2022
• Deposit Date: Aug 29, 2022
• Journal: Mechanics of Advanced Materials and Structures
• Print ISSN: 1537-6494
• Electronic ISSN: 1537-6532
• Publisher: Taylor & Francis
• Peer Reviewed: Peer Reviewed
• Volume: 29
• Issue: 2
• Pages: 267-284
• DOI: https://doi.org/10.1080/15376494.2020.1762952
• Keywords: Bézier elements, finite element analysis, hyperelasticity, incompressibility, mixed formulation
• Public URL: http://researchrepository.napier.ac.uk/Output/2893858