Consistent polynomial expansions of stored energy function for incompressible hyperelastic materials

TL;DR

This paper discusses polynomial expansion models for the stored energy function in incompressible hyperelastic materials, comparing third order and Rivlin models using experimental data to highlight their advantages.

Contribution

It introduces a consistent polynomial expansion approach based on deformation gradient decomposition, demonstrating advantages of the third order model over traditional Rivlin models.

Findings

Third order expansion model shows improved accuracy.

Model comparison highlights qualitative and quantitative benefits.

Advantages demonstrated using Treloar's experimental data.

Abstract

In the article, hyperelastic material models which state consistent polynomial expansions of the stored energy function are discussed. The approach follows from the muliplicative decomposition of the deformation gradient. Some advantages of the third order expansion model over the five-parameter Rivlin model using Treloar's experimental data are shown. The models are qualitatively and quantitatively compared to highlight these advantages of the discussed MV model.