Strain energy function for isotropic non-linear elastic incompressible solids with linear finite strain response in shear and torsion

TL;DR

This paper derives a strain energy function for isotropic incompressible nonlinear elastic solids that maintains linear shear and torsion responses at large strains, extending classical models to include additional nonlinear effects.

Contribution

It introduces a generalized strain energy function that encompasses neo-Hookean, Mooney-Rivlin, and other models, capturing nonlinear effects like strain stiffening.

Findings

Includes well-known models as special cases

Can model strain stiffening effects

Applicable to large shear and torsion deformations

Abstract

We find the strain energy function for isotropic incompressible solids exhibiting a linear relationship between shear stress and amount of shear, and between torque and amount of twist, when subject to large simple shear or torsion deformations. It is inclusive of the well-known neo-Hookean and the Mooney-Rivlin models, but also can accommodate other terms, as certain arbitrary functions of the principal strain invariants. Effectively, the extra terms can be used to account for several non-linear effects observed experimentally but not captured by the neo-Hookean and Mooney-Rivlin models, such as strain stiffening effects due to limiting chain extensibility.