Non-Hookean elasticity with arbitrary Poisson's ratios

TL;DR

This paper introduces a hyperelastic isotropic material model capable of exhibiting arbitrary Poisson's ratios (except -1), maintaining positive-definiteness and thermodynamic consistency, with stable and plausible responses under deformation.

Contribution

It proposes a new strain energy function that allows for arbitrary Poisson's ratios while ensuring positive-definiteness and thermodynamic laws.

Findings

Model can produce Poisson's ratios greater than 0.5.

The energy function remains positive-definite for all ratios except -1.

Model response is stable and plausible across deformation states.

Abstract

In a previous paper \cite{Itskov-MoSM} we presented a hyperelastic isotropic material model whose stress-strain response is nonlinear even at infinitesimal deformations and cannot thus be linearized. As a result values of Poisson's ratio greater than one half were obtained. In this contribution, we further propose an isotropic strain energy function which is always positive-definite and depending on material constants delivers arbitrary values of Poisson's ratio (except of $-1$) in agreement with the laws of thermodynamics. The model response appears stable and plausible in various deformation states.