Slight compressibility and sensitivity to changes in Poisson's ratio

TL;DR

Finite element simulations of soft materials are highly sensitive to Poisson's ratio, especially in shearing deformations, which can significantly affect normal stress predictions and challenge common modeling assumptions.

Contribution

This paper demonstrates the extreme sensitivity of normal stress distribution to Poisson's ratio in shearing deformations of soft materials, highlighting the need for precise parameter determination.

Findings

Normal stress distribution is highly sensitive to Poisson's ratio in shear.

Arbitrarily choosing Poisson's ratio near 0.5 can lead to inaccurate stress predictions.

Sensitivity arises from small volume changes during deformation.

Abstract

Finite Element simulations of rubbers and biological soft tissue usually assume that the material being deformed is slightly compressible. It is shown here that in shearing deformations the corresponding normal stress distribution can exhibit extreme sensitivity to changes in Poisson's ratio. These changes can even lead to a reversal of the usual Poynting effect. Therefore the usual practice of arbitrarily choosing a value of Poisson's ratio when numerically modelling rubbers and soft tissue will, almost certainly, lead to a significant difference between the simulated and actual normal stresses in a sheared block because of the difference between the assumed and actual value of Poisson's ratio. The worrying conclusion is that simulations based on arbitrarily specifying Poisson's ratio close to 1/2 cannot accurately predict the normal stress distribution even for the simplest of shearing deformations. It is shown analytically that this sensitivity is due to the small volume changes which inevitably accompany all deformations of rubber-like materials. To minimise these effects, great care should be exercised to accurately determine Poisson's ratio before simulations begin.