Shear, pure and simple

TL;DR

This paper investigates the relationship between pure shear stresses and deformations in nonlinear elastic materials, confirming previous results under weaker assumptions and introducing new concepts of shear deformation.

Contribution

It extends prior work by weakening assumptions and exploring the case of shear load, also proposing a new notion of idealized finite simple shear.

Findings

Pure shear stress does not necessarily correspond to simple shear deformation.

Conditions are identified where pure shear stresses align with pure shear stretches.

A new concept of idealized finite simple shear is introduced for certain nonlinear materials.

Abstract

In a 2012 article in the International Journal of Non-Linear Mechanics, Destrade et al. showed that for nonlinear elastic materials satisfying Truesdell's so-called empirical inequalities, the deformation corresponding to a Cauchy pure shear stress is not a simple shear. Similar results can be found in a 2011 article of L. A. Mihai and A. Goriely. We confirm their results under weakened assumptions and consider the case of a shear load, i.e. a Biot pure shear stress. In addition, conditions under which Cauchy pure shear stresses correspond to (idealized) pure shear stretch tensors are stated and a new notion of idealized finite simple shear is introduced, showing that for certain classes of nonlinear materials, the results by Destrade et al. can be simplified considerably.