English

Shear, pure and simple

Analysis of PDEs 2019-06-26 v2

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.

Keywords

Cite

@article{arxiv.1806.07749,
  title  = {Shear, pure and simple},
  author = {Christian Thiel and Jendrik Voss and Robert J. Martin and Patrizio Neff},
  journal= {arXiv preprint arXiv:1806.07749},
  year   = {2019}
}
R2 v1 2026-06-23T02:36:02.600Z