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Shear, pure and simple
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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.
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The corotational stability postulate: positive incremental Cauchy stress moduli for diagonal, homogeneous deformations in isotropic nonlinear elasticity
The corotational stability postulate implies that all standard incremental Cauchy stress moduli (Young, equibiaxial, planar tension, bulk) are positive in diagonal homogeneous deformations of isotropic hyperelastic materials.
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