Hyperelastic bodies under homogeneous Cauchy stress induced by three-dimensional non-homogeneous deformations

Abstract

In isotropic finite elasticity, unlike in the linear elastic theory, a homogeneous Cauchy stress may be induced by non-homogeneous strains. To illustrate this, we identify compatible non-homogeneous three-dimensional deformations producing a homogeneous Cauchy stress on a cuboid geometry, and provide an example of an isotropic hyperelastic material, which is not rank-one convex, and for which the homogeneous stress and the associated non-homogeneous strains on a domain similar to those analysed are given explicitly.

arXiv admin note: substantial text overlap with arXiv:1608.05040

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Cited by in corpus (3)

• Instabilities in liquid crystal elastomers
• Do we need Truesdell's empirical inequalities? On the coaxiality of stress and stretch
• A note on non-homogeneous deformations with homogeneous Cauchy stress for a strictly rank-one convex energy in isotropic hyperelasticity