Hyperelastic bodies under homogeneous Cauchy stress induced by non-homogeneous finite deformations

Abstract

We discuss whether homogeneous Cauchy stress implies homogeneous strain in isotropic nonlinear elasticity. While for linear elasticity the positive answer is clear, we exhibit, through detailed calculations, an example with inhomogeneous continuous deformation but constant Cauchy stress. The example is derived from a non rank-one convex elastic energy.

References in corpus (4)

• Geometry of logarithmic strain measures in solid mechanics
• The exponentiated Hencky-logarithmic strain energy. Part II: Coercivity, planar polyconvexity and existence of minimizers
• The exponentiated Hencky-logarithmic strain energy. Improvement of planar polyconvexity
• Injectivity of the Cauchy-stress tensor along rank-one connected lines under strict rank-one convexity condition

Cited by in corpus (8)

• Instabilities in liquid crystal elastomers
• Injectivity of the Cauchy-stress tensor along rank-one connected lines under strict rank-one convexity condition
• A non-ellipticity result, or the impossible taming of the logarithmic strain measure
• Do we need Truesdell's empirical inequalities? On the coaxiality of stress and stretch
• The exponentiated Hencky energy: Anisotropic extension and case studies
• A note on non-homogeneous deformations with homogeneous Cauchy stress for a strictly rank-one convex energy in isotropic hyperelasticity
• Hyperelastic bodies under homogeneous Cauchy stress induced by three-dimensional non-homogeneous deformations
• A finite element implementation of the isotropic exponentiated Hencky-logarithmic model and simulation of the eversion of elastic tubes