Hyperelastic bodies under homogeneous Cauchy stress induced by non-homogeneous finite deformations
This work challenges a fundamental assumption in nonlinear elasticity, providing a theoretical counterexample that may impact the understanding of stress-strain relations for researchers in continuum mechanics.
The paper investigates whether homogeneous Cauchy stress implies homogeneous strain in isotropic nonlinear elasticity, and demonstrates a counterexample with inhomogeneous deformation but constant stress, derived from a non rank-one convex elastic energy.
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.