Hyperelastic bodies under homogeneous Cauchy stress induced by   non-homogeneous finite deformations
  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. 
L. Angela Mihai and Patrizio Neff
physics.class-ph math.NA