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We discuss whether homogeneous Cauchy stress implies homogeneous strain inisotropic nonlinear elasticity. While for linear elasticity the positive answeris clear, we exhibit, through detailed calculations, an example withinhomogeneous continuous deformation but constant Cauchy stress. The example isderived from a non rank-one convex elastic energy.

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