  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.
