Two-sided estimates in the stability problem for compressed elastic blocks

We theoretically study stability problems for the equilibria of homogeneously compressed block-shaped nonlinearly elastic bodies of arbitrary proportions under certain specially kinematic boundary conditions on two out of three pairs of faces. The study is based on the static energy criterion for stability (instability) in small. (The perturbations are small with respect to states with large initial strains and stresses.) The properties of the material under arbitrary strains are determined by the proposed and investigated family of elastic potentials, which generalize the Mooney-Rivlin potential to the case of orthotropy and compressibility.