Stability of Pure Homogeneous Deformations of an Elastic Cube under Dead Loading

Abstract

In a previous paper [1], the problem was considered of the pure homogeneous deformation of a unit cube of incompressible neo-Hookean elastic material by three pairs of equal and opposite forces acting normally on the faces of the cube and distributed uniformly over them. It was found that, for certain specified values of the forces, more than one equilibrium state of pure homogeneous deformation can exist. The stability of each of these states was investigated, with respect to superposed infinitesimal pure homogeneous deformations, with the same principal directions as the equilibrium state. It was found that for certain ranges of values of the applied forces, more than one equilibrium state of pure homogeneous deformation which is stable in this sense can exist. Which of these stable states is actually attained in practice will depend on the order in which the forces are applied.

Received March 28, 1973. This work was carried out with the support of the Office of Naval Research under Contract No. N00014–67–0370–0001 with Lehigh University.