INSTABILITY OF THICK ELASTIC SOLIDS

The stability of equilibrium of several homogeneous isotropic elastic solids is investigated. The problems considered are treated by making use of a nonlinear three-dimensional theory of elasticity. No restrictive assumptions are made concerning the thickness of the bodies, and the displacements and strains are assumed not to be small. The strain energy function, from which the stress-strain relations come, could in principle be chosen arbitrarily. In this paper a special, but for many materials reasonable, choice for the strain energy function is made. In each problem a simple solution is derived which satisfies all conditions of the exact nonlinear theory. A small perturbation with respect to this simple state is then made, and the question is raised as to whether other possible equilibrium states exist within the framework of the basic theory. Critical pressures and strains needed to cause such buckled solutions are found, together with the corresponding modes of buckling. (Author)