A lower bound estimate of the critical load in bifurcation analysis for incompressible elastic solids

A procedure for obtaining a lower bound estimate of the critical load for arbitrary incompressible hyperelastic solids is presented. By considering a lower bound estimate for the Hadamard functional based on the Korn inequality, we establish sufficient conditions for the infinitesimal stability of a distorted configuration. We then determine an optimal lower bound estimate of the critical load in a monotonic loading process and specialize our procedure to the case of homogeneous deformations of incompressible, hyperelastic bodies. We apply our procedure to some representative dead-load boundary value problems for Mooney–Rivlin elastic solids and discuss its effectiveness and handiness for applications by comparing our results to other estimates.