New sufficient conditions for the Hadamard stability of a Mooney-Rivlin elastic solid in uniaxial deformation

A procedure for obtaining a lower bound estimate of the critical load for a homogeneously deformed Mooney-Rivlin incompressible cylinder is presented. By considering a lower bound estimate for the second variation of the total energy functional based on the Korn inequality, we establish sufficient conditions for the infinitesimal Hadamard stability of a distorted configuration. We then sketch the procedure for determining an optimal lower bound estimate of the critical load in a uniaxial compressive loading process and discuss its effectiveness for applications by comparing our results to other estimates proposed in the literature.