Stability and Post-Bifurcation behavior of a Mooney-Rivlin elastic body in multiaxial stress states

In this paper the equilibrium homogeneous deformations of a Mooney-Rivlin parallelepiped subject to a distribution of dead-load surface tractions corresponding to an equibiaxial tensile stress state accompanied by an orthogonal uniaxial compression of the same amount is studied. It is shown that only two classes of homogeneous equilibrium solutions are possible and then the necessary and sufficient stability conditions for the equilibrium deformations by adopting the classical Hadamard criterion of infinitesimal stability are found. Finally, by analysing the mechanical response of the parallelepiped in a monotonic dead loading process, the actual occurrence of a bifurcation from a primary branch of locally stable deformations with two equal principal stretches to a secondary, post-critical branch of locally stable solutions having all different principal stretches are modelled.