Infinitesimal elastic stability of homogeneous deformations and the zero moment condition

We investigate the relationships between the infinitesimal elastic stability of homogeneous deformations and the zero moment condition. Under dead loading, for physically reasonable constitutive assumptions, we find that if the infinitesimal deformation satisfies the zero moment condition, it is stable under a very weak condition, one which includes an all-round compressive state. We show further that for a given stretching D the deformation L with the zero moment condition is the minimum (maximum) stable deformation in the state 53-1. Here 53-2 and t _a, a=1, 2, 3, are the principal Biot and Cauchy stresses, respectively. Finally, we examine stability when the prescribed traction rate is controlled such that the zero moment condition is satisfied for any deformation.