STABILITY-CRITERIA FOR HOMOGENEOUSLY STRESSED MATERIALS AND THE CALCULATION OF ELASTIC-CONSTANTS

Second-order elastic constants cannot be applied directly to the study of the mechanical stability of a stressed material. We derive general expressions for stability criteria by constructing appropriate thermo dynamic potentials. For a system under isotropic initial stress, elast ic stiffness coefficients which govern stress-strain relations can be used as stability criteria. However, for a system under anisotropic in itial stress, stability criteria are different from either elastic con stants or elastic stiffness coefficients. We show that stability condi tions in the constant pressure ensemble are stronger than in the const ant volume ensemble, i.e., a state can be stable in the constant volum e ensemble but unstable in the constant pressure ensemble. From the ge neral formalism simple fluctuation formulas for the stability criteria are deduced for systems in the canonical ensemble, for arbitrary stre ss.