Strong ellipticity of comparison solids in elastoplasticity with volumetric non-associativity

Abstract

Reference is made to non-associative, time independent infinitesimal elastoplasticity with non-associative flow rule. The non-associativity is restricted to the volumetric component of the plastic flow. Loss of strong ellipticity is shown to occur before the snap-back modulus is reached. An analytical solution for the condition of loss of strong ellipticity is obtained for the best chosen comparison solid of the family introduced by Raniecki (1979, Bull. Acad. Polon. Sci. XXVII, 391–399). Finally, this solution is shown to coincide with the loss of strong ellipticity in the comparison solid “in loading”. Therefore, for volumetric non-associative flow-rules, strong ellipticity is lost simultaneously in the best chosen comparison solid of Raniecki and in the comparison solid “in loading”.