ELASTOPLASTIC RESPONSE OF PRESSURE SENSITIVE SOLIDS

Abstract

Tensorially invariant constitutive relations are systematically derived for large strain elastoplastic response of geomaterials. The analysis centres on Mohr–Coulomb (MC) and Drucker–Prager (DP) models with arbitrary hardening and non-associated response. Both flow and deformation theories are constructed for each model with emphasis on linear incremental relations between the Eulerian strain rate tensor and the objective Jaumann stress rate tensor. Specifying the results for plane strain compression we find that deformation theory produces a much smaller tangent instantaneous shear modulus than flow theory. It follows that failure of ellipticity and onset of surface instabilities predicted by deformation theory for associated solids occur at much lower levels of strain than the corresponding flow theory results. On the other hand, flow theory predictions admit a considerable sensitivity to the level of non-associativity. In fact, at high levels of non-associativity flow theory predictions for loss of ellipticity can be at strains below those obtained from deformation theory. © 1997 John Wiley & Sons, Ltd.