On Finite Plastic Flow of Crystalline Solids and Geomaterials

Abstract

Certain fundamentals of finite-deformation elastoplastic flow of crystalline solids and geomaterials are discussed from microscopic and macroscopic phenomenological points of view. In the first case, physically based constitutive relations for microelements are formulated on the basis of slip-induced plastic deformation with due account of possible frictional or pressure dependencies and inelastic volumetric changes. The close relation between the double-slip theory of single crystals and that of granular materials is discussed. The calculation of overall instantaneous moduli in terms of the local quantities for arbitrary strains and rotations is examined, and some recent results for polycrystals and granular materials are reviewed. Then, attention is focused on phenomenological constitutive relations which apply to both metals and geomaterials. Specific results are given for an isotropic-kinematic hardening model, including frictional and plastic dilatancy effects. Finally, certain fundamental thermodynamic aspects of finite-deformation inelasticity are reviewed, emphasizing conditions under which flow potentials exist.