Finite deformation analysis of restrictions on moving strong discontinuity surfaces in elastic-plastic materials : Quasi-static and dynamic deformations

Abstract

This paper reports the results of a finite deformation study of the conditions under which propagating surfaces of strong discontinuity (across which components of stress, strain or material velocity jump) can exist in a general class of purely mechanical elastic-plastic solids. By enforcing the standard weak continuum-mechanical requirements of momentum conservation and geometrical compatibility, together with skeletal constitutive assumptions that are in broad agreement with experimental results and that subsume many specific material models, we derive explicit jump conditions that must be satisfied by such moving surfaces (and which in many cases rule out their existence). Our results confirm many of the restrictions derived previously via a small-displacement-gradient formulation, showing how those must be interpreted in a finite deformation situation. But they also demonstrate that certain conditions adopt a more complex form. especially in the presence of material anisotropy. The cases of quasi-static and dynamic deformations are considered separately, and it is shown how the results are related. Finally, we derive a thermodynamically motivated jump dissipation inequality that is sensibly applied to an extremely broad class of elastic-plastic materials ; the quasi-static version of this is identical in form to a dissipation inequality derived in a different manner by knowles ( J. Elasticity 9, 131. 1979) for propagating equilibrium shocks in purely hyperelastic materials.