THERMODYNAMIC EQUIVALENCE OF STEADY-STATE SHOCKS AND SMOOTH WAVES IN GENERAL MEDIA - APPLICATIONS TO ELASTIC-PLASTIC SHOCKS AND DYNAMIC FRACTURE

By comparing the First Law of thermodynamics in its shock wave form to its smooth wave form, and applying standard continuum mechanical cons ervation laws and geometrical compatibility, we prove for, arbitrary m edia that a shock wave which propagates without rotating under steady- state conditions is thermodynamically identical to a suitably-chosen s teadily propagating smooth wave (and that this is not so in general fo r nonsteady shocks). This legitimizes the derivation of restrictions o n steady-state shock waves by the analysis of suitably-chosen steady s mooth waves in purely mechanical material models. Doing so for a broad class of rate-independent elastic-plastic materials rigorously corrob orates several recently-published shuck restrictions whose derivations involved some (now validated) heuristic arguments, and substantially generalizes the material class for which these restrictions apply. Thu s, e.g. within small-displacement-gradient theory, stress jumps are ru led out across steadily propagating shock waves in quasi static deform ations of any nonsoftening material satisfying plastic normality and p ositive-definiteness of the elastic modulus tensor (removing the previ ous limitation of this result to materials that satisfy the global max imum plastic work inequality and whose current yield locus always inco rporates all prior yield loci). We also confirm that steady-state shoc k waves in dynamic anti-plane strain or plane strain deformations cann ot exist except at elastic wave speeds for nonhardening materials in t he same broad constitutive class unless the yield surface contains a l inear segment. Application of these results to steady-state dynamic su bsonic plane strain crack growth in elastic-ideally plastic Prandtl-Re uss-Mises material proves that this problem's solution must be shock-f ree. This implies that certain solutions containing strong discontinui ty surfaces, obtained in a recently-published numerical finite element study of this dynamic I:rack growth problem, are not physically reali zable. The conclusion is that either a more robust numerical procedure is necessary which incorporates the thermodynamics-mandated shock res trictions derived here, or that steady-state subsonic dynamic plane-st rain elastic-plastic crack growth is not possible in this material mod el (and potentially not in nature for materials exhibiting plastic nor mality, purely nonlinear yield surfaces and no hardening). (C) 1998 Pu blished by Elsevier Science Ltd. All rights reserved.