Analysis of the Propagation of Plane Elastic-Plastic Waves at Finite Strain

The propagation of plane elastic-plastic waves of one-dimensional strain is analyzed. Such waves are generated by the detonation of explosives in contact with the surfaces of plates and by impact of plates and are commonly utilized for measuring material characteristics under high pressures. Only one nonzero displacement component occurs—that normal to the plate surface. The resulting dilatation leads to dominant thermomechanical coupling effects, and these, and influences of finite strain, are included in the analysis. Because plasticity plays a secondary role, a simple rate-independent theory is adequate. Since heat conduction can be neglected because of the high speed of wave propagation, the dynamic equations and the constitutive relations are effectively uncoupled, and the problem reduces to one in the classical Karman-Taylor-Rakhmatulin theory of plastic waves. Appropriate stress-strain relations for inclusion in that theory are developed here for an aluminum alloy. The analysis for shock propagation is also given.