8.1 Introduction

Problems of plastic waves were considered by a lot of authors from variety points of view. Some restrictive relations for possible constitutive equations are due to B da [1997]. Problems of plastic waves, problems of perforation etc. were considered; for a review of the subject see Davids [1960], Shewmon and Zackay [1961], Kolsky and Prager [1964], Cristescu [1967], Campbell [1972], Burke and Weiss [1971], Ezra [1973], Rinehart [1975], Cristescu et al. [2003], Zukas [2004] and the papers Backman and Goldsmith [1978], Zhu et al. [1992], Fomin and Kiselev [1997], Cheeseman and Bogetti [2003].

Chernyshov [1966] has shown that the structure of shock waves is practically the same as for gases. A sufficient condition is established by Lee [1975] for uniqueness of the dynamic path of an elastic-plastic body subject to prescribed kinematic boundary conditions on a part of the surface and prescribed time-dependent Lagrangian tractions on the remainder. The problems considered until now are of some importance for civil engineering, mechanical engineering, seismology, military applications, etc. The history of soil history is older than that of theory of plasticity. In the last times the theory of plasticity has developed faster, since the experimental facts are easier than in the soils or rock mechanics. Also it is more difficult to interpret the results of soil and rock mechanics. While the plastic deformation in metallic bodies is studied in more than half a century, the experiments with soils and rock mechanics are done only in the last decades. The...