Stress Waves in Non-Elastic Solids

Stress Waves in Non-Elastic Solids is a comprehensive presentation of the principles underlying the propagation of stress waves in non-elastic solids, with emphasis on wave problems in the theory of plasticity. This book exposes wave propagation problems for a range of material responses and justifies the hypotheses introduced in specialized theories and the simplifications made in the analysis of particular problems. Both analytical and numerical methods of solving problems are described, and a large number of solutions to specific problems of wave propagation in inelastic solids are given. This book is comprised of six chapters and begins with an overview of the fundamental equations of the dynamics of inelastic media. The dynamical properties of metals and soils are discussed, offering an account of the most representative theories of plasticity and viscoplasticity. The next chapter considers the basic definitions of discontinuity surfaces and the conditions that must to be satisfied across these surfaces. Certain mathematical fundamentals are given, referring to systems of differential equations, quasi-linear and semi-linear, of the first order. Initial and boundary value problems for hyperbolic equations are also formulated. The remaining chapters focus on methods of solving stress wave propagation problems, including one-dimensional plane waves and longitudinal-transverse waves. Wave propagation problems for elastic-plastic and elastic/viscoplastic media are treated in detail, along with the most important problem of shock waves in metals and soils. The last chapter deals with thermal wave propagation problems. This monograph will be a valuable resource for students and practitioners of engineering, physics, and mathematics.