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.

Contenu

Preface
Introduction
Chapter I. Fundamental Equations of the Dynamics of Inelastic Media

1. Dynamical Properties of Materials
   1.1. Dynamical Properties of Metals
   1.2. Dynamical Properties of Soils
2. Basic Theories of Plasticity
   2.1. Strain Theory of Plasticity
   2.2. Bilinear Theory
   2.3. Theory of Plastic Flow
3. Strain Rate Sensitive Plastic Media
   3.1. Elastic/Viscoplastic Medium
   3.2. Elastic/Visco-Ideally-Plastic Media
   3.3. Elastic/Viscoplastic Medium with Temperature Dependent Properties
4. Soil Dynamics Equations
   4.1. Grigorian's Equations
   4.2. Elastic/Visco-Ideally-Plastic Soils
   4.3. Rigid Unloading
5. Equations of Motion and Continuity
   Chapter II. Waves, Continuity Conditions, Mathematical Fundamentals
6. Discontinuity Fronts, Definitions
7. Dynamic Continuity Conditions across Discontinuity Fronts
8. Conditions of Kinematic Continuity across Discontinuity Fronts
9. Mathematical Methods Applied in Problems of Plastic Wave Propagation
   9.1. Systems of Quasi-Linear Partial Differential Equations of the First Order with Two Independent Variables x and t
   9.2. Characteristic Curves and Characteristic Equations
   9.3. Initial and Boundary Value Problems for Quasi-Linear Systems of Two Hyperbolic Differential Equations of the First Order with Two Independent Variables
   Chapter III. One-Dimensional Plane Waves
10. Propagation of a Plane, Longitudinal Wave of Loading in a Semi-Infinite, Homogeneous, Elastic-Plastic Bar
11. Plane Wave of Unloading in a Homogeneous Elastic-Plastic Medium
12. Reflection of an Unloading Plane Wave from an Obstacle in an Elastic-Plastic Medium
13. Propagation of Plane Shock Waves
14. Propagation of Plane Stress Waves in an Elastic-Plastic Medium with Rigid Unloading
15. Propagation of Plane, Longitudinal Waves in an Elastic/Viscoplastic Medium
    Chapter IV. Spherical and Cylindrical Waves
16. Formulation of Problems
    16.1. Spherical Waves
    16.2. Cylindrical Radial Waves
    16.3. Cylindrical Shear Waves
17. Spherical Waves in an Elastic-Plastic Medium with Elastic Unloading
18. Spherical Shock Waves in a Homogeneous Elastic-Plastic Medium
19. Propagation of a Spherical Unloading Wave in an Elastic-Plastic Medium with Rigid Unloading Behavior
20. Spherical Waves and Radial Cylindrical Waves in a Homogeneous Elastic/Viscoplastic Medium
21. Cylindrical Shear Waves
    Chapter V. Plastic Longitudinal-Transverse Waves
22. Simple Waves in an Elastic-Plastic Half-Space
23. Plane Longitudinal-Transverse Waves in an Isotropic, Elastic/Viscoplastic Space
    23.1. Waves of Weak Discontinuity
    23.2. Waves of Strong Discontinuity
    23.3. Analysis of Numerical Results
24. Longitudinal-Transverse Waves in a Non-Homogeneous Elastic/Viscoplastic Medium
    24.1. Plane Waves
    24.2. Radial Cylindrical Waves
25. Stress Waves in Beams
26. Stress Waves in Plates
27. Propagation of Plane, Two-Dimensional Stress Waves
    Chapter VI. Thermal Stress Waves
28. Solution of the Differential Equations of the Theory of Thermal Stresses
29. Thermal Shock on the Boundary of an Elastic/Viscoplastic Half-Space
30. Thermal Shock on the Boundary of a Spherical Cavity in an Elastic/Viscoplastic Space
    Bibliography
    Name Index
    Subject Index