Stress Waves in Non-Elastic Solids - 1st Edition - ISBN: 9780080212944, 9781483153933

Stress Waves in Non-Elastic Solids

1st Edition

Authors: W. K. Nowacki
eBook ISBN: 9781483153933
Imprint: Pergamon
Published Date: 1st January 1978
Page Count: 258
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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.

Table of Contents



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


Name Index

Subject Index


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About the Author

W. K. Nowacki

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