Nonlinear Elastic Waves in Materials

1. Front Matter

   Pages i-xiii

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2. Introduction

   • Jeremiah J. Rushchitsky

   Pages 1-23

3. Preliminary Information About Waves and Materials

   • Jeremiah J. Rushchitsky

   Pages 25-43

4. Elastic Materials

   • Jeremiah J. Rushchitsky

   Pages 45-77

5. The Simplest Linear Waves in Elastic Materials

   • Jeremiah J. Rushchitsky

   Pages 79-119

6. Nonlinear Plane Longitudinal Waves in Elastic Materials (Murnaghan Model, Five-Constant Model)

   • Jeremiah J. Rushchitsky

   Pages 121-173

7. Nonlinear Plane Longitudinal Waves in Elastic Materials (John Model, Two-Constant Model and Signorini Model, Three-Constant Model)

   • Jeremiah J. Rushchitsky

   Pages 175-197

8. Nonlinear Plane Transverse Waves in Elastic Materials (Murnaghan Model, Five-Constant Model)

   • Jeremiah J. Rushchitsky

   Pages 199-211

9. Nonlinear Plane Waves in Hypoelastic Materials

   • Jeremiah J. Rushchitsky

   Pages 213-230

10. Nonlinear Plane Waves in Elastic Mixtures (Elastic Composite Materials)

    • Jeremiah J. Rushchitsky

    Pages 231-302

11. Nonlinear Cylindrical and Torsional Waves in Hyperelastic Materials

    • Jeremiah J. Rushchitsky

    Pages 303-379

12. Nonlinear Rayleigh and Love Surface Waves in Elastic Materials

    • Jeremiah J. Rushchitsky

    Pages 381-428

13. Afterword

    • Jeremiah J. Rushchitsky

    Pages 429-431

14. Back Matter

    Pages 433-440

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The main goal of the book is a coherent treatment of the theory of propagation in materials of nonlinearly elastic waves of displacements, which corresponds to one modern line of development of the nonlinear theory of elastic waves.
The book is divided on five basic parts: the necessary information on waves and materials; the necessary information on nonlinear theory of elasticity and elastic materials; analysis of one-dimensional nonlinear elastic waves of displacement – longitudinal, vertically and horizontally polarized transverse plane nonlinear elastic waves of displacement; analysis of one-dimensional nonlinear elastic waves of displacement – cylindrical and torsional nonlinear elastic waves of displacement; analysis of two-dimensional nonlinear elastic waves of displacement – Rayleigh and Love nonlinear elastic surface waves.
The book is addressed first of all to people working in solid mechanics – from the students at an advanced undergraduate and graduate level to the scientists, professionally interesting in waves. But mechanics is understood in the broad sense, when it includes mechanical and other engineering, material science, applied mathematics and physics and so forth. The genesis of this book can be found in author’s years of research and teaching while a head of department at SP Timoshenko Institute of Mechanics (National Academy of Sciences of Ukraine), a member of Center for Micro and Nanomechanics at Engineering School of University of Aberdeen(Scotland) and a professor at Physical-Mathematical Faculty of National Technical University of Ukraine “KPI”.
The book comprises 11 chapters. Each chapter is complemented by exercises, which can be used for the next development of the theory of nonlinear waves.

• Five-constant Model
• Hypoelastic Materials
• John Model
• Murnaghan Model
• Nonlinear Love Surface Waves
• Nonlinear Rayleigh Surface Waves
• Signorini Model

From the book reviews:

“In this monograph, the author presents the theory of elastic waves in nonlinear elastic materials. The book requires the knowledge of basic mathematics and continuum mechanics, and is aimed at senior undergraduates, postgraduates and researchers working in nonlinear elasticity. … The book will be quite useful to engineers and applied mathematicians as a source of different nonlinear models and constitutive equations for elastic waves.” (Fiazud Din Zaman, zbMATH, Vol. 1302, 2015)

• Department of Rheology, The National Academy of Sciences S.P.Timoshenko Institute of Mechanics, Kyiv, Ukraine

  Jeremiah J. Rushchitsky

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