The Physics and Mathematics of Adiabatic Shear Bands

Establishes the mathematical setting within which shear bands may be studied.

T. W. Wright (Author)

9780521631952, Cambridge University Press

Hardback, published 22 July 2002

260 pages, 105 b/w illus.
22.9 x 15.2 x 1.9 cm, 0.55 kg

' … an admirable attempt to set down clearly the results of a research community over a lifetime. As a library reference or a guide to the researcher, it will be extremely valuable.' Contemporary Physics

This book is a research monograph on the material instability known as adiabatic shear banding which often occurs in a plastically deforming material as it undergoes rapid shearing. Plastic deformation generates heat, which eventually softens most materials with continued straining, a process which is usually unstable. In this case the instability results in thin regions of highly deformed material, which are often the sites of further damage and complete failure. The main body of the book examines a series of one-dimensional problems of increasing complexity. In this way a comprehensive and quantitative picture of the complete phenomena is built up. Particular care is taken to use well established asymptotic techniques to find simple, but universal, analytic expressions or scaling laws that encapsulate various aspects of the dynamic formation and the final morphology of shear bands. A fully developed mechanics of shear is just beginning to emerge as a major companion to fracture mechanics, this book may speed the process along.

Preface
1. Introduction: Qualitative description and one dimensional experiments
2. Balance laws and nonlinear elasticity: a brief summary
3. Thermoplasticity
4. Models for thermoviscoplasticity
5. One-dimensional problems, part I: general considerations
6. One-dimensional problems, part II. linearization and growth of perturbations
7. One-dimensional problems, part III: nonlinear solutions
8. Two-dimensional experiments
9. Two-dimensional solutions.

Subject Areas: Applied mathematics [PBW]