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This monograph covers the material instability known as adiabatic shear banding which often occurs in a plastically deforming material as it undergoes rapid shearing. This book surveys these exciting developments at the frontier of mathematics and presents many new results. 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. Divided into three parts, the book first reviews the physical phenomena and the standard methods of testing and characterization. It then establishes a general theory of isotropic plasticity with finite deformations as a setting for the simpler, but still nonlinear and highly coupled, equations of adiabatic shearing and the idealizations that are necessary to establish them. The main body of the book examines a series of one-dimensional problems of increasing complexity.Read more
- Equations are established within the setting of finite deformation plasticity
- Summarizes results in two dimensional experiments and analyses
- Establishes the foundations from which shear mechanics may grow to take its place as a major companion to fracture mechanics
Reviews & endorsements
"This book is written carefully and it is readable by non-experts, in spite of the difficulty of the subject. It is complimented by ample bibliographical references, and by two chapters on experiments. Particularly useful are the concluding remarks at the end of each chapter." AMS Mathmatical Reviews, Gianpietro Del Piero
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- Date Published: July 2002
- format: Hardback
- isbn: 9780521631952
- length: 260 pages
- dimensions: 229 x 152 x 19 mm
- weight: 0.55kg
- contains: 105 b/w illus.
- availability: Available
Table of Contents
1. Introduction: Qualitative description and one dimensional experiments
2. Balance laws and nonlinear elasticity: a brief summary
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.
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