Elasticity and Plasticity of Large Deformations

1. Front Matter

   Pages I-2

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2. Mathematical Preparation

   • Albrecht Bertram

   Pages 3-90

3. Kinematics

   • Albrecht Bertram

   Pages 91-120

4. Balance Laws

   • Albrecht Bertram

   Pages 121-152

5. The Principles of Material Theory

   • Albrecht Bertram

   Pages 153-165

6. Internal Constraints

   • Albrecht Bertram

   Pages 167-175

7. Elasticity

   • Albrecht Bertram

   Pages 177-207

8. Hyperelasticity

   • Albrecht Bertram

   Pages 209-227

9. Solutions

   • Albrecht Bertram

   Pages 229-247

10. Inelasticity

    • Albrecht Bertram

    Pages 249-252

11. Plasticity

    • Albrecht Bertram

    Pages 253-315

12. Back Matter

    Pages 317-339

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This book is based on the lecture notes of courses given by the author over the last decade at the Otto-von-Guericke University of Magdeburg and the Technical University of Berlin. Since the author is concerned with researching material t- ory and, in particular, elasto-plasticity, these courses were intended to bring the students close to the frontiers of today’s knowledge in this particular field, an opportunity now offered also to the reader. The reader should be familiar with vectors and matrices, and with the basics of calculus and analysis. Concerning mechanics, the book starts right from the - ginning without assuming much knowledge of the subject. Hence, the text should be generally comprehensible to all engineers, physicists, mathematicians, and others. At the beginning of each new section, a brief Comment on the Literature c- tains recommendations for further reading. Throughout the text we quote only the important contributions to the subject matter. We are far from being complete or exhaustive in our references, and we apologise to any colleagues not mentioned in spite of their important contributions to the particular items. It is intended to indicate any corrections to this text on our website http://www.uni-magdeburg.de/ifme/l-festigkeit/elastoplasti.html along with remarks from the readers, who are encouraged to send their frank cri- cisms, comments and suggestions to bertram@mb.uni-magdeburg.de. All the author’s royalties from this issue will be donated to charitable organi- tions like Terres des Hommes.

• continuum mechanics
• deformation
• large (finite) deformations
• material theory
• mechanics
• non-linear continuum mechanics
• plasticity

From the reviews:

"The book is divided in four parts of similar importance, 80 pages for each of the first three respectively devoted to the mathematical background, continuum mechanics in general and elasticity, while the remaining 60 pages deal with the central subject, plasticity. … As a conclusion this book will be appreciated by two different types of readers: somebody looking for an introduction to modern continuum mechanics for solid materials … . More advanced readers will be interested by an original vision of plasticity … ." (Technische Mechanik, Vol. 27 (2), 2007)

"This is a textbook containing some modern topics in the field of nonlinear description of solid continua. … It contains the mathematical tools needed in the domain, the basic elements of mechanics of continua, as well as the most important models in the field of solid continua, namely elasticity and plasticity. … This book is useful to students and researchers in the area of solid mechanics." (Olivian Simionescu, Zentralblatt MATH, Vol. 1154, 2009)

• Otto-von-Guericke-Univ. Inst. Mechanik, Germany

  Albrecht Bertram

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