Continuum Mechanics and Linear Elasticity

1. Front Matter

   Pages i-xv

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2. Elements of Continuum Mechanics

   1. Front Matter

      Pages 1-1

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   2. Vector, Tensors, and Related Matters

      • Ciprian D. Coman

      Pages 3-120

   3. Kinematics

      • Ciprian D. Coman

      Pages 121-160

   4. Balance Laws

      • Ciprian D. Coman

      Pages 161-196

   5. Constitutive Relationships

      • Ciprian D. Coman

      Pages 197-240

3. Topics in Linear Elasticity

   1. Front Matter

      Pages 241-241

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   2. Linear Elasticity: General Considerations and Boundary-Value Problems

      • Ciprian D. Coman

      Pages 243-280

   3. Compatibility of the Infinitesimal Deformation Tensor

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      Pages 281-318

   4. Torsion

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      Pages 319-370

   5. Two-Dimensional Approximations

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      Pages 371-418

   6. Special Two-Dimensional Problems: Unbounded Domains

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      Pages 419-458

4. Back Matter

   Pages 459-519

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This is an intermediate book for beginning postgraduate students and junior researchers, and offers up-to-date content on both continuum mechanics and elasticity. The material is self-contained and should provide readers sufficient working knowledge in both areas. Though the focus is primarily on vector and tensor calculus (the so-called coordinate-free approach), the more traditional index notation is used whenever it is deemed more sensible.


With the increasing demand for continuum modeling in such diverse areas as mathematical biology and geology, it is imperative to have various approaches to continuum mechanics and elasticity. This book presents these subjects from an applied mathematics perspective. In particular, it extensively uses linear algebra and vector calculus to develop the fundamentals of both subjects in a way that requires minimal use of coordinates (so that beginning graduate students and junior researchers come to appreciate the power of the tensor notation). 

• Boundary-Value Problems
• Continuum Mechanics
• Linear Elasticity
• Tensor Analysis
• Vector Calculus

“My opinion about the book is really positive. … I advise everybody interested in teaching linear elasticity to have a look at it.” (Giuseppe Saccomandi, Mathematical Reviews, June, 2020)

• School of Computing and Engineering, University of Huddersfield, Huddersfield, UK

  Ciprian D. Coman

Ciprian D. Coman is currently a Senior Lecturer at the School of Computing and Engineering at the University of Huddersfield in the UK. A seasoned applied mathematician with over two decades of professional experience, Dr. Coman has held academic positions at various universities in the UK (Leicester, Glasgow, Nottingham), as well as in several industrial organisations (Institute of Solid Mechanics of the Romanian Academy, Schlumberger Ltd, and National Physical Laboratory/UK). His main research interests are in the areas of theoretical and applied mechanics, with a special focus on mathematical modelling involving differential equations and singular perturbation techniques, elastic stability problems, and the micromechanics of particulate solids. He has published more than 50 peer-reviewed journal articles and has co-authored over 25 technical reports.

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