The Geometrical Language of Continuum Mechanics

Epstein presents the fundamental concepts of modern differential geometry within the framework of continuum mechanics. Divided into three parts of roughly equal length, the book opens with a motivational chapter to impress upon the reader that differential geometry is indeed the natural language of continuum mechanics or, better still, that the latter is a prime example of the application and materialisation of the former. In the second part, the fundamental notions of differential geometry are presented with rigor using a writing style that is as informal as possible. Differentiable manifolds, tangent bundles, exterior derivatives, Lie derivatives, and Lie groups are illustrated in terms of their mechanical interpretations. The third part includes the theory of fiber bundles, G-structures, and groupoids, which are applicable to bodies with internal structure and to the description of material inhomogeneity. The abstract notions of differential geometry are thus illuminated by practical and intuitively meaningful engineering applications. 'The book is suitable for graduate students in the field of continuum mechanics who seek an introduction to the fundamentals of modern differential geometry and its applications in theoretical continuum mechanics. It will also be useful to researchers in the field of mechanics who look for overviews of the more specialized topics. The book is written in a very enjoyable and literary style in which the rich and picturesque language sheds light on the mathematics.' Mathematical Reviews 'I warmly recommend this book to all interested in differential geometry and mechanics.' Zentralblatt MATHPart I. Motivation and Background: 1. The case for differential geometry; 2. Vector and affine spaces; 3. Tensor algebras and multivectors; Part II. Differential Geometry: 4. Differentiable manifolds; 5. Lie derivatives, lie groups, lie algebras; 6. Integration and fluxes; Part III. Further Topics: 7. Fibre bundles; 8. Inhomogeneity theory; 9. Connection, curvature, torsion; Appendix A. A primer in continuum mechanics.