The Geometrical Language of Continuum Mechanics

This book presents the fundamental concepts of modern differential geometry within the framework of continuum mechanics. It is 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 materialization 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.

Marcelo Epstein is currently a Professor of Mechanical Engineering at the University of Calgary, Canada. His main research has centered around the various aspects of modern continuum mechanics and its applications. A secondary related area of interest is biomechanics. He is a Fellow of the American Academy of Mechanics, recipient of the Cancam prize and University Professor of Rational Mechanics. He is also adjunct Professor in the Faculties of Humanities and Kinesiology at the University of Calgary.