The Geometrical Language of Continuum Mechanics


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.


 Reviews:

The Geometrical Language of Continuum Mechanics brings a fresh quality to this subject by blending differential topology with tensor analysis....the author is commended for making the materials accessible to the reader by including in the first chapter excellent introductory background topics, which are essential for unraveling interconnected abstractions in subsequent chapters." R.N Laoulache, University of Massachusetts Dartmouth

"...the author is commended for making the materials accessible to the reader by including in the first chapter excellent introductory background topics, which are essential for unraveling interconnected abstractions in subsequent chapters. ...Recommended." CHOICE

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