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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 motiva-
tional 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 materializa-
tion 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 bun-
dles, exterior derivatives, Lie derivatives, and Lie groups are illustrated
in terms of their mechanical interpretations. The third part includes
the theory of fibre 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 revolves
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 Can-
cam prize, and University Professor of Rational Mechanics. He is also
adjunct Professor in the Faculties of Humanities and Kinesiology at the
University of Calgary.
The Geometrical Language of
Continuum Mechanics
Marcelo Epstein
University of Calgary
CAMBRIDGE UNIVERSITY PRESS
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