This contributed volume explores the applications of various topics
in modern differential geometry to the foundations of continuum
mechanics. In particular, the contributors use notions from areas
such as global analysis, algebraic topology, and geometric measure
theory. Chapter authors are experts in their respective areas, and
provide important insights from the most recent research. Organized
into two parts, the book first covers kinematics, forces, and
stress theory, and then addresses defects, uniformity, and
homogeneity. Specific topics covered include: Global stress and
hyper-stress theories Applications of de Rham currents to singular
dislocations Manifolds of mappings for continuum mechanics
Kinematics of defects in solid crystals Geometric Continuum
Mechanics will appeal to graduate students and researchers in the
fields of mechanics, physics, and engineering who seek a more
rigorous mathematical understanding of the area. Mathematicians
interested in applications of analysis and geometry will also find
the topics covered here of interest.
General
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