Geometric Continuum Mechanics

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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.

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ReiheAdvances in Mechanics and Mathematics
ISBN 9783030426859
Sprache Englisch
Ausgabe 1st ed. 2020
Erscheinungsdatum 14.05.2021
Umfang 416 Seiten
Genre Mathematik/Geometrie
Format Taschenbuch
Verlag Springer International Publishing
Herausgegeben von Reuven Segev, Marcelo Epstein
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