Overview
- Explores the mathematical foundations of continuum mechanics with a particular focus on geometric methods
- Introduces applications of global analysis, algebraic topology, algebroids, groupoids, and geometric measure theory to continuum mechanics
- Includes chapters written by authors who are experts in their respective areas, providing important insights from recent research
Part of the book series: Advances in Mechanics and Mathematics (AMMA, volume 43)
Part of the book sub series: Advances in Continuum Mechanics (ACM)
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Table of contents (10 chapters)
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Front Matter
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Kinematics, Forces and Stress Theory
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Front Matter
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Defects, Uniformity and Homogeneity
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Front Matter
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Keywords
About this book
- 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.
Editors and Affiliations
Bibliographic Information
Book Title: Geometric Continuum Mechanics
Editors: Reuven Segev, Marcelo Epstein
Series Title: Advances in Mechanics and Mathematics
DOI: https://doi.org/10.1007/978-3-030-42683-5
Publisher: Birkhäuser Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2020
Hardcover ISBN: 978-3-030-42682-8Published: 14 May 2020
Softcover ISBN: 978-3-030-42685-9Published: 14 May 2021
eBook ISBN: 978-3-030-42683-5Published: 13 May 2020
Series ISSN: 1571-8689
Series E-ISSN: 1876-9896
Edition Number: 1
Number of Pages: VII, 416
Number of Illustrations: 47 b/w illustrations, 28 illustrations in colour
Topics: Differential Geometry, Global Analysis and Analysis on Manifolds, Theoretical and Applied Mechanics, Classical and Continuum Physics, Mathematical Applications in the Physical Sciences