Geometric continuum mechanics
by Epstein, M., (Marcelo) Segev, Reuven
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 def…
Read More ↓Title Statements
- Full title :Geometric continuum mechanics / Reuven Segev, Marcelo Epstein, editors.
Summary
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.
Read More ↓Edition Statements
- Publication Date:2020
Publication Statements
- Publisher(s):Birkhäuser
- Place of Publication:Cham, Switzerland
- Language:eng
- Publication Date:2020
Notes
"ISSN 1876-9896 (electronic)."--Title page verso.
"ISSN 2524-4647 (electronic)."--Title page verso.
The Physical Object
- Description:vi, 416 pages : : illustrations (black and white, and colour) ; : 25 cm.
Edition Identifiers
- ISBN:9783030426828, 3030426823
- oclc:on1202867394
- LC Classification:QA641-670
- Dewey Decimal:516.36
Table of Contents
Part I: Kinematics, Forces, and Stress Theory -- Manifolds of Mappings for Continuum Mechanics -- Notes on Global Stress and Hyper-Stress Theories -- Applications of Algebraic Topology in Elasticity -- De Donder Construction for Higher Jets -- Part II: Defects, Uniformity, and Homogeneity -- Regular and Singular Dislocations -- Homogenization of Edge-Dislocations as a Weak Limit of de-Rham Currents -- A Kinematics of Defects in Solid Crystals -- Limits of Distributed Dislocations in Geometric and Constitutive Paradigms -- On the Homogeneity of Non-Uniform Material Bodies.
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