Geometric Continuum Mechanics

Reuven Segev, Marcelo Epstein (Herausgeber)

Buch | Softcover

VII, 416 Seiten

2021 | 1st ed. 2020
Springer International Publishing (Verlag)
978-3-030-42685-9 (ISBN)

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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.

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.

Erscheinungsdatum	15.05.2021
Reihe/Serie	Advances in Continuum Mechanics
Reihe/Serie	Advances in Mechanics and Mathematics
Zusatzinfo	VII, 416 p. 75 illus., 28 illus. in color.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	652 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
Schlagworte	Analysis of Homogeneity of Material Bodies • Continuum Mechanics • de Rham Currents • de Rham differential • Differential Geometry • Force and Stress Theory • Geometric Continuum Mechanics • Geometry and Mechanics • Geometry of Defects and Dislocations • Groupoids • Manifolds of Mappings • Stress functions
ISBN-10	3-030-42685-8 / 3030426858
ISBN-13	978-3-030-42685-9 / 9783030426859
Zustand	Neuware