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Geometric continuum mechanics

Epstein, Marcelo.

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Geometric continuum mechanics

Record Type:	Electronic resources : Monograph/item
Title/Author:	Geometric continuum mechanics/ edited by Reuven Segev, Marcelo Epstein.
other author:	Epstein, Marcelo.
Published:	Cham :Springer International Publishing : : 2020.,
Description:	vii, 416 p. :ill., digital ;24 cm.
[NT 15003449]:	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.
Contained By:	Springer eBooks
Subject:	Continuum mechanics. -
Online resource:	https://doi.org/10.1007/978-3-030-42683-5
ISBN:	9783030426835

Geometric continuum mechanics
Geometric continuum mechanics[electronic resource] /edited by Reuven Segev, Marcelo Epstein. - Cham :Springer International Publishing :2020. - vii, 416 p. :ill., digital ;24 cm. - Advances in mechanics and mathematics,v.431571-8689 ;. - Advances in mechanics and mathematics ;v.43..

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.

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.

ISBN: 9783030426835

Standard No.: 10.1007/978-3-030-42683-5doiSubjects--Topical Terms:

535472
Continuum mechanics.

LC Class. No.: QA808.2 / .G466 2020

Dewey Class. No.: 531.7

Geometric continuum mechanics
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245 0 0 $a Geometric continuum mechanics $h [electronic resource] / $c edited by Reuven Segev, Marcelo Epstein.
260 $a Cham : $b Springer International Publishing : $b Imprint: Birkhauser, $c 2020.
300 $a vii, 416 p. : $b ill., digital ; $c 24 cm.
490 1 $a Advances in mechanics and mathematics, $x 1571-8689 ; $v v.43
505 0 $a 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.
520 $a 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.
650 0 $a Continuum mechanics. $3 535472
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650 2 4 $a Global Analysis and Analysis on Manifolds. $3 891107
650 2 4 $a Theoretical and Applied Mechanics. $3 896500
650 2 4 $a Classical and Continuum Physics. $3 3218450
650 2 4 $a Mathematical Applications in the Physical Sciences. $3 1566152
700 1 $a Epstein, Marcelo. $3 2072592
700 1 $a Segev, Reuven. $3 3524846
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950 $a Mathematics and Statistics (Springer-11649)