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Geometric continuum mechanics

Epstein, Marcelo.

Geometric continuum mechanics

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

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. 17..

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$q(electronic bk.)

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

190274
Continuum mechanics.

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

Dewey Class. No.: 531.7

Geometric continuum mechanics
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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.
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