Geometrical Foundations of Continuum Mechanics: An Application to First- and Sec

Description: Geometrical Foundations of Continuum Mechanics by Paul Steinmann Geometrical Foundations of Continuum Mechanics FORMAT Paperback LANGUAGE English CONDITION Brand New Publisher Description This book illustrates the deep roots of the geometrically nonlinear kinematics ofgeneralized continuum mechanics in differential geometry. Besides applications to first-order elasticity and elasto-plasticity an appreciation thereof is particularly illuminatingfor generalized models of continuum mechanics such as second-order (gradient-type)elasticity and elasto-plasticity. After a motivation that arises from considering geometrically linear first- and second-order crystal plasticity in Part I several concepts from differential geometry, relevantfor what follows, such as connection, parallel transport, torsion, curvature, and metricfor holonomic and anholonomic coordinate transformations are reiterated in Part II.Then, in Part III, the kinematics of geometrically nonlinear continuum mechanicsare considered. There various concepts of differential geometry, in particular aspectsrelated to compatibility, are generically applied to the kinematics of first- and second-order geometrically nonlinear continuum mechanics. Together with the discussion onthe integrability conditions for the distortions and double-distortions, the conceptsof dislocation, disclination and point-defect density tensors are introduced. Forconcreteness, after touching on nonlinear first- and second-order elasticity, a detaileddiscussion of the kinematics of (multiplicative) first- and second-order elasto-plasticityis given. The discussion naturally culminates in a comprehensive set of different typesof dislocation, disclination and point-defect density tensors. It is argued, that thesecan potentially be used to model densities of geometrically necessary defects and theaccompanying hardening in crystalline materials. Eventually Part IV summarizes theabove findings on integrability whereby distinction is made between the straightforwardconditions for the distortion and the double-distortion being integrable and the moreinvolved conditions for the strain (metric) and the double-strain (connection) beingintegrable. The book addresses readers with an interest in continuum modelling of solids fromengineering and the sciences alike, whereby a sound knowledge of tensor calculus andcontinuum mechanics is required as a prerequisite. Back Cover This book illustrates the deep roots of the geometrically nonlinear kinematics of generalized continuum mechanics in differential geometry. Besides applications to first- order elasticity and elasto-plasticity an appreciation thereof is particularly illuminating for generalized models of continuum mechanics such as second-order (gradient-type) elasticity and elasto-plasticity. After a motivation that arises from considering geometrically linear first- and second- order crystal plasticity in Part I several concepts from differential geometry, relevant for what follows, such as connection, parallel transport, torsion, curvature, and metric for holonomic and anholonomic coordinate transformations are reiterated in Part II. Then, in Part III, the kinematics of geometrically nonlinear continuum mechanics are considered. There various concepts of differential geometry, in particular aspects related to compatibility, are generically applied to the kinematics of first- and second- order geometrically nonlinear continuum mechanics. Together with the discussion on the integrability conditions for the distortions and double-distortions, the concepts of dislocation, disclination and point-defect density tensors are introduced. For concreteness, after touching on nonlinear fir st- and second-order elasticity, a detailed discussion of the kinematics of (multiplicative) first- and second-order elasto-plasticity is given. The discussion naturally culminates in a comprehensive set of different types of dislocation, disclination and point-defect density tensors. It is argued, that these can potentially be used to model densities of geometrically necessary defects and the accompanying hardening in crystalline materials. Eventually Part IV summarizes the above findings on integrability whereby distinction is made between the straightforward conditions for the distortion and the double-distortion being integrable and the more involved conditions for the strain (metric) and the double-strain (connection) being integrable. The book addresses readers with an interest in continuum modelling of solids from engineering and the sciences alike, whereby a sound knowledge of tensor calculus and continuum mechanics is required as a prerequisite. Table of Contents Part I Prologue.- Part II Differential Geometry.- Part III Nonlinear Continuum Mechanics.- Part IV Epilogue. Review "This new, comprehensive book by P. Steinmann consists of three main parts. … This book is of very high rigor, scope, and quality, written by an expert in the field, and is thus strongly recommended as a reference for scholars and advanced graduate students. It could also possibly serve as a textbook or supplementary reference for graduate or professional level course(s)." (John D. Clayton, Mathematical Reviews, August, 2015) Review Quote "This new, comprehensive book by P. Steinmann consists of three main parts. ... This book is of very high rigor, scope, and quality, written by an expert in the field, and is thus strongly recommended as a reference for scholars and advanced graduate students. It could also possibly serve as a textbook or supplementary reference for graduate or professional level course(s)." (John D. Clayton, Mathematical Reviews, August, 2015) Feature Comprehensive presentation of the main concepts of differential geometry Presents applications of differential geometry concepts to nonlinear continuum mechanics Written by a leading expert in the field Details ISBN3662464594 Author Paul Steinmann Publisher Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Series Lecture Notes in Applied Mathematics and Mechanics Year 2015 ISBN-10 3662464594 ISBN-13 9783662464595 Format Paperback Imprint Springer-Verlag Berlin and Heidelberg GmbH & Co. K Subtitle An Application to First- and Second-Order Elasticity and Elasto-Plasticity Place of Publication Berlin Country of Publication Germany DEWEY 516.36 Short Title GEOMETRICAL FOUNDATIONS OF CON Language English Media Book Edition 2015th Pages 517 Illustrations 59 Illustrations, black and white; XXIV, 517 p. 59 illus. DOI 10.1007/978-3-662-46460-1 Series Number 2 Publication Date 2015-04-07 Edited by Kozo Kuchitsu Birth 1974 Affiliation Massachusetts Institute of Technology Position journalist Qualifications S. J. Edition Description 2015 ed. Audience Professional & Vocational We've got this At The Nile, if you're looking for it, we've got it. With fast shipping, low prices, friendly service and well over a million items - you're bound to find what you want, at a price you'll love! TheNile_Item_ID:96264076;

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