Nonlinear Continuum Mechanics and Large Inelastic Deformations by Yuriy I. Dimit

Description: Nonlinear Continuum Mechanics and Large Inelastic Deformations by Yuriy I. Dimitrienko The book provides a rigorous axiomatic approach to continuum mechanics under large deformation. - the book presents the theory of co-rotational derivatives, dynamic deformation compatibility equations, and the principles of material indifference and symmetry, all in systematized form. FORMAT Hardcover LANGUAGE English CONDITION Brand New Publisher Description The book provides a rigorous axiomatic approach to continuum mechanics under large deformation. In addition to the classical nonlinear continuum mechanics – kinematics, fundamental laws, the theory of functions having jump discontinuities across singular surfaces, etc. - the book presents the theory of co-rotational derivatives, dynamic deformation compatibility equations, and the principles of material indifference and symmetry, all in systematized form.The focus of the book is a new approach to the formulation of the constitutive equations for elastic and inelastic continua under large deformation. This new approach is based on using energetic and quasi-energetic couples of stress and deformation tensors. This approach leads to a unified treatment of large, anisotropic elastic, viscoelastic, and plastic deformations.The author analyses classical problems, including some involving nonlinear wave propagation, using different models for continua under large deformation, and shows how different models lead to different results. The analysis is accompanied by experimental data and detailed numerical results for rubber, the ground, alloys, etc.The book will be an invaluable text for graduate students and researchers in solid mechanics, mechanical engineering, applied mathematics, physics and crystallography, as also for scientists developing advanced materials. Notes Rgorous axiomatic approach to continuum mechanicsNew approach to the formulation of constitutive equations for nonlinear continuaAdvanced models for visco-elastic materials under large deformationAdvanced models for plastic materials under large deformationComparison of experimental data and results computed by different models Back Cover The book provides a rigorous axiomatic approach to continuum mechanics under large deformation. In addition to the classical nonlinear continuum mechanics - kinematics, fundamental laws, the theory of functions having jump discontinuities across singular surfaces, etc. - the book presents the theory of co-rotational derivatives, dynamic deformation compatibility equations, and the principles of material indifference and symmetry, all in systematized form.The focus of the book is a new approach to the formulation of the constitutive equations for elastic and inelastic continua under large deformation. This new approach is based on using energetic and quasi-energetic couples of stress and deformation tensors. This approach leads to a unified treatment of large, anisotropic elastic, viscoelastic, and plastic deformations.The author analyses classical problems, including some involving nonlinear wave propagation, using different models for continua under large deformation, and shows how different models lead to different results. The analysis is accompanied by experimental data and detailed numerical results for rubber, the ground, alloys, etc.The book will be an invaluable text for graduate students and researchers in solid mechanics, mechanical engineering, applied mathematics, physics and crystallography, as also for scientists developing advanced materials. Table of Contents Preface.- Introduction. Fundamental Axioms of Continuum Mechanics .- 1. Kinematics of Continua.- 2. Balance Laws.- 3. Constitutive Equations.- 4. Relations at Singular Surfaces.- 5. Elastic Continua at Large Deformations.- 6. Continua of the Differential Type.- 7. Viscoelastic Continua at Large Deformations.- 8. Plastic Continua at Large Deformations.- References.- Basic Notation .- Subject Index. Review From the reviews:"The present book is a textbook for master and PhD students studying the mathematical continuum mechanics. Based on a strong mathematical framework, the author presents the basics of continuum mechanics and materials theory. … For further studies 60 references are given." (Holm Altenbach, Zeitschrift fÜr Angewandte Mathematik und Mechanik, Vol. 92 (6), 2012) Review Quote From the reviews:The present book is a textbook for master and PhD students studying the mathematical continuum mechanics. Based on a strong mathematical framework, the author presents the basics of continuum mechanics and materials theory. … For further studies 60 references are given. (Holm Altenbach, Zeitschrift fÜr Angewandte Mathematik und Mechanik, Vol. 92 (6), 2012) Feature Rgorous axiomatic approach to continuum mechanicsNew approach to the formulation of constitutive equations for nonlinear continuaAdvanced models for visco-elastic materials under large deformationAdvanced models for plastic materials under large deformationComparison of experimental data and results computed by different models Details ISBN9400700334 Author Yuriy I. Dimitrienko Publisher Springer Year 2010 ISBN-10 9400700334 ISBN-13 9789400700338 Format Hardcover Imprint Springer Place of Publication Dordrecht Country of Publication Netherlands DEWEY 531.382 Short Title NONLINEAR CONTINUUM MECHANICS Language English Media Book Series Number 174 Publication Date 2010-11-11 Illustrations XXIV, 721 p. Pages 721 DOI 10.1007/978-94-007-0034-5 Edition Description 2011 ed. 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