Format:
Online-Ressource (XV, 421 p. 41 illus, digital)
Edition:
2nd ed. 2013
ISBN:
9781461459408
,
1283910004
,
9781283910002
Series Statement:
Interdisciplinary Applied Mathematics 9
Content:
Preface to the Second Edition -- Preface to the First Edition.-Preliminaries -- Continuum Mechanics and Linearized Elasticity -- Elastoplastic Media -- The Plastic Flow Law in a Convex-Analytic Setting -- Basics of Functional Analysis and Function Spaces -- Variational Equations and Inequalities -- The Primal Variational Problem of Elastoplasticity -- The Dual Variational Problem of Classical Elastoplasticity -- Introduction to Finite Element Analysis -- Approximation of Variational Problems -- Approximations of the Abstract Problem -- Numerical Analysis of the Primal Problem -- References -- Index.-.
Content:
This book focuses on the theoretical aspects of small strain theory of elastoplasticity with hardening assumptions. It provides a comprehensive and unified treatment of the mathematical theory and numerical analysis. It is divided into three parts, with the first part providing a detailed introduction to plasticity, the second part covering the mathematical analysis of the elasticity problem, and the third part devoted to error analysis of various semi-discrete and fully discrete approximations for variational formulations of the elastoplasticity. This revised and expanded edition includes material on single-crystal and strain-gradient plasticity. In addition, the entire book has been revised to make it more accessible to readers who are actively involved in computations but less so in numerical analysis. Reviews of earlier edition: “The authors have written an excellent book which can be recommended for specialists in plasticity who wish to know more about the mathematical theory, as well as those with a background in the mathematical sciences who seek a self-contained account of the mechanics and mathematics of plasticity theory.” (ZAMM, 2002) “In summary, the book represents an impressive comprehensive overview of the mathematical approach to the theory and numerics of plasticity. Scientists as well as lecturers and graduate students will find the book very useful as a reference for research or for preparing courses in this field.” (Technische Mechanik) "The book is professionally written and will be a useful reference to researchers and students interested in mathematical and numerical problems of plasticity. It represents a major contribution in the area of continuum mechanics and numerical analysis." (Math Reviews).
Note:
Description based upon print version of record
,
Plasticity; Preface to the Second Edition; Preface to the First Edition; Contents; Part I Continuum Mechanics and Elastoplasticity Theory; 1 Preliminaries; 1.1 Introduction; 1.2 Some Historical Remarks; 1.3 Notation; 2 Continuum Mechanics and Linearized Elasticity; 2.1 Kinematics; 2.2 Balance of Momentum; Stress; 2.3 Linearly Elastic Materials; 2.4 Isotropic Elasticity; 2.5 A Thermodynamic Framework for Elasticity; 2.6 Initial-Boundary and Boundary Value Problems for Linearized Elasticity; 2.7 Thermodynamics with Internal Variables; 3 Elastoplastic Media
,
3.1 Physical Background and Motivation3.2 Three-Dimensional Elastoplastic Behavior; 3.3 Examples of Yield Criteria; 3.4 Yield Criteria for Dilatant Materials; 3.4.1 Examples; 3.4.2 A further note on non-smooth yield surfaces; 3.5 Hardening Laws; 3.6 Single-crystal Plasticity; 3.7 Strain-gradient Plasticity; 3.7.1 Polycrystalline plasticity; 3.7.2 Gradient single-crystal plasticity; 3.8 Bibliographical Remarks; 4 The Plastic Flow Law in a Convex-Analytic Setting; 4.1 Some Results from Convex Analysis; 4.2 Basic Plastic Flow Relations of Elastoplasticity; 4.3 Strain-gradient Plasticity
,
4.3.1 The Aifantis model4.3.2 Polycrystalline strain-gradient plasticity; 4.3.3 Strain-gradient single-crystal plasticity; Part II The Variational Problems of Elastoplasticity; 5 Basics of Functional Analysis and Function Spaces; 5.1 Results from Functional Analysis; 5.2 Function Spaces; 5.2.1 The Spaces Cm(Ω), Cm(Ω), and Lp(Ω); 5.2.2 Sobolev Spaces; 5.2.3 Spaces of Vector-Valued Functions; 6 Variational Equations and Inequalities; 6.1 Variational Formulation of Elliptic Boundary Value Problems; 6.2 Elliptic Variational Inequalities; 6.3 Parabolic Variational Inequalities
,
6.4 Qualitative Analysis of an Abstract Problem7 The Primal Variational Problem of Elastoplasticity; 7.1 Classical Elastoplasticity with Hardening; 7.1.1 Variational formulation; 7.1.2 Analysis of the problem; 7.2 Classical Single-crystal Plasticity; 7.3 Strain-gradient Plasticity; 7.3.1 The Aifantis model; 7.3.2 The Gurtin model of strain-gradient plasticity; 7.4 Strain-gradient Single-crystal Plasticity; 7.4.1 Weak formulation of the problem; 7.4.2 Well-posedness; 7.5 Stability Analysis; 8 The Dual Variational Problem of Classical Elastoplasticity; 8.1 The Dual Variational Problem
,
8.2 Analysis of the Stress Problem8.3 Analysis of the Dual Problem; 8.4 Rate Form of Stress-Strain Relation; Part III Numerical Analysis of the Variational Problems; 9 Introduction to Finite Element Analysis; 9.1 Basics of the Finite Element Method; 9.2 Affine Families of Finite Elements; 9.3 Local Interpolation Error Estimates; 9.4 Global Interpolation Error Estimates; 10 Approximation of Variational Problems; 10.1 Approximation of Elliptic Variational Equations; 10.2 Numerical Approximation of Elliptic Variational Inequalities; 10.3 Approximation of Parabolic Variational Inequalities
,
11 Approximations of the Abstract Problem
,
Preface to the Second Edition -- Preface to the First Edition.-Preliminaries -- Continuum Mechanics and Linearized Elasticity -- Elastoplastic Media -- The Plastic Flow Law in a Convex-Analytic Setting -- Basics of Functional Analysis and Function Spaces -- Variational Equations and Inequalities -- The Primal Variational Problem of Elastoplasticity -- The Dual Variational Problem of Classical Elastoplasticity -- Introduction to Finite Element Analysis -- Approximation of Variational Problems -- Approximations of the Abstract Problem -- Numerical Analysis of the Primal Problem -- References -- Index -- .
Additional Edition:
ISBN 9781461459392
Additional Edition:
Buchausg. u.d.T. Han, Weimin, 1963 - Plasticity New York : Springer, 2013 ISBN 9781461459392
Additional Edition:
ISBN 1461459397
Additional Edition:
ISBN 9781489995940
Language:
English
Subjects:
Physics
,
Mathematics
Keywords:
Plastizität
;
Numerisches Verfahren
;
Elastoplastizität
;
Plastizität
;
Mathematisches Modell
;
Elastoplastizität
DOI:
10.1007/978-1-4614-5940-8
URL:
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