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Introduction to finite strain theory for continuum elasto-plasticity

Author: Koichi Hashiguchi; Yuki Yamakawa
Publisher: Hoboken : Wiley, 2013.
Series: Wiley series in computational mechanics.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
Comprehensive introduction to finite elastoplasticity, addressing various analytical and numerical analyses & including state-of-the-art theories Introduction to Finite Elastoplasticitypresents introductory explanations that can be readily understood by readers with only a basic knowledge of elastoplasticity, showing physical backgrounds of concepts in detail and derivation processes of almost all equations. The  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Hashiguchi, Koichi.
Introduction to finite strain theory for continuum elasto-plasticity.
Hoboken : Wiley, 2013
(DLC) 2012011797
(OCoLC)785870326
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Koichi Hashiguchi; Yuki Yamakawa
ISBN: 9781118437711 1118437713 9781118437735 111843773X 9781118437728 1118437721 1283645432 9781283645430 6613957933 9786613957931
OCLC Number: 812917756
Description: 1 online resource.
Contents: INTRODUCTION TOFINITE STRAIN THEORYFOR CONTINUUMELASTO-PLASTICITY; Contents; Preface; Series Preface; Introduction; 1 Mathematical Preliminaries; 1.1 Basic Symbols and Conventions; 1.2 Definition of Tensor; 1.2.1 Objective Tensor; 1.2.2 Quotient Law; 1.3 Vector Analysis; 1.3.1 Scalar Product; 1.3.2 Vector Product; 1.3.3 Scalar Triple Product; 1.3.4 Vector Triple Product; 1.3.5 Reciprocal Vectors; 1.3.6 Tensor Product; 1.4 Tensor Analysis; 1.4.1 Properties of Second-Order Tensor; 1.4.2 Tensor Components; 1.4.3 Transposed Tensor; 1.4.4 Inverse Tensor; 1.4.5 Orthogonal Tensor. 1.4.6 Tensor Decompositions1.4.7 Axial Vector; 1.4.8 Determinant; 1.4.9 On Solutions of Simultaneous Equation; 1.4.10 Scalar Triple Products with Invariants; 1.4.11 Orthogonal Transformation of Scalar Triple Product; 1.4.12 Pseudo Scalar, Vector and Tensor; 1.5 Tensor Representations; 1.5.1 Tensor Notations; 1.5.2 Tensor Components and Transformation Rule; 1.5.3 Notations of Tensor Operations; 1.5.4 Operational Tensors; 1.5.5 Isotropic Tensors; 1.6 Eigenvalues and Eigenvectors; 1.6.1 Eigenvalues and Eigenvectors of Second-Order Tensors. 1.6.2 Spectral Representation and Elementary Tensor Functions1.6.3 Calculation of Eigenvalues and Eigenvectors; 1.6.4 Eigenvalues and Vectors of Orthogonal Tensor; 1.6.5 Eigenvalues and Vectors of Skew-Symmetric Tensor and Axial Vector; 1.6.6 Cayley-Hamilton Theorem; 1.7 Polar Decomposition; 1.8 Isotropy; 1.8.1 Isotropic Material; 1.8.2 Representation Theorem of Isotropic Tensor-Valued Tensor Function; 1.9 Differential Formulae; 1.9.1 Partial Derivatives; 1.9.2 Directional Derivatives; 1.9.3 Taylor Expansion; 1.9.4 Time Derivatives in Lagrangian and Eulerian Descriptions. 1.9.5 Derivatives of Tensor Field1.9.6 Gauss's Divergence Theorem; 1.9.7 Material-Time Derivative of Volume Integration; 1.10 Variations and Rates of Geometrical Elements; 1.10.1 Variations of Line, Surface and Volume; 1.10.2 Rates of Changes of Surface and Volume; 1.11 Continuity and Smoothness Conditions; 1.11.1 Continuity Condition; 1.11.2 Smoothness Condition; 2 General (Curvilinear) Coordinate System; 2.1 Primary and Reciprocal Base Vectors; 2.2 Metric Tensors; 2.3 Representations of Vectors and Tensors; 2.4 Physical Components of Vectors and Tensors. 2.5 Covariant Derivative of Base Vectors with Christoffel Symbol2.6 Covariant Derivatives of Scalars, Vectors and Tensors; 2.7 Riemann-Christoffel Curvature Tensor; 2.8 Relations of Convected and Cartesian Coordinate Descriptions; 3 Description of Physical Quantities in Convected Coordinate System; 3.1 Necessity for Description in Embedded Coordinate System; 3.2 Embedded Base Vectors; 3.3 Deformation Gradient Tensor; 3.4 Pull-Back and Push-Forward Operations; 4 Strain and Strain Rate Tensors; 4.1 Deformation Tensors; 4.2 Strain Tensors; 4.2.1 Green and Almansi Strain Tensors.
Series Title: Wiley series in computational mechanics.
Responsibility: Koichi Hashiguchi, Yuki Yamakawa.
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Abstract:

This book provides an easy-to-understand introduction to finite elastoplasticity. It addresses various analytical and numerical finite strain analyses, including new theories developed in recent  Read more...

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