List of Figures
List of Tables
Preface
CHAPTER 1 General Problems in Solid Mechanics and Nonlinearity
1.1 Introduction
1.2 Small deformation solid mechanics problems
1.2.1 Strong form of equation： Indicial notation
1.2.2 Matrix notation
1.2.3 Two—dimensionalproblems
1.3 Variational forms for nonlinear elasticity
1.4 Weak forms of governing equations
1.4.1 Weak form for equilibrium equation
1.5 Concluding remarks
CHAPTER 2 Galerkin Method of Approximation： Irreducible and Mixed Forms
2.1 Introduction
2.2 Finite element approximation： Galerkin method
2.2.1 Displacement approximation
2.2.2 Derivatives
2.2.3 Strain—displacement equations
2.2.4 Weak form
2.2.5 Irreducible displacement method
2.3 Numericalintegration： Quadrature
2.3.1 Volume integrals.
2.3.2 Surface integrals
2.4 Nonlinear transient and steady—state problems
2.4.1 Explicit Newmark method
2.4.2 Implicit Newmark method
2.4.3 Generalized midpoint implicit form
2.5 Boundary conditions： Nonlinear problems
2.5.1 Displacement condition
2.5.2 Traction condition
2.5.3 Mixed displacemen／traction condition
2.6 Mixed orirreducible forms
2.6.1 Deviatoric and mean stress and strain components
2.6.2 A three—field nuxed method for general constitutive models
2.6.3 Local approximation of p and o
2.6.4 Contmuous u—p approximation
2.7 Nonlinear quasi—harmonic field problems
2.8 Typical examples of transient nonlinear calculations
2.8.1 Transient heat conduction
2.8.2 Structuraldynamics
2.8.3 Earthquake response of soil structures
2.9 Concluding remarks
References
CHAPTER 3 Solution of Nonlinear Algebraic Equations
3.1 Introduction
3.2 Iterative techniques
3.2.1 General remarks
3.2.2 Newton’’s method
3.2.3 Modified Newton’’s method
3.2.4 Incremental—secant or quasi—Newton methods
3.2.5 Line search procedures： Acceleration of convergence
3.2.6 ”Softening” behavior and displacement control
3.2.7 Convergencec riteria
3.3 General remarks： Incremental and rate methods
References
CHAPTER 4 Inelastic and Nonlinear Materials
4.1 Introduction
4.2 Tensor to matrix representation
4.3 Viscoelasticity： History dependence of deformation
4.3.1 Linear models for viscoelasticity
4.3.2 Isotropic models
4.3.3 Solution by analogies
4.4 Classical time—independent plasticity theory
4.4.1 Yield functions
4.4.2 Flow rule （normality principle）
4.4.3 Hardening／softening rules
4.4.4 Plastic stress—strain relations
4.5 Computation of stressincrements
4.5.1 Explicit methods
4.5.2 Implicit methods： Retum map algorithm
4.6 Isotropic plasticity models
4.6.1 Isotropic yield surfaces
4.6.2 J2 model with isotropic and kinematic hardening （Prandtl—Reuss equations）
4.6.3 Plane stress
4.7 Generalized plasticity
4.7.1 Nonassociative case： Frictional materials
4.7.2 Associative case： J2 generalized plasticity
4.8 Some examples of plastic computation
4.8.1 Perforated plate： Plane stress solutions
4.8.2 Perforated plate： Plane strain solutions
4.8.3 Steel pressure vessel
4.9 Basic formulation of creep problems
4.9.1 Fully explicit solutions
4，10 Viscoplasticity：A generalization
4.10.1 General remarks
4.10.2 Implicitsolution
4.10.3 Creep of metals
4.10.4 Soilmechanics applications
4.11 Some special problems of brittle materials
4.11.1 The no—tension material
4.11.2 ”Laminar” material and joint elements
4.12 Nonuniqueness and localization in elasto—plastic deformations
4，13 Nonlinear quasi—harmonic field problems
4.14 Concluding remarks
References
CHAPTER 5 Geometrically Nonlinear Problems： Finite Deformation
5.1 Introduction
5.2 Governing equations
5.2.1 Kinematics and deformation
5.2.2 Stress and traction for reference and deformed states
5.2.3 Equilibrium equations
5.2.4 Boundary conditions
5.2.5 Initial conditions
5.2.6 Constitutive equations： Hyperelastic material
5.3 Variational description for finite deformation
5.3.1 Reference configuration formulation
5.3.2 First Piola—Kirchhoff formulation
5.3.3 Current configuration formulation
5.4 Two—dimensional forms
5.4.1 Plane strain
5.4.2 Plane stress
5.4.3 Axisymmetric with torsion
5.5 A three—field， mixed finite deformation formulation
5.5.1 Finite element equations： Matrix notation
5.6 Forces dependent on deformation： Pressure loads
5.7 Concluding remarks
References
CHAPTER 6 Material Constitution for Finite Deformation
6.1 Introduction
6.2 Isotropic elasticity
6.2.1 Isotropic elasticity： Formulation in invariants
6.2.2 Isotropic elasticity：Formulationin modified invariants
6.2.3 Isotropic elasticity： Formulation in principal stretches
6.2.4 Plane stress applications
6.3 Isotropic viscoelasticity
6.4 Plasticity models
6.5 Incrementalformulations
6.6 Rate constitutive models
6.7 Numerical examples
6.7.1 Necking of circular bar
6.7.2 Adaptive refinement and localization （slip—line） capture
6.8 Concluding remarks
References
……
CHAPTER 7 Material Constitution Using Representative Volume Elements
CHAPTER 8 Treatment of Constraints： Contact and Tied Interfaces
CHAPTER 9 Pseudo—Rigid and Rigid—Flexible Bodies
CHAPTER 10 Background Mathematics and Linear Shell Theory
CHAPTER 11 Differential Geometry and Calculus on Manifolds
CHAPTER 12 Geometrically Nonlinear Problems in Continuum Mechanics
CHAPTER 13 A Nonlinear Geometrically Exact Rod Model
CHAPTER 14 A Nonlinear Geometrically Exact Shell Model
CHAPTER 15 Computer Procedures for Finite Element Analysis
APPENDIX A Isoparametric Finite Element Approximations
APPENDIX B Invariants of Second—Order Tensors
Author Index
Subject Index
