Preface |
Introduction / 1: |
Nonlinear Computational Mechanics / 1.1: |
Simple Examples of Nonlinear Structural Behavior / 1.2: |
Cantilever / 1.2.1: |
Column / 1.2.2: |
Nonlinear Strain Measures / 1.3: |
One-Dimensional Strain Measures / 1.3.1: |
Nonlinear Truss Example / 1.3.2: |
Continuum Strain Measures / 1.3.3: |
Directional Derivative, Linearization and Equation Solution / 1.4: |
Directional Derivative / 1.4.1: |
Linearization and Solution of Nonlinear Algebraic Equations / 1.4.2: |
Mathematical Preliminaries / 2: |
Vector and Tensor Algebra / 2.1: |
Vectors / 2.2.1: |
Second-Order Tensors / 2.2.2: |
Vector and Tensor Invariants / 2.2.3: |
Higher-Order Tensors / 2.2.4: |
Linearization and the Directional Derivative / 2.3: |
One Degree of Freedom / 2.3.1: |
General Solution to a Nonlinear Problem / 2.3.2: |
Properties of the Directional Derivative / 2.3.3: |
Examples of Linearization / 2.3.4: |
Tensor Analysis / 2.4: |
The Gradient and Divergence Operators / 2.4.1: |
Integration Theorems / 2.4.2: |
Analysis of Three-Dimensional Truss Structures / 3: |
Kinematics / 3.1: |
Linearization of Geometrical Descriptors / 3.2.1: |
Internal Forces and Hyperelastic Constitutive Equations / 3.3: |
Nonlinear Equilibrium Equations and the Newton-Raphson Solution / 3.4: |
Equilibrium Equations / 3.4.1: |
Newton-Raphson Procedure / 3.4.2: |
Tangent Elastic Stiffness Matrix / 3.4.3: |
Elasto-Plastic Behavior / 3.5: |
Multiplicative Decomposition of the Stretch / 3.5.1: |
Rate-independent Plasticity / 3.5.2: |
Incremental Kinematics / 3.5.3: |
Time Integration / 3.5.4: |
Stress Update and Return Mapping / 3.5.5: |
Algorithmic Tangent Modulus / 3.5.6: |
Revised Newton-Raphson Procedure / 3.5.7: |
Examples / 3.6: |
Inclined Axial Rod / 3.6.1: |
Trussed Frame / 3.6.2: |
The Motion / 4: |
Material and Spatial Descriptions / 4.3: |
Deformation Gradient / 4.4: |
Strain / 4.5: |
Polar Decomposition / 4.6: |
Volume Change / 4.7: |
Distortional Component of the Deformation Gradient / 4.8: |
Area Change / 4.9: |
Linearized Kinematics / 4.10: |
Linearized Deformation Gradient / 4.10.1: |
Linearized Strain / 4.10.2: |
Linearized Volume Change / 4.10.3: |
Velocity and Material Time Derivatives / 4.11: |
Velocity / 4.11.1: |
Material Time Derivative / 4.11.2: |
Directional Derivative and Time Rates / 4.11.3: |
Velocity Gradient / 4.11.4: |
Rate of Deformation / 4.12: |
Spin Tensor / 4.13: |
Rate of Change of Volume / 4.14: |
Superimposed Rigid Body Motions and Objectivity / 4.15: |
Stress and Equilibrium / 5: |
Cauchy Stress Tensor / 5.1: |
Definition / 5.2.1: |
Stress Objectivity / 5.2.2: |
Equilibrium / 5.3: |
Translational Equilibrium / 5.3.1: |
Rotational Equilibrium / 5.3.2: |
Principle of Virtual Work / 5.4: |
Work Conjugacy and Alternative Stress Representations / 5.5: |
The Kirchhoff Stress Tensor / 5.5.1: |
The First Piola-Kirchhoff Stress Tensor / 5.5.2: |
The Second Piola-Kirchhoff Stress Tensor / 5.5.3: |
Deviatoric and Pressure Components / 5.5.4: |
Stress Rates / 5.6: |
Hyperelasticity / 6: |
Elasticity Tensor / 6.1: |
The Material or Lagrangian Elasticity Tensor / 6.3.1: |
The Spatial or Eulerian Elasticity Tensor / 6.3.2: |
Isotropic Hyperelasticity / 6.4: |
Material Description / 6.4.1: |
Spatial Description / 6.4.2: |
Compressible Neo-Hookean Material / 6.4.3: |
Incompressible and Nearly Incompressible Materials / 6.5: |
Incompressible Elasticity / 6.5.1: |
Incompressible Neo-Hookean Material / 6.5.2: |
Nearly Incompressible Hyperelastic Materials / 6.5.3: |
Isotropic Elasticity in Principal Directions / 6.6: |
Material Elasticity Tensor / 6.6.1: |
Spatial Elasticity Tensor / 6.6.4: |
A Simple Stretch-based Hyperelastic Material / 6.6.5: |
Nearly Incompressible Material in Principal Directions / 6.6.6: |
Plane Strain and Plane Stress Cases / 6.6.7: |
Uniaxial Rod Case / 6.6.8: |
Large Elasto-Plastic Deformations / 7: |
The Multiplicative Decomposition / 7.1: |
Rate Kinematics / 7.3: |
Rate-Independent Plasticity / 7.4: |
Principal Directions / 7.5: |
The Radial Return Mapping / 7.6: |
Two-Dimensional Cases / 7.6.2: |
Linearized Equilibrium Equations / 8: |
Linearization and Newton-Raphson Process / 8.1: |
Lagrangian Linearized Internal Virtual Work / 8.3: |
Eulerian Linearized Internal Virtual Work / 8.4: |
Linearized External Virtual Work / 8.5: |
Body Forces / 8.5.1: |
Surface Forces / 8.5.2: |
Variational Methods and Incompressibility / 8.6: |
Total Potential Energy and Equilibrium / 8.6.1: |
Lagrange Multiplier Approach to Incompressibility / 8.6.2: |
Penalty Methods for Incompressibility / 8.6.3: |
Hu-Washizu Variational Principle for Incompressibility / 8.6.4: |
Mean Dilatation Procedure / 8.6.5: |
Discretization and Solution / 9: |
Discretized Kinematics / 9.1: |
Discretized Equilibrium Equations / 9.3: |
General Derivation / 9.3.1: |
Derivation in Matrix Notation / 9.3.2: |
Discretization of the Linearized Equilibrium Equations / 9.4: |
Constitutive Component: Indicial Form / 9.4.1: |
Constitutive Component: Matrix Form / 9.4.2: |
Initial Stress Component / 9.4.3: |
External Force Component / 9.4.4: |
Tangent Matrix / 9.4.5: |
Mean Dilatation Method for Incompressibility / 9.5: |
Implementation of the Mean Dilatation Method / 9.5.1: |
Newton-Raphson Iteration and Solution Procedure / 9.6: |
Newton-Raphson Solution Algorithm / 9.6.1: |
Line Search Method / 9.6.2: |
Arc-Length Method / 9.6.3: |
Computer Implementation / 10: |
User Instructions / 10.1: |
Output File Description / 10.3: |
Element Types / 10.4: |
Solver Details / 10.5: |
Constitutive Equation Summary / 10.6: |
Program Structure / 10.7: |
Main Routine flagshyp / 10.8: |
Routine elemtk / 10.9: |
Routine radialrtn / 10.10: |
Routine ksigma / 10.11: |
Routine bpress / 10.12: |
Simple Patch Test / 10.13: |
Nonlinear Truss / 10.13.2: |
Strip With a Hole / 10.13.3: |
Plane Strain Nearly Incompressible Strip / 10.13.4: |
Elasto-plastic Cantilever / 10.13.5: |
Appendix: Dictionary of Main Variables / 10.14: |
Bibliography |
Index |
Preface |
Introduction / 1: |
Nonlinear Computational Mechanics / 1.1: |