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Nonlinear Continuum Mechanics for Finite Element Analysis

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ISBN-10: 0521838703

ISBN-13: 9780521838702

Edition: 2nd 2008 (Revised)

Authors: Javier Bonet, Richard D. Wood

List price: $129.00
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The first edition of this successful text considered nonlinear geometrical behavior and nonlinear hyperelastic materials, and the numerics needed to model such phenomena. By presenting both nonlinear continuum analysis and associated finite element techniques in one, Bonet and Wood provide, in the new edition of this successful text, a complete, clear, and unified treatment of these important subjects. New chapters dealing with hyperelastic plastic behavior are included, and the authors have thoroughly updated the FLagSHyP program, freely accessible at
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Book details

List price: $129.00
Edition: 2nd
Copyright year: 2008
Publisher: Cambridge University Press
Publication date: 3/13/2008
Binding: Hardcover
Pages: 340
Size: 7.00" wide x 10.00" long x 0.75" tall
Weight: 1.628
Language: English

Javier Bonet is a Professor of Engineering and the Deputy Head of the School of Engineering at Swansea University, and a visiting professor at the Universitat Politecnica de Catalunya in Spain. He has extensive experience of teaching topics in structural mechanics, including large strain nonlinear solid mechanics, to undergraduate and graduate engineering students. He has been active in research in the area of computational mechanics for over 25 years and has written over 60 papers and over 70 conference contributions on many topics within the subject and given invited, keynote and plenary lectures at numerous international conferences.

Richard D. Wood is an Honorary Research Fellow in the Civil and Computational Engineering Centre at Swansea University. He has over 20 years experience of teaching the course Nonlinear Continuum Mechanics for Finite Element Analysis at Swansea University, which he originally developed at the University of Arizona and also taught at IIT Roorkee, India and the Institute of Structural Engineering at the Technical University in Graz. Dr Wood's academic career has focused on finite element analysis, and he has written over 60 papers in international journals, and many chapter contributions, on topics related to nonlinear finite element analysis.

Nonlinear Computational Mechanics
Simple Examples of Nonlinear Structural Behavior
Nonlinear Strain Measures
One-Dimensional Strain Measures
Nonlinear Truss Example
Continuum Strain Measures
Directional Derivative, Linearization and Equation Solution
Directional Derivative
Linearization and Solution of Nonlinear Algebraic Equations
Mathematical Preliminaries
Vector and Tensor Algebra
Second-Order Tensors
Vector and Tensor Invariants
Higher-Order Tensors
Linearization and the Directional Derivative
One Degree of Freedom
General Solution to a Nonlinear Problem
Properties of the Directional Derivative
Examples of Linearization
Tensor Analysis
The Gradient and Divergence Operators
Integration Theorems
Analysis of Three-Dimensional Truss Structures
Linearization of Geometrical Descriptors
Internal Forces and Hyperelastic Constitutive Equations
Nonlinear Equilibrium Equations and the Newton-Raphson Solution
Equilibrium Equations
Newton-Raphson Procedure
Tangent Elastic Stiffness Matrix
Elasto-Plastic Behavior
Multiplicative Decomposition of the Stretch
Rate-independent Plasticity
Incremental Kinematics
Time Integration
Stress Update and Return Mapping
Algorithmic Tangent Modulus
Revised Newton-Raphson Procedure
Inclined Axial Rod
Trussed Frame
The Motion
Material and Spatial Descriptions
Deformation Gradient
Polar Decomposition
Volume Change
Distortional Component of the Deformation Gradient
Area Change
Linearized Kinematics
Linearized Deformation Gradient
Linearized Strain
Linearized Volume Change
Velocity and Material Time Derivatives
Material Time Derivative
Directional Derivative and Time Rates
Velocity Gradient
Rate of Deformation
Spin Tensor
Rate of Change of Volume
Superimposed Rigid Body Motions and Objectivity
Stress and Equilibrium
Cauchy Stress Tensor
Stress Objectivity
Translational Equilibrium
Rotational Equilibrium
Principle of Virtual Work
Work Conjugacy and Alternative Stress Representations
The Kirchhoff Stress Tensor
The First Piola-Kirchhoff Stress Tensor
The Second Piola-Kirchhoff Stress Tensor
Deviatoric and Pressure Components
Stress Rates
Elasticity Tensor
The Material or Lagrangian Elasticity Tensor
The Spatial or Eulerian Elasticity Tensor
Isotropic Hyperelasticity
Material Description
Spatial Description
Compressible Neo-Hookean Material
Incompressible and Nearly Incompressible Materials
Incompressible Elasticity
Incompressible Neo-Hookean Material
Nearly Incompressible Hyperelastic Materials
Isotropic Elasticity in Principal Directions
Material Description
Spatial Description
Material Elasticity Tensor
Spatial Elasticity Tensor
A Simple Stretch-based Hyperelastic Material
Nearly Incompressible Material in Principal Directions
Plane Strain and Plane Stress Cases
Uniaxial Rod Case
Large Elasto-Plastic Deformations
The Multiplicative Decomposition
Rate Kinematics
Rate-Independent Plasticity
Principal Directions
Incremental Kinematics
The Radial Return Mapping
Algorithmic Tangent Modulus
Two-Dimensional Cases
Linearized Equilibrium Equations
Linearization and Newton-Raphson Process
Lagrangian Linearized Internal Virtual Work
Eulerian Linearized Internal Virtual Work
Linearized External Virtual Work
Body Forces
Surface Forces
Variational Methods and Incompressibility
Total Potential Energy and Equilibrium
Lagrange Multiplier Approach to Incompressibility
Penalty Methods for Incompressibility
Hu-Washizu Variational Principle for Incompressibility
Mean Dilatation Procedure
Discretization and Solution
Discretized Kinematics
Discretized Equilibrium Equations
General Derivation
Derivation in Matrix Notation
Discretization of the Linearized Equilibrium Equations
Constitutive Component: Indicial Form
Constitutive Component: Matrix Form
Initial Stress Component
External Force Component
Tangent Matrix
Mean Dilatation Method for Incompressibility
Implementation of the Mean Dilatation Method
Newton-Raphson Iteration and Solution Procedure
Newton-Raphson Solution Algorithm
Line Search Method
Arc-Length Method
Computer Implementation
User Instructions
Output File Description
Element Types
Solver Details
Constitutive Equation Summary
Program Structure
Main Routine flagshyp
Routine elemtk
Routine radialrtn
Routine ksigma
Routine bpress
Simple Patch Test
Nonlinear Truss
Strip With a Hole
Plane Strain Nearly Incompressible Strip
Elasto-plastic Cantilever
Appendix: Dictionary of Main Variables