Nonlinear Continuum Mechanics for Finite Element Analysis

Name: Nonlinear Continuum Mechanics for Finite Element Analysis
Availability: OutOfStock
ISBN: 9780521838702

ISBN-10: 0521838703

ISBN-13: 9780521838702

Edition: 2nd 2008 (Revised)

Authors: Javier Bonet, Richard D. Wood

List price: $129.00

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Description:

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 www.flagshyp.com.

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.



Preface



Introduction



Nonlinear Computational Mechanics



Simple Examples of Nonlinear Structural Behavior



Cantilever



Column



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



Introduction



Vector and Tensor Algebra



Vectors



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



Introduction



Kinematics



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



Examples



Inclined Axial Rod



Trussed Frame



Kinematics



Introduction



The Motion



Material and Spatial Descriptions



Deformation Gradient



Strain



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



Velocity



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



Introduction



Cauchy Stress Tensor



Definition



Stress Objectivity



Equilibrium



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



Hyperelasticity



Introduction



Hyperelasticity



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



Introduction



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



Introduction



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



Introduction



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



Introduction



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



Examples



Simple Patch Test



Nonlinear Truss



Strip With a Hole



Plane Strain Nearly Incompressible Strip



Elasto-plastic Cantilever



Appendix: Dictionary of Main Variables


Bibliography


Index