Nonlinear Solid Mechanics: A Continuum Approach for Engineering

✍ Scribed by Gerhard A. Holzapfel

• Publisher: Wiley
• Year: 2000
• Tongue: English
• Leaves: 470
• Edition: 1
• Category: Library

✦ Synopsis

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Nonlinear Solid Mechanics a Continuum Approach for Engineering Gerhard A. Holzapfel Graz University of Technology, Austria With a modern, comprehensive approach directed towards computational mechanics, this book covers a unique combination of subjects at present unavailable in any other text. It includes vital information on 'variational principles' constituting the cornerstone of the finite element method. In fact this is the only method by which Nonlinear Solid Mechanics is utilized in engineering practice. The book opens with a fundamental chapter on vectors and tensors. The following chapters are based on nonlinear continuum mechanics - an inevitable prerequisite for computational mechanicians. In addition, continuum field theory (applied to a representative sample of hyperelastic materials currently used in nonlinear computations such as incompressible and compressible materials) is presented, as are transversely isotropic materials, composite materials, viscoelastic materials and hyperelastic materials with isotropic damage. Another central chapter is devoted to the thermodynamics of materials, covering both finite thermoelasticity and finite thermoviscoelasticity. Also included are:
* an up-to-date list of almost 300 references and a comprehensive index
* useful examples and exercises for the student
* selected topics of statistical and continuum thermodynamics.
Furthermore, the principle of virtual work (in both the material and spatial descriptions) is compared with two and three-field variational principles particularly designed to capture kinematic constraints such as incompressibility. All of the features combined result in an essential text for final year undergraduates, postgraduates and researchers in mechanical, civil and aerospace engineering and applied maths and physics.

✦ Table of Contents

Title
Contents
Preface
Acknowledgements
1 Introduction to Vectors and Tensors
1.1 Algebra of Vectors
1.2 Algebra of Tensors
1.3 Higher-order Tensors
1.4 Eigenvalues, Eigenvectors of Tensors
1.5 Transformation Laws for Basis Vectors and Components
1.6 General Bases
1.7 Scalar, Vector, Tensor Functions
1.8 Gradients and Related Operators
1.9 Integral Theorems
2 Kinematics
2.1 Configurations, and Motions of Continuum Bodies
2.2 Displacement, Velocity, Acceleration Fields
2.3 Material, Spatial Derivatives
2.4 Deformation Gradient
2.5 Strain Tensors
2.6 Rotation, Stretch Tensors
2.7 Rates of Deformation Tensors
2.8 Lie Time Derivatives
3 The Concept of Stress
3.1 Traction Vectors, and Stress Tensors
3.2 Extremal Stress Values
3.3 Examples of States of Stress
3.4 Alternative Stress Tensors
4 Balance Principles
4.1 Conservation of Mass
4.2 Reynolds' Transport Theorem
4.3 Momentum Balance Principles
4.4 Balance of Mechanical Energy
4.5 Balance of Energy in Continuum Thermodynamics
4.6 Entropy Inequality Principle
4.7 Master Balance Principle
5 Some Aspects of Objectivity
5.1 Change of Observer, and Objective Tensor Fields
5.2 Superimposed Rigid-body Motions
5.3 Objective Rates
5.4 Invariance of Elastic Material Response
6 Hyperelastic Materials
6.1 General Remarks on Constitutive Equations
6.2 Isotropic Hyperelastic Materials
6.3 Incompressible Hyperelastic Materials
6.4 Compressible Hyperelastic Materials
6.5 Some Forms of Strain-energy Functions
6.6 Elasticity Tensors
6.7 Transversely Isotropic Materials
6.8 Composite Materials with Two Families of Fibers
6.9 Constitutive Models with Internal Variables
6.10 Viscoelastic Materials at Large Strains
6.11 Hyperelastic Materials with Isotropic Damage
7 Thermodynamics of Materials
7.1 Physical Preliminaries
7.2 Thermoelasticity of Macroscopic Networks
7.3 Thermodynamic Potentials
7.4 Calorimetry
7.5 Isothermal, Isentropic Elasticity Tensors
7.6 Entropic Elastic Materials
7.7 Thermodynamic Extension of Ogden's Material Model
7.8 Simple Tension of Entropic Elastic Materials
7.9 Thermodynamics with Internal Variables
8 Variational Principles
8.1 Virtual Displacements, Variations
8.2 Principle of Virtual Work
8.3 Principle of Stationary Potential Energy
8.4 Linearization of the Principle of Virtual Work
8.5 Two-field Variational Principles
8.6 Three-field Variational Principles
References
Index