Continuum Mechanics

Name: Continuum Mechanics
Price: 6890 ISK
Availability: InStock
Author: Franco M. Capaldi
ISBN: 9781139508032

Höfundur: Franco M. Capaldi (Útgáfa: 1)

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This is a modern textbook for courses in continuum mechanics. It provides both the theoretical framework and the numerical methods required to model the behaviour of continuous materials. This self-contained textbook is tailored for advanced undergraduate or first-year graduate students with numerous step-by-step derivations and worked-out examples. The author presents both the general continuum theory and the mathematics needed to apply it in practice.

The derivation of constitutive models for ideal gases, fluids, solids and biological materials, and the numerical methods required to solve the resulting differential equations, are also detailed. Specifically, the text presents the theory and numerical implementation for the finite difference and the finite element methods in the MatlabĀ® programming language. It includes thirteen detailed MatlabĀ® programs illustrating how constitutive models are used in practice.

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Útgefandi: Cambridge University Press

ISBN: 9781139508032

Print ISBN: 9781107011816

Format: ePub

Útgáfa: 1

Höfundar: Franco M. Capaldi

Tungumál: English

Útgefið: 2012-06-18

Prent takmörkun á líftíma: 10

Prent takmörkun: 5

Afritunar takmörkun: 5

Kaflar

Cover Page
Half Title
Title Page
Copyright Page
Dedication
Table of Contents
Preface
1 Mathematics
1.1 Vectors
1.2 Second-Order Tensors
1.3 Eigenvalues and Eigenvectors
1.4 Spectral Decomposition of a Symmetric Tensor
1.5 Coordinate Transformation
1.6 Invariants
1.7 Cayley-Hamilton Theorem
1.8 Scalar, Vector, and Tensor Functions and Fields
1.9 Integral Theorems
Exercises
Matlab® Exercises
2 Kinematics
2.1 Configurations
2.2 Velocity and Acceleration
2.3 Displacement
2.4 Deformation Gradient
2.5 Jacobian
2.6 Nanson’s Formula
2.7 Homogenous Deformation, Isochoric Deformation, and Rigid Body Rotation
2.8 Material and Spatial Derivatives
2.9 Polar Decomposition of the Deformation Gradient
2.10 Stretch Ratios
2.11 Left and Right Cauchy Deformation Tensor
2.12 Green Strain Tensor
2.13 Almansi Strain Tensor
2.14 Infinitesimal Strain Tensor
2.15 Velocity Gradient, Rate of Deformation, Vorticity
2.16 Reynolds’ Transport Theorem
Exercises
Matlab® Exercises
3 The Stress Tensor
3.1 Mass, Density, and Forces
3.2 Traction Vector
3.3 Cauchy Stress Tensor
3.4 First Piola-Kirchhoff Stress Tensor
3.5 Second Piola-Kirchhoff Stress Tensor
3.6 Maximum Normal and Shear Stress
3.7 Decomposition of the Stress Tensor
Exercises
4 Introduction to Material Modeling
4.1 Forces and Fields
4.2 Balance Laws
4.2.1 Conservation of Mass
4.2.2 Conservation of Linear Momentum
4.2.3 Conservation of Angular Momentum
4.2.4 Conservation of Energy
4.2.5 The Second Law of Thermodynamics
4.2.6 Summary of the Field Equations
4.3 Stress Power
4.4 Jump Conditions
4.5 Constitutive Modeling
4.5.1 Constitutive Modeling Principles
4.5.2 Principle of Dissipation
4.5.3 Principle of Material Frame Indifference
4.6 Material Symmetry
4.6.1 Isotropic Scalar-Valued Functions
4.6.2 Isotropic Tensor-Valued Functions
4.7 Internal Variables
4.8 Thermodynamics of Materials
4.9 Heat Transfer
Exercises
5 Ideal Gas
5.1 Historical Perspective
5.2 Forces and Fields
5.3 Balance Laws
5.4 Constitutive Model
5.4.1 Constraints
5.4.2 Constitutive Relations
5.4.3 Molecular Model of an Ideal Gas
5.5 Governing Equations
5.6 Acoustic Waves
5.6.1 Finite Difference Method
5.6.2 Explicit Algorithm
5.6.3 Implicit Algorithm
5.6.4 Example Problem
5.6.5 Matlab® File – Explicit Algorithm
5.6.6 Matlab® File – Implicit Algorithm
6 Fluids
6.1 Historical Perspective
6.2 Forces and Fields
6.3 Balance Laws
6.4 Constitutive Model
6.4.1 Constraints
6.4.2 Constitutive Relations for the Newtonian Fluid
6.4.3 Stokes Condition
6.5 Governing Equations
6.5.1 Compressible Newtonian Fluid
6.5.2 Incompressible Newtonian Fluid
6.5.3 Irrotational Steady Flow of an Incompressible Newtonian Fluid
6.6 Non-Newtonian Fluid Models
6.6.1 Power Law Model
6.6.2 Cross Model
6.6.3 Bingham Model
6.7 Couette Viscometer
6.7.1 Newtonian Fluid
6.7.2 Power Law Fluid Model
6.7.3 General Non-Newtonian Fluid
7 Elastic Material Models
7.1 Historical Perspective
7.2 Finite Thermoelastic Material Model
7.2.1 Forces and Fields
7.2.2 Balance Laws
7.2.3 Constitutive Model
7.2.4 Constraints Due to Material Frame Indifference
7.2.5 Constraints Due to the Second Law of Thermodynamics
7.3 Hyperelastic Material Model
7.3.1 Balance Laws
7.3.2 Constitutive Model
7.3.3 Constraints Due to Material Frame Indifference
7.3.4 Clausius-Duhem Inequality
7.3.5 Material Symmetry
7.3.6 Isotropic Materials
7.3.7 Transversely Isotropic Materials
7.3.8 Incompressible Materials
7.3.9 Common Hyperelastic Constitutive Models
7.3.10 Freely Jointed Chain
7.4 Linear Thermoelastic Material Model
7.4.1 Balance Laws
7.4.2 Constitutive Model
7.4.3 Clausius-Duhem Inequality
7.4.4 Linear Thermoelastic Constitutive Relation
7.4.5 Material Symmetry
7.4.6 Governing Equations for the Isotropic Linear Elastic Material
7.5 Uniaxial Tension Test
7.5.1 Kinematics
7.5.2 Isotropic Linear Thermoelastic Material
7.5.3 Incompressible Isotropic Neo-Hookean Model
8 Continuum Mixture Theory
8.1 Forces and Fields
8.2 Balance Laws
8.2.1 Conservation of Mass
8.2.2 Conservation of Momentum
8.2.3 Conservation of Angular Momentum
8.2.4 Conservation of Energy
8.2.5 Second Law of Thermodynamics
8.3 Biphasic Model
8.4 Isothermal Biphasic Model
8.5 Application to Soft Tissue
8.5.1 Confined Compression Experiment
8.5.2 Unconfined Compression
9 Growth Models
9.1 Forces and Fields
9.2 Balance Laws
9.2.1 Conservation of Mass
9.2.2 Reynolds’ Transport Theorem
9.2.3 Conservation of Momentum
9.2.4 Conservation of Angular Momentum
9.2.5 Conservation of Energy
9.3 Decomposition of the Deformation Gradient
9.4 Summary of the Field Equations
9.5 Constitutive Model
9.6 Uniaxial Loading
9.6.1 Kinematics
9.6.2 Governing Equation
9.6.3 Finite Difference Algorithm
9.6.4 Example Problem
9.6.5 Matlab® File
10 Parameter Estimation and Curve Fitting
10.1 Propagation of Error
10.2 Least Squares Fit
11 Finite Element Method
11.1 Introduction
11.1.1 Element Types
11.1.2 Natural Versus Global Coordinates for a Quadrilateral Element
11.1.3 Field Variable Representation Within an Element
11.1.4 Matrix Representation
11.1.5 Integration of a Field Variable
11.1.6 Gaussian Quadrature
11.1.7 Differentiation of a Field Variable
11.2 Formulation of the Governing Equations
11.3 Plane Strain Deformation
11.3.1 Statement of Virtual Work
11.3.2 Discretization of Space
11.3.3 Approximation of the Field Variables
11.3.4 FEM Formulation
11.3.5 Element Stiffness Tensor
11.3.6 Body Force Vector
11.3.7 Traction Force Vector
11.3.8 Single Element Implementation
11.4 Axisymmetric Deformation
11.4.1 Statement of Virtual Work
11.4.2 Discretization of Space
11.4.3 Approximation of the Field Variables
11.4.4 FEM Formulation
11.4.5 Element Stiffness Tensor
11.4.6 Body Force Vector
11.4.7 Single Element Implementation
11.4.8 Multiple Element Implementation
11.5 Infinitesimal Plane Strain FEM with Material Nonlinearity
11.5.1 Statement of Virtual Work
11.5.2 Discretization of Space
11.5.3 Approximation of the Field Variables
11.5.4 FEM Formulation
11.6 Plane Strain Finite Deformation
11.6.1 Total Lagrangian Method
11.6.2 Updated Lagrangian Method
11.6.3 Updated Lagrangian Method Single Element Implementation
12 Appendix
12.1 Introduction to Matlab®
12.2 Reference Tables
Index