Computational continuum mechanics / Ahmed A. Shabana, Richard and Loan Hill Professor of Engineering, University of Illinois at Chicago, Chicago, Illinois, USA.

Format:

Book

Author/Creator:

Shabana, Ahmed A., 1951- author.

Language:

English

Subjects (All):

Continuum mechanics.

Engineering mathematics.

Physical Description:

1 online resource (365 pages)

Edition:

Third edition.

Place of Publication:

Hoboken, New Jersey : Wiley, 2018.

System Details:

text file

Summary:

An updated and expanded edition of the popular guide to basic continuum mechanics and computational techniques This updated third edition of the popular reference covers state-of-the-art computational techniques for basic continuum mechanics modeling of both small and large deformations. Approaches to developing complex models are described in detail, and numerous examples are presented demonstrating how computational algorithms can be developed using basic continuum mechanics approaches. The integration of geometry and analysis for the study of the motion and behaviors of materials under varying conditions is an increasingly popular approach in continuum mechanics, and absolute nodal coordinate formulation (ANCF) is rapidly emerging as the best way to achieve that integration. At the same time, simulation software is undergoing significant changes which will lead to the seamless fusion of CAD, finite element, and multibody system computer codes in one computational environment. Computational Continuum Mechanics , Third Edition is the only book to provide in-depth coverage of the formulations required to achieve this integration. Provides detailed coverage of the absolute nodal coordinate formulation (ANCF), a popular new approach to the integration of geometry and analysis Provides detailed coverage of the floating frame of reference (FFR) formulation, a popular well-established approach for solving small deformation problems Supplies numerous examples of how complex models have been developed to solve an array of real-world problems Covers modeling of both small and large deformations in detail Demonstrates how to develop computational algorithms using basic continuum mechanics approaches Computational Continuum Mechanics , Third Edition is designed to function equally well as a text for advanced undergraduates and first-year graduate students and as a working reference for researchers, practicing engineers, and scientists working in computational mechanics, bio-mechanics, computational biology, multibody system dynamics, and other fields of science and engineering using the general continuum mechanics theory.

Contents:

Cover

Title Page

Copyright

Contents

Preface

Chapter 1 Introduction

1.1 Matrices

Definitions

Determinant

Inverse and Orthogonality

Matrix Operations

1.2 Vectors

Dot Product

Cross Product

Dyadic Product

Projection

1.3 Summation Convention

Unit Dyads

1.4 Cartesian Tensors

Double Product or Double Contraction

Invariants of the Second-Order Tensor

Symmetric Tensors

Higher-Order Tensors

1.5 Polar Decomposition Theorem

Other Decompositions

1.6 D'Alembert's Principle

Particle Mechanics

Rigid-Body Kinematics

Application of D'Alembert's Principle

Continuum Forces

1.7 Virtual Work Principle

Relationship with D'Alembert's Principle

1.8 Approximation Methods

1.9 Discrete Equations

1.10 Momentum, Work, and Energy

Linear and Angular Momentum

Work and Energy

1.11 Parameter Change and Coordinate Transformation

Change of Parameters

Coordinate Transformation

Deformation and Strains

Position Vector Gradients and Rigid Body Kinematics

Problems

Chapter 2 Kinematics

2.1 Motion Description

Line Elements

Rigid-Body Motion

Floating Frame of Reference (FFR)

Displacement Vector Gradients

2.2 Strain Components

Geometric Interpretation of the Strains

Eulerian Strain Tensor

2.3 Other Deformation Measures

Right and Left Cauchy-Green Deformation Tensors

Infinitesimal Strain Tensor

2.4 Decomposition of Displacement

Homogeneous Motion

Nonhomogeneous Motion

2.5 Velocity and Acceleration

Eulerian Description

Rate of Deformation and Spin Tensors

Rate of Change of the Green-Lagrange Strain

2.6 Coordinate Transformation

Strain Transformation

Gradients and Strains

Principal Strains

Strain Invariants

2.7 Objectivity

2.8 Change of Volume and Area

Volume

Area.

2.9 Continuity Equation

2.10 Reynolds' Transport Theorem

2.11 Examples of Deformation

Planar Displacement

Extension and Stretch

Shear Deformation

2.12 Geometry Concepts

Chapter 3 Forces and Stresses

3.1 Equilibrium of Forces

3.2 Transformation of Stresses

3.3 Equations of Equilibrium

3.4 Symmetry of the cauchy Stress Tensor

Principal Stresses

3.5 Virtual Work of the Forces

Tensor Double Product (Contraction)

Volume Change

Virtual Work

Other Stress Measures

First and Second Piola-Kirchhoff Stress Tensors

Notation and Procedure

Surface Forces

Total and Updated Lagrangian Formulations

Physical Interpretation

3.6 Deviatoric Stresses

3.7 Stress Objectivity

Stress Rate

Truesdell Stress Rate o

Oldroyd and Convective Stress Rates o and o

Green-Naghdi Stress Rate

Jaumann Stress Rate

3.8 Energy Balance

Chapter 4 Constitutive Equations

4.1 Generalized Hooke's Law

4.2 Anisotropic Linearly Elastic Materials

4.3 Material Symmetry

Reflection

Rotations

4.4 Homogeneous Isotropic Material

Poisson Effect and Locking

Stress and Strain Invariants

Plane-Stress and Plane-Strain Problems

Finite Dimensional Model

Generalized Elastic Forces

Homogeneous Displacement

4.5 Principal Strain Invariants

4.6 Special Material Models for Large Deformations

Compressible Neo-Hookean Material Models

Incompressible Mooney-Rivlin Materials

Objectivity

4.7 Linear Viscoelasticity

One-Dimensional Model

Other Viscoelastic Models

Generalization

Elastic Energy and Dissipation

Another Form of the Viscoelastic Equations

Three-Dimensional Linear Viscoelasticity

4.8 Nonlinear Viscoelasticity

Another Model

4.9 A Simple Viscoelastic Model for Isotropic Materials

4.10 Fluid Constitutive Equations.

4.11 Navier-Stokes Equations

Chapter 5 Finite Element Formulation: Large-Deformation, Large-Rotation Problem

Small- and Large-Deformation Problems

Absolute Nodal Coordinate Formulation (ANCF)

Organization

5.1 Displacement Field

Separation of Variables

Modes of Displacement

Nodal Coordinates

5.2 Element Connectivity

5.3 Inertia and Elastic Forces

Inertia Forces

Elastic Forces

5.4 Equations of Motion

Curved Geometry

5.5 Numerical Evaluation of the Elastic Forces

Gaussian Quadrature

5.6 Finite Elements and Geometry

General Continuum Mechanics Approach and Classical Theories

Gradient Vectors

Locking Problems

Theory of Curves

Theory of Surfaces

Surface Curvature

5.7 Two-Dimensional Euler-Bernoulli Beam Element

Kinematics of the Element

Formulation of the Element Elastic Forces

Special Case

5.8 Two-Dimensional Shear Deformable Beam Element

Formulation of the Elastic Forces

5.9 Three-Dimensional Cable Element

5.10 Three-Dimensional Beam Element

5.11 Thin-Plate Element

5.12 Higher-Order Plate Element

5.13 Brick Element

5.14 Element Performance

Patch Test

Locking Problem

Reduced Integration

5.15 Other Finite Element Formulations

Isoparametric Finite Elements

Use of Infinitesimal Rotation Coordinates

Use of Finite Rotation Coordinates

5.16 Updated Lagrangian and Eulerian Formulations

5.17 Concluding Remarks

ANCF Finite Elements

Constrained Motion

ANCF Reference Node

Deformation Modes

Chapter 6 Finite Element Formulation: Small-Deformation, Large-Rotation Problem

6.1 Background

Translations

6.2 Rotation and Angular Velocity

Identities

General Displacement

Illustrative Example

Euler Angles Singularity.

6.3 Floating Frame of Reference (FFR)

6.4 Intermediate Element Coordinate System

6.5 Connectivity and Reference Conditions

Connectivity Conditions

Reference Conditions

Rigid-Body and Reference Motion

6.6 Kinematic Equations

6.7 Formulation of the Inertia Forces

Body Inertia Shape Integrals

6.8 Elastic Forces

6.9 Equations of Motion

6.10 Coordinate Reduction

6.11 Integration of Finite Element and Multibody System Algorithms

Linear Theory of Elastodynamics

Nodal and Modal Coordinates

Numerical Evaluation of the Inertia Shape Integrals

Scaling of the Modal Coordinates

Limitations of the FFR Formulation

Chapter 7 Computational Geometry and Finite Element Analysis

7.1 Geometry and Finite Element Method

Bezier Geometry

B-Spline Geometry

NURBS Geometry

7.2 Ancf Geometry

ANCF Element Geometry

Control-Point Representation

7.3 Bezier Geometry

7.4 B-Spline Curve Representation

Control Points and Degree of Continuity

Knot Insertion

Comparison with FE Formulations

7.5 Conversion of B-Spline Geometry to ANCF Geometry

7.6 ANCF and B-Spline Surfaces

B-Spline Surfaces

ANCF Surfaces

7.7 Structural and Nonstructural Discontinuities

B-Spline Model

ANCF Model

Chapter 8 Plasticity Formulations

8.1 One-Dimensional Problem

8.2 Loading and Unloading Conditions

8.3 Solution of the Plasticity Equations

Numerical Solution

Plasticity Equations

Trial Step

The Return Mapping Algorithm

8.4 Generalization of the Plasticity Theory: Small Strains

Associative Plasticity

Numerical Solution of the Plasticity Equations

Explicit Solution

Implicit Solution

8.5 J2 Flow Theory with Isotropic/Kinematic Hardening

Nonlinear Isotropic/Kinematic Hardening.

Return Mapping Algorithm for Nonlinear Isotropic/Kinematic Hardening

Linear Kinematic/Isotropic Hardening

8.6 Nonlinear Formulation for Hyperelastic-Plastic Materials

Multiplicative Decomposition

Hyperelastic Potential

Rate of Deformation Tensors

Flow Rule and Hardening Law

Rate-Dependent Plasticity

8.7 Hyperelastic-Plastic J2 Flow Theory

References

Index

EULA.

Notes:

Includes bibliographical references and index.

Description based on print version record.

ISBN:

9781523123438

1523123435

9781119293231

1119293235

9781119293248

1119293243

OCLC:

995162609