Linked e-resources
Details
Table of Contents
Intro
Foreword
Preface
References
Contents
Abbreviations
Chapter 1: Introduction
1.1 What Is the Mechanics of Continuous Medium?
References
Chapter 2: Stress and Strain in Continuum
2.1 Newtonś Universal Laws of Motion
2.1.1 First Universal Law of Motion
2.1.1.1 Formulation of the First Law
2.1.2 Second Universal Law of Motion
2.1.2.1 Formulation of Newtonś Second Law
2.1.3 Third Universal Law of Motion
2.1.4 Range of Validity of Newtonś Universal Laws of Motion
2.1.5 Relation to the Thermodynamics and Conservation Laws
2.2 Stress
2.2.1 Definitions of Stress and Traction
2.2.2 Stress Vector on an Arbitrary Plane
2.2.3 Symmetry of Stress Tensor
2.2.4 Couple Stresses
2.2.5 Principal Stresses and Principal Axes
2.2.6 Stress Tensor Invariants
2.2.6.1 Stress Invariants in Principal Axes
2.2.6.2 Representation of Stress Tensor in Spherical and Deviatoric Components
2.2.6.3 Invariants of the Deviatoric Stress Tensor
2.2.7 Octahedral Plane and Octahedral Stresses
2.3 Deformation and Strain
2.3.1 Small Strain Definition
2.3.1.1 Elementary Definition of Pure Uniaxial Strain
2.3.1.2 Pure Shear Strain
2.3.1.3 Pure Rigid Body Motion
2.3.2 Small Strain and Small Rotation Formulation
2.3.2.1 Definition of Material (Local) Coordinates
2.3.2.2 Small Strain in Local Coordinates
2.3.2.3 Shear Strain in Local (Material) Coordinates
2.3.3 Small Strain and Rotation in 3-D
2.4 Kinematics of Continuous Medium
2.4.1 Material (Local) Description
2.4.2 Referential Description (Lagrangian Description)
2.4.3 Spatial Description (Eulerian Description)
2.4.4 Material Time Derivative in Spatial Coordinates (Substantial Derivative)
2.5 Rate of Deformation Tensor and Rate of Spin Tensor
2.5.1 Comparison of Rate of Deformation Tensor, D, and Time Derivative of the Strain Tensor,
2.5.2 True Strain (Natural Strain) (Logarithmic Strain)
2.6 Finite Strain and Deformation
2.6.1 Green Deformation Tensor, C, Cauchy Deformation Tensor, B-1
2.6.2 Relation Between Deformation, Strain, and Deformation-Gradient Tensors
2.6.3 Comparing Small Strain and Large (Finite) Strain
2.6.4 Strain Rate and Rate of Deformation Tensor Relations
Foreword
Preface
References
Contents
Abbreviations
Chapter 1: Introduction
1.1 What Is the Mechanics of Continuous Medium?
References
Chapter 2: Stress and Strain in Continuum
2.1 Newtonś Universal Laws of Motion
2.1.1 First Universal Law of Motion
2.1.1.1 Formulation of the First Law
2.1.2 Second Universal Law of Motion
2.1.2.1 Formulation of Newtonś Second Law
2.1.3 Third Universal Law of Motion
2.1.4 Range of Validity of Newtonś Universal Laws of Motion
2.1.5 Relation to the Thermodynamics and Conservation Laws
2.2 Stress
2.2.1 Definitions of Stress and Traction
2.2.2 Stress Vector on an Arbitrary Plane
2.2.3 Symmetry of Stress Tensor
2.2.4 Couple Stresses
2.2.5 Principal Stresses and Principal Axes
2.2.6 Stress Tensor Invariants
2.2.6.1 Stress Invariants in Principal Axes
2.2.6.2 Representation of Stress Tensor in Spherical and Deviatoric Components
2.2.6.3 Invariants of the Deviatoric Stress Tensor
2.2.7 Octahedral Plane and Octahedral Stresses
2.3 Deformation and Strain
2.3.1 Small Strain Definition
2.3.1.1 Elementary Definition of Pure Uniaxial Strain
2.3.1.2 Pure Shear Strain
2.3.1.3 Pure Rigid Body Motion
2.3.2 Small Strain and Small Rotation Formulation
2.3.2.1 Definition of Material (Local) Coordinates
2.3.2.2 Small Strain in Local Coordinates
2.3.2.3 Shear Strain in Local (Material) Coordinates
2.3.3 Small Strain and Rotation in 3-D
2.4 Kinematics of Continuous Medium
2.4.1 Material (Local) Description
2.4.2 Referential Description (Lagrangian Description)
2.4.3 Spatial Description (Eulerian Description)
2.4.4 Material Time Derivative in Spatial Coordinates (Substantial Derivative)
2.5 Rate of Deformation Tensor and Rate of Spin Tensor
2.5.1 Comparison of Rate of Deformation Tensor, D, and Time Derivative of the Strain Tensor,
2.5.2 True Strain (Natural Strain) (Logarithmic Strain)
2.6 Finite Strain and Deformation
2.6.1 Green Deformation Tensor, C, Cauchy Deformation Tensor, B-1
2.6.2 Relation Between Deformation, Strain, and Deformation-Gradient Tensors
2.6.3 Comparing Small Strain and Large (Finite) Strain
2.6.4 Strain Rate and Rate of Deformation Tensor Relations