Chapter 1 Introduction

Chapter 2 Deformations

2.1 Classical Strain

2.2 Underformed and Deformed Coordinates

2.3 Discussions on Classical Strain

2.4.1 Deformation Gradient

2.4.2 A Circular material must deformed into an Elliptical material

2.5.1 Mathematical Formulae

2.5.2 Proof that U and V are Symmetric

2.5.3 Proof that R is Orthogonal

2.5.4 dy=Rdx is a rigid body rotation

2.5.5 dy=Udx is a deformation without rotations

2.5.6 General Deformation

2.5.7 How to compute √FTF

2.6 Lagrangian Strain and Principle

2.7 Properties of Lagrangian Stain

2.7.3 E11 and E12

2.7.4 Principle Lagrangian Strain

2.8 Compatibility Equation

2.9 Material Time Derivative and Velocity Gradient

Chapter 3 Stresses and Conservation Laws

3.1 Conservation of Mass

3.2 Stress Principle

3.3 Cauchy’s Equations of Motion

Chapter 4 Constitutive Laws and Field Equations

4.1 Linear Elasticity Small Deformation Theorem

4.2 Plasticity and Fluid Mechanics

Chapter 5 Virtual Work Principle and Finite Element Formulation

5.1 Virtual Work Principle

5.2.1 Finite Element Formulation for Linear Elastic Solid (Part1)

5.2.2 Finite Element Formulation for Linear Elastic Solid (Part2)