## Example Problems

2. Governing Equations2.1 Mathematical Description of Shape Changes in Solids

2.2 Mathematical Description of Internal Forces in Solids 2.3 Equations of motion and equilibrium for deformable solids 2.4 Work done by stresses; Principle of Virtual Work3. Constitutive Equations: Relations between Stress and Strain

3.1 General Requirements for Constitutive Equations 3.2 Linear Elastic Material Behavior

3.3 Hypoelasticity - elasticity with nonlinear stress-strain behavior

3.4 Generalized Hooke’s law – elastic materials subjected to small stretches but large rotations

3.5 Hyperelasticity - time independent behavior of rubbers and foams subjected to large strains

3.6 Viscoelasticity - time dependent behavior of polymers at small strains

3.7 Small strain, rate independent plasticity - metals loaded beyond yield

3.8 Small strain viscoplasticity - creep and high rate deformation of metals

3.9 Large strain, rate dependent plasticity

3.10 Large strain viscoelasticity

3.11 Critical State Models for Soils

3.12 Constitutive models for metal single crystal

3.13 Constitutive models for contacting surfaces and interfaces in solids4. Solutions to simple boundary and initial value problems4.1 Axially & Spherically Symmetric Solutions for Linear Elastic Solids Under Quasi-Static Loading

4.2 Axially & Spherically Symmetric Solutions for Elastic-Plastic Solids Under Quasi-Static Loading

4.3 Spherically Symmetric Solution for Large Strain Elasticity Problems

4.4 Simple Dynamic Solutions for Linear Elastic Solids5. Analytical Techniques and Solutions for Linear Elastic Solids5.1 General Principles

5.2 Airy Function Solutions to Plane Stress and Plane Strain Problems for Linear Elastic Solids

5.3 Complex Variable Solution to Plane Strain Static Elasticity Problems

5.4 Solutions to 3D Static Elasticity Problems

5.5 Solutions to Plane Problems for Anisotropic Elastic Solids

5.6 Solutions to Dynamic Problems for Isotropic Elastic Solids

5.7 Energy Methods for Solving Static Linear Elasticity Problems

5.8 The Reciprocal Theorem and its Applications

5.9 Energetics of Dislocations in Elastic Solid

5.10 Rayleigh-Ritz Method for Estimating Natural Frequencies6. Analytical Techniques and Solutions for Plastic Solids6.1 Slip Line Field Theory

6.2 Bounding Theorems in Plasticity and their Applications

7. Introduction to Finite Element Analysis in Solid Mechanics7.1 A Guide to Using Finite Element Software

7.2 A Simple Finite Element Program8. Theory and Implementation of the Finite Element Method8.1 Generalized FEA for Static Linear Elasticity

8.2 The Finite Element Method for Dynamic Linear Elasticity

8.3 The Finite Element Method for Nonlinear (Hypoelastic) Materials

8.4 The Finite Element Method for Large Deformations: Hyperelasticity

8.5 The Finite Element Method for Viscoplasticity

8.6 Advanced Element Formulations: Incompatible Modes; Reduced Integration and Hybrid Elements9. Modeling Material Failure9.1 Summary of Mechanisms of Fracture and Fatigue under Static and Cyclic Loading

9.2 Stress and Strain Based Failure Criteria

9.3 Modeling Failure by Crack Growth: Linear Elastic Fracture Mechanics

9.4 Energy Methods in Fracture Mechanics

9.5 Plastic Fracture Mechanics

9.6 Linear Elastic Fracture Mechanics for Interfaces10. Approximate Theories for Solids with Special Shapes: Rods, Beams, Plates and Shells10.1 Preliminaries: Dyadic Notation for Vectors and Tensors

10.2 Motion and Deformation of Slender Rods

10.3 Simplified Versions of the General Theory of Deformable Rods

10.4 Exact Solutions to Simple Problems Involving Elastic Rods

10.5 Motion and Deformation of Thin Shells: General Theory

10.6 Simplified Versions of the General Shell Theory

10.7 Solutions to Problems Involving Membranes, Plates and ShellsAppendix A: Review of Vectors and MatricesAppendix B: A Brief Introduction to Tensors and their PropertiesAppendix C: Index Notation for Vector and Tensor OperationsAppendix D: Vector and Tensor Operations in Polar CoordinatesAppendix E: Miscellaneous Derivations