## Introduction to Elasticity

Welcome to the **Introduction** to **Elasticity** learning project. Here you will find notes, assignments, and other useful information that will introduce you to this exciting subject. Contents 1 Learning Project Summary 2 Objectives 3 Syllabus 4 Quizzes and Exams 5 Assignments 6

**wikiversity.org**| 2018/3/25 9:56:21

## Introduction to Elasticity/Tensors

papers on solid mechanics and finite element modeling of complex material behavior. This brief **introduction** gives you an overview of tensors and tensor notation. For more details you can read A Brief on Tensor Analysis by J. G. Simmonds, the appendix on vector and tensor notation from Dynamics

**wikiversity.org**| 2018/3/29 6:22:37

## Introduction to finite elements/Partial differential equations

Partial differential equations (PDEs) are the most common method by which we model physical problems in engineering. Finite element methods are one of many ways of solving PDEs. This handout reviews the basics of PDEs and discusses some of the classes of PDEs in brief. The contents are based

**wikiversity.org**| 2018/4/10 1:55:35

## Introduction to Elasticity/Vectors

Vector notation is ubiquitous in the modern literature on solid mechanics, fluid mechanics, biomechanics, nonlinear finite elements and a host of other subjects in mechanics. A student has to be familiar with the notation in order to be able to read the literature. In this section we introduce

**wikiversity.org**| 2018/3/29 14:32:30

## Introduction to Elasticity/Compatibility

For an arbitrary strain field ε {\displaystyle \textstyle {\boldsymbol {\varepsilon }}} , the strain-displacement relation ε = 1 2 ( ∇ u + ∇ u T ) {\displaystyle \textstyle {\boldsymbol {\varepsilon }}={\cfrac {1}{2

**wikiversity.org**| 2018/3/26 2:06:00

## Introduction to Elasticity/Equilibrium example 1

Euler's second law for the conservation of angular momentum (1) ∫ ∂ B e i j k x j n l σ l k d S + ∫ B ρ e i j k x j b k d V = d d t ( ∫ B ρ e i

**wikiversity.org**| 2018/3/26 16:40:24

## Introduction to Elasticity/Constitutive example 3

If the strain energy density is given by equation (1), then (for linear elastic materials) the stress and strain can be related using (3) σ i j = ∂ U ( ε ) ∂ ε i j {\displaystyle {\text{(3)}}\qquad \sigma _{ij}={\frac {\partial U({\boldsymbol

**wikiversity.org**| 2018/3/26 6:24:11

## Introduction to Elasticity/Equilibrium example 3

If a material is incompressible ( ν {\displaystyle \nu } = 0.5), a state of hydrostatic stress ( σ 11 = σ 22 = σ 33 {\displaystyle \sigma _{11}=\sigma _{22}=\sigma _{33}} ) produces no strain. The corresponding stress-strain relation can be written

**wikiversity.org**| 2018/3/26 19:20:45