Introduction

Elastic deformation is reversible. When a body deforms elastically under a load, it will revert to its original shape as soon as the load is removed. A rubber band is a familiar example. Most materials, however, can undergo much less elastic deformation than rubber. In crystalline materials, elastic strain is small, usually less than ½%. It is safe for most materials other than rubber to assume that the amount of deformation is proportional to the stress. This assumption is the basis of the following treatment. Because elastic strains are small, it does not matter whether the relations are expressed in terms of engineering strains, e, or true strains, ε.

The treatment in this chapter will start with the elastic behavior of isotropic materials, the temperature dependence of elasticity, and thermal expansion. Then anisotropic elastic behavior and thermal expansion will be covered.

Isotropic Elasticity

An isotropic material is one that has the same properties in all directions. If uni-axial tension is applied in the x-direction, the tensile strain is εx = σx/E, where E is Young's modulus. Uniaxial tension also causes lateral strains, εy = εz = −νεx, where ν is Poisson's ratio.