Published online by Cambridge University Press: 05 June 2012
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. However, most materials can undergo very much less elastic deformation than rubber. In crystalline materials elastic strains are small, usually less than 0.5%. For most materials other than rubber, it is safe 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 covers elastic behavior of isotropic materials, the temperature dependence of elasticity, and thermal expansion. Anisotropic elastic behavior is covered in Chapter 15.
An isotropic material is one that has the same properties in all directions. If uniaxial 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 = −υεx, where υ is Poisson's ratio. Consider the strain, εx, produced by a general stress state, σx, σy, σz. The stress, σx, causes a contribution εx = σx/E. The stresses σy, σz cause Poisson contractions εx = −υσy/E and εx = −υσz/E.