Elastic Deformations

Abstract

In many materials (steel, rubber, wood, etc) a deformation (i.e. a change of shape) can be sustained only if a system of forces (loads) is applied, so setting up internally a distribution of stress (i.e. force per unit area). If the body returns to its original shape when these loads are removed, the material is said to be elastic. The state in which no loads are applied is often taken as the natural state, or reference configuration. (The elastic string in §5.1 is a one-dimensional example which is rather degenerate, since resistance to bending is neglected. With T(λ) chosen such that T = 0 whenever λ = 1, any unstretched state, even if curved, is a reference configuration if |∂r/∂X| ≡ λ = 1.)