ABSTRACT
A homogeneous deformation is one in which points that initially are collinear remain so after the deformation. It follows that a plane will similarly remain a plane in such circumstances. Each volume element in the solid therefore experiences the same change in shape. This chapter illustrates the difference between a homogeneous and heterogeneous deformation. It describes deformations that alter the length and/or direction of vectors, i.e., physical deformations, with the initial and resultant vectors referred to a fixed reference frame. Elastic strain energy calculations often are based on the assumption that the deformations are homogeneous and this usually is justified given that the elastic strain fields may extend over large distances whereas atomic perturbations are just that. Any real deformation can in general be factorized into a pure strain and a rigid body rotation, but it is important to realize that the factorization is simply a mathematical convenience and the deformation does not actually occur in the two stages.
