Introduction

The basic elements of anisotropic linear elasticity are presented in concise form. First, the deformation of an elastically strained body is described in terms of the local displacements, strains, and rotations that occur throughout the body. Requirements on the strains that ensure compatibility of the medium are then described. Next, the forces acting throughout the body are described in terms of surface tractions, body forces, and stresses. Conditions for mechanical equilibrium are derived. The stresses and strains are then linearly coupled via elastic constants, and various stress–strain relationships are derived. Finally, the energy stored in an elastically strained medium is formulated. Elements of the theory for the special case when the medium is elastically isotropic are included, along with several formulations of additional elastic quantities required for treating crystal defects.

References include: Love (1944); Sokolnikoff (1946); Muskhelishvili (1953); Nye (1957); Lekhnitskii (1963); Bacon, Barnett and Scattergood (1979b); Soutas-Little (1999); Hetnarski and Ignaczak (2004) and Asaro and Lubarda (2006).