Elasticity

Abstract

The stiffness and compliance tensors, which relate the stress tensor to the resulting strain tensor, are symmetric tensors of rank 4. This chapter shows how the intrinsic symmetry of the strain and stress tensors reduces the number of independent components of the compliance and stiffness tensors, and then how the symmetry of the crystal, described by its point group, can further reduce this number. A short notation, called Voigt’s notation, is often used for these tensors. It represents the stress and the strain tensors through 6-component vectors, and the compliance and stiffness tensors by symmetric 6 × 6 matrices which are inverse to each other.