The Structures and Identities of the Elasticity Matrices

The matrices Q, R, T, A, B, N1, N2, N3, S, H, L, and M introduced in the previous chapter are the elasticity matrices. They depend on elastic constants only, and appear frequently in the solutions to two-dimensional problems. The matrices A, B, and M are complex while the others are real. We present their structures and identities relating them in this chapter. In Chapter 7 we will show that A and B are tensors of rank one and S, H, L, and M are tensors of rank two when the transformation is a rotation about the x3-axis. Readers who are not interested in how the structures of these matrices and the identities relating them are derived may skip this chapter. They may return to this chapter when they read later chapters on applications where the results presented here are employed.