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Constitutive Equations for Linearly Anisotropic Elastic Solid 293

Part B Linear Anisotropic Elastic Solid

5.22 Constitutive Equations for Linearly Anisotropic Elastic Solid
In Section 5. 2, we concluded that due to the symmetry of the strain and the stress tensors
EJJ and 7^- respectively, and the assumption that there exists a strain energy function U given
by U = l/2Cp/E«Ejy, the most general anisotropic elastic solid requires 21 elastic constants
for its description. We can write the stress-strain relation for this general case in the following
matrix notation:

The indices in Eq. (5.22.1) are quite cumbersome, but they emphasize the tensorial character
of the tensors T,E and C. Equation (5.22.1) is often written in the following "contracted form"
in which the indices are simplified or "contracted."

or

We note that Eq. (5.22.3a) can also be written in indicial notation

However, it must be emphasized that C,y are not components of a second order tensor and
Tf are not those of a vector.