Discussion
The number of independent elastic constants that a fully anisotropic linear elastic material can have is ______.
Answer: B
A fully anisotropic linear elastic material has 21 independent elastic constants.
Hooke's law relates the six stress components to the six strain components through a 6 x 6 stiffness matrix of 36 entries. The existence of a strain energy function makes this matrix symmetric, which leaves
\[ \frac{6 \times 7}{2} = 21 \]
independent constants.
36 counts every entry and ignores that symmetry. 2 is the number for an isotropic material (for example E and \(\nu\), or the two Lame constants), and 9 is the orthotropic case; 10 does not correspond to the general anisotropic material.
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