I am currently working on 3D topology optimization using finite element methods, and I'm looking for literature, blog posts, or precomputed resources that explicitly provide template stiffness matrices (24×24) for 8-node hexahedral elements corresponding to each of the 9 elasticity components in Voigt notation.

Specifically, I’m referring to the 9 individual stiffness templates Kij that are used to represent:

• Normal stiffness components: K00 → axial stiffness in the x-direction (C11) K11 → axial stiffness in the y-direction (C22) K22 → axial stiffness in the z-direction (C33)
• Shear stiffness components: K44 → shear stiffness in the yz-plane (C44) K55 → shear stiffness in the xz-plane (C55) K66 → shear stiffness in the xy-plane (C66)
• Coupling stiffness components (symmetric terms): K01 → coupling between x and y (C12) K02 → coupling between x and z (C13) K12 → coupling between y and z (C23)

I understand that these templates are often precomputed as part of the stiffness assembly process using the relation:

Ke​=∑​Cij​Kij​

I am looking for:

• Any public implementations or academic references that provide these 9 template matrices.
• Discussions or notes that derive them explicitly from the integral ∫BTDB dV\int B^T D B \, dV∫BTDBdV for hexahedral elements.
• Ways to validate or verify the correctness of these templates for symmetric elasticity tensors.

Any insights or references would be highly appreciated!