tetragonal_symmetry

torch_sim.elastic.tetragonal_symmetry(strains)[source]

Generate equation matrix for tetragonal crystal symmetry.

Constructs the stress-strain relationship matrix for tetragonal symmetry, which has 7 independent elastic constants: C11, C12, C13, C16, C33, C44, C66.

Parameters:

strains (Tensor) – Tensor of shape (6,) containing strain components [εxx, εyy, εzz, εyz, εxz, εxy] where: - εxx, εyy, εzz are normal strains - εyz, εxz, εxy are shear strains

Returns:

Matrix of shape (6, 7) where columns correspond to

coefficients for C11, C12, C13, C16, C33, C44, C66

Return type:

Tensor

Notes

The resulting matrix M has the form: ⎡ εxx εyy εzz 2εxy 0 0 0 ⎤ ⎢ εyy εxx εzz -2εxy 0 0 0 ⎥ ⎢ 0 0 εxx+εyy 0 εzz 0 0 ⎥ ⎢ 0 0 0 0 0 2εyz 0 ⎥ ⎢ 0 0 0 0 0 2εxz 0 ⎥ ⎣ 0 0 0 εxx-εyy 0 0 2εxy ⎦