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:
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 ⎦