trigonal_symmetry¶
- torch_sim.elastic.trigonal_symmetry(strains)[source]¶
Generate equation matrix for trigonal crystal symmetry.
Constructs the stress-strain relationship matrix for trigonal symmetry, which has 7 independent elastic constants: C11, C12, C13, C14, C15, C33, C44. Matrix construction follows the standard form for trigonal symmetry.
- Parameters:
strains (Tensor) – Tensor of shape (6,) containing strain components [εxx, εyy, εzz, εyz, εxz, εxy]
- Returns:
- Matrix of shape (6, 7) where columns correspond to
coefficients for C11, C12, C13, C14, C15, C33, C44
- Return type:
Notes
The resulting matrix M has the form: ⎡ εxx εyy εzz 2εyz 2εxz 0 0 ⎤ ⎢ εyy εxx εzz -2εyz -2εxz 0 0 ⎥ ⎢ 0 0 εxx+εyy 0 0 εzz 0 ⎥ ⎢ 0 0 0 εxx-εyy -2εxy 0 2εyz ⎥ ⎢ 0 0 0 2εxy εxx-εyy 0 2εxz ⎥ ⎣ εxy -εxy 0 2εxz -2εyz 0 0 ⎦