hexagonal_symmetry¶
- torch_sim.elastic.hexagonal_symmetry(strains)[source]¶
Generate equation matrix for hexagonal crystal symmetry.
Constructs the stress-strain relationship matrix for hexagonal symmetry, which has 5 independent elastic constants: C11, C33, C12, C13, C44. Note: C66 = (C11-C12)/2 is dependent.
- Parameters:
strains (Tensor) – Tensor of shape (6,) containing strain components [εxx, εyy, εzz, εyz, εxz, εxy]
- Returns:
- Matrix of shape (6, 5) where columns correspond to
coefficients for C11, C33, C12, C13, C44
- Return type:
Notes
The resulting matrix M has the form: ⎡ εxx εyy εzz 0 0 ⎤ ⎢ εyy εxx εzz 0 0 ⎥ ⎢ 0 0 εxx+εyy εzz 0 ⎥ ⎢ 0 0 0 0 2εyz⎥ ⎢ 0 0 0 0 2εxz⎥ ⎣ εxy -εxy 0 0 0 ⎦