monoclinic_symmetry¶
- torch_sim.elastic.monoclinic_symmetry(strains)[source]¶
Generate equation matrix for monoclinic crystal symmetry.
Constructs the stress-strain relationship matrix for monoclinic symmetry, which has 13 independent elastic constants: C11, C12, C13, C15, C22, C23, C25, C33, C35, C44, C46, C55, C66.
- Parameters:
strains (Tensor) – Tensor of shape (6,) containing strain components [εxx, εyy, εzz, εyz, εxz, εxy]
- Returns:
- Matrix of shape (6, 13) where columns correspond to
coefficients for the 13 independent constants in order: [C11, C12, C13, C15, C22, C23, C25, C33, C35, C44, C46, C55, C66]
- Return type:
Notes
For monoclinic symmetry with unique axis b (y), the matrix has the form: ⎡ εxx εyy εzz 2εxz 0 0 0 0 0 0 0 0 0 ⎤ ⎢ 0 εxx 0 0 εyy εzz 2εxz 0 0 0 0 0 0 ⎥ ⎢ 0 0 εxx 0 0 εyy 0 εzz 2εxz 0 0 0 0 ⎥ ⎢ 0 0 0 0 0 0 0 0 0 2εyz 2εxy 0 0 ⎥ ⎢ 0 0 0 εxx 0 0 εyy 0 εzz 0 0 2εxz 0 ⎥ ⎣ 0 0 0 0 0 0 0 0 0 0 2εyz 0 2εxy⎦