orthorhombic_symmetry¶
- torch_sim.elastic.orthorhombic_symmetry(strains)[source]¶
Generate equation matrix for orthorhombic crystal symmetry.
Constructs the stress-strain relationship matrix for orthorhombic symmetry, which has nine independent elastic constants: C11, C12, C13, C22, C23, C33, C44, C55, and C66.
- Parameters:
strains (Tensor) – Tensor of shape (6,) containing strain components [εxx, εyy, εzz, εyz, εxz, εxy]
- Returns:
- Matrix of shape (6, 9) where columns correspond to
coefficients for C11, C12, C13, C22, C23, C33, C44, C55, C66
- Return type:
Notes
The resulting matrix M has the form: ⎡ εxx εyy εzz 0 0 0 0 0 0 ⎤ ⎢ 0 εxx 0 εyy εzz 0 0 0 0 ⎥ ⎢ 0 0 εxx 0 εyy εzz 0 0 0 ⎥ ⎢ 0 0 0 0 0 0 2εyz 0 0 ⎥ ⎢ 0 0 0 0 0 0 0 2εxz 0 ⎥ ⎣ 0 0 0 0 0 0 0 0 2εxy⎦