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:

Tensor

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 ⎦