regular_symmetry

torch_sim.elastic.regular_symmetry(strains)

Generate equation matrix for cubic (regular) crystal symmetry.

Constructs the stress-strain relationship matrix for cubic symmetry, which has three independent elastic constants: C11, C12, and C44.

The matrix relates strains to stresses according to the equation: σᵢ = Σⱼ Cᵢⱼ εⱼ

Parameters:

strains (Tensor) – Tensor of shape (6,) containing strain components [εxx, εyy, εzz, εyz, εxz, εxy] where: - εxx, εyy, εzz are normal strains - εyz, εxz, εxy are shear strains

Returns:

Matrix of shape (6, 3) where columns correspond to

coefficients for C11, C12, and C44 respectively

Return type:

Tensor

Notes

The resulting matrix M has the form: ⎡ εxx (εyy + εzz) 0 ⎤ ⎢ εyy (εxx + εzz) 0 ⎥ ⎢ εzz (εxx + εyy) 0 ⎥ ⎢ 0 0 2εyz ⎥ ⎢ 0 0 2εxz ⎥ ⎣ 0 0 2εxy ⎦

This represents the relationship: σxx = C11*εxx + C12*(εyy + εzz) σyy = C11*εyy + C12*(εxx + εzz) σzz = C11*εzz + C12*(εxx + εyy) σyz = 2*C44*εyz σxz = 2*C44*εxz σxy = 2*C44*εxy