mechmean.hill_polarization

Polarizations for isotropic matrices

class mechmean.hill_polarization.Factory[source]

Factory layer for Hill polarization tensors based on mechmean.hill_polarization.Castaneda

Alternative implementations based on other references are given in mechmean.hill_polarization_alternatives and tested against this factory.

spheroid(aspect_ratio, matrix)[source]

Parameters

aspect_ratio (float) – Ratio of first half axis and remaining half axes of spheroid
matrix (mechkit.material.Isotropic) – Isotropic matrix material

Returns

Hill polarization tensor

Return type

np.array (mandel6_4)

sphere(matrix)[source]

Parameters: matrix (mechkit.material.Isotropic) – Isotropic matrix material
Returns: Hill polarization tensor
Return type: np.array (mandel6_4)

needle(matrix)[source]

Parameters: matrix (mechkit.material.Isotropic) – Isotropic matrix material
Returns: Hill polarization tensor
Return type: np.array (mandel6_4)

class mechmean.hill_polarization.Castaneda[source]

Hill polarization tensor

spheroid(aspect_ratio, matrix)[source]

Combination of appendix C of [Castaneda1997], equation (4.39) [Willis1981], formulas (2.57) and (2.58) in [Brylka2017].

The first principle semi-axis is aligned with the global axis e_0.