elastic_constants.continuum_mechanics module#

Continuum mechanics module.

class elastic_constants.continuum_mechanics.Compliance[source]#

Bases: elastic_constants.tensor.Tensor

Compliance tensor class.

class elastic_constants.continuum_mechanics.DeformationGradient[source]#

Bases: elastic_constants.tensor.Tensor

Deformation gradient tensor class.

class elastic_constants.continuum_mechanics.Elasticity[source]#

Bases: elastic_constants.tensor.Tensor

Elasticity tensor class.

class elastic_constants.continuum_mechanics.Strain[source]#

Bases: elastic_constants.tensor.Tensor

Strain tensor class.

class elastic_constants.continuum_mechanics.Stress[source]#

Bases: elastic_constants.tensor.Tensor

Stress tensor class.

to_second_piola_kirchhoff(deformation_gradient)[source]#

Convert Cauchy stress to second Piola-Kirchhoff stress tensor.

Parameters:: deformation_gradient (DeformationGradient) – Deformation gradient tensor.
Returns:: Second Piola-Kirchhoff stress tensor.
Return type:: numpy.typing.NDArray[numpy.double]

Notes

The second Piola-Kirchhoff stress tensor \(S\) is related to the Cauchy stress tensor \(\sigma\) by the relation

\[S = J \, F^{-1} \cdot \sigma \cdot F^{-T}\]

where \(J\) is the determinant of the deformation gradient \(F\).