homopy.elasticity module

Created on Wed Apr 27 21:09:24 2022

@author: nicolas.christ@kit.edu

Module that contains the linear elastic stiffness classes of Isotropy and Transverse Isotropy.

class homopy.elasticity.Elasticity[source]

Bases: Tensor

Elasticity class to express generic elasitc stiffness tensors. The class inherits from the Tensor class.

Variables:

  • ~Elasticity.stiffness3333 (ndarray of shape (3, 3, 3, 3)) – Stiffness values in the regular tensor notation in Pa.

  • ~Elasticity.stiffness66 (ndarray of shape (6, 6)) – Stiffness values in the normalized Voigt notation in Pa.

class homopy.elasticity.TransverseIsotropy(E1, E2, G12, G23, nu12)[source]

Bases: Elasticity

Transverse Isotropy class to express transverse-isotropic elasitc stiffness tensors. The class inherits from the Elasticity class.

Parameters:

  • E1 (float) – Young’s modulus in longitudinal direction in Pa.

  • E2 (float) – Young’s modulus in transverse direction in Pa.

  • G12 (float) – Shear modulus in the longitudinal-transverse plane in Pa.

  • G23 (float) – Shear modulus in the transverse-transverse plane in Pa.

  • nu12 (float) – Poisson’s ratio in longitudinal direction (dimensionless).

Variables:

  • ~TransverseIsotropy.E1 (float) – Young’s modulus in longitudinal direction in Pa.

  • ~TransverseIsotropy.E2 (float) – Young’s modulus in transverse direction in Pa.

  • ~TransverseIsotropy.G12 (float) – Shear modulus in the longitudinal-transverse plane in Pa.

  • ~TransverseIsotropy.G23 (float) – Shear modulus in the transverse-transverse plane in Pa.

  • ~TransverseIsotropy.nu12 (float) – Poisson’s ratio in longitudinal direction (dimensionless).

  • ~TransverseIsotropy.nu23 (float) – Poisson’s ratio in transverse direction (dimensionless).

_get_stiffness()[source]

Calculate the stiffness parameters for both notations.

class homopy.elasticity.Isotropy(E, nu)[source]

Bases: TransverseIsotropy

Isotropy class to express isotropic elasitc stiffness tensors. The class inherits from the Transverse Isotropy class.

Parameters:

  • E (float) – Young’s modulus in Pa.

  • nu (float) – Poisson’s ratio (dimensionless).

Variables:

  • ~Isotropy.E (float) – Young’s modulus in Pa.

  • ~Isotropy.nu (float) – Poisson’s ratio (dimensionless).

  • ~Isotropy.lam (float) – First Lamé constant in Pa.

  • ~Isotropy.mu (float) – Second Lamé constant in Pa.

_get_lambda()[source]

Return the first Lamé constant from other material parameters.

Returns:

float – First Lamé constant in Pa.

_get_mu()[source]

Return the second Lamé constant from other material parameters.

Returns:

float – Second Lamé constant in Pa.