homopy.stiffness_plot module

Created on Thu Apr 28 16:24:54 2022

@author: nicolas.christ@kit.edu

3D and Polar plot of Young’s modulus body based on [Boehlke2001].

class homopy.stiffness_plot.ElasticPlot(USEVOIGT=False)[source]

Bases: Tensor

Plot class to visualize tensorial results.

Parameters:

USEVOIGT (boolean) – Flag which determines the usage of Voigt (USEVOIGT=True), or Normalized Voigt / Mandel (USEVOIGT=False).

Variables:

~ElasticPlot.USEVOIGT (boolean) – Flag which determines the usage of Voigt (USEVOIGT=True), or Normalized Voigt / Mandel (USEVOIGT=False).

matrix_reduction(matrix)[source]

Return the reduced notation (Voigt or normalized Voigt) depending on which one is ought to be used.

Parameters:

matrix (ndarray of shape (3, 3)) – Tensor in regular tensor notation.

Returns:

ndarray of shape (6,) – Tensor in Voigt or normalized Voigt notation.

static _get_reciprocal_E(didi, S)[source]

Return the reciprocal of Young’s modulus (compliance) in the direction of di.

Parameters:

  • didi (ndarray of shape (6,)) – Directional tensor.

  • S (ndarray of shape (6, 6)) – Compliance tensor in Voigt or normalized Voigt notation.

Returns:

float – Scalar compliance value in direction of di.

_get_E(di, S)[source]

Return Young’s modulus in the direction of di.

Parameters:

  • di (ndarray of shape (3,)) – Directional vector.

  • S (ndarray of shape (6, 6)) – Compliance tensor in Voigt or normalized Voigt notation.

Returns:

float – Scalar stiffness value in direction of didi.

static _dir_vec(phi, theta)[source]

Return directional vector based on angular parametrization.

Parameters:

  • phi (float) – First angle in [0, 2*pi].

  • theta (float) – Second angle in [0, pi].

Returns:

ndarray of shape (3,) – Directional vector.

plot_E_body(C, o, p, bound=None, rcount=200, ccount=200)[source]

Plot stiffness body.

Parameters:

  • C (ndarray of shape (6, 6)) – Stiffness tensor in Voigt or normalized Voigt notation.

  • o (int) – Number of discretization steps for first angle.

  • p (int) – Number of discretization steps for second angle.

  • bound (array of shape (3,), default=None) – Boundaries for the 3 axis for the visualization. If None, boundaries are set automatically.

  • rcount (int) – Maximum number of samples used in first angle direction. If the input data is larger, it will be downsampled (by slicing) to these numbers of points. Defaults to 200.

  • ccount (int) – Maximum number of samples used in second angle direction. If the input data is larger, it will be downsampled (by slicing) to these numbers of points. Defaults to 200.

polar_plot_E_body(C, o, angle, plot=True)[source]

Plot slice of stiffness body.

Parameters:

  • C (ndarray of shape (6, 6)) – Stiffness tensor in Voigt or normalized Voigt notation.

  • o (int) – Number of discretization steps for first angle.

  • angle (float) – Angle to determine the angular orientation of the slice. Does not work yet.

  • plot (boolean) – Determines whether the plot will be displayed. If False, only the metadata of the plot will be returned.

Returns:

  • rad (ndarray of shape (n+1,)) – Angular positions for polar plot.

  • E (ndarray of shape (n+1,)) – Sitffness at corresponding angle.

static polar_plot(data)[source]

Polar plot of multiple Stiffness bodies in one plot. For this use the data generated from polar_plot_E_body or polar_plot_laminate with plot=False.

Parameters:

data (list) – Data to be plotted with angluar position, stiffness and an optional string for the label in the plot.

polar_plot_laminate(laminate_stiffness, o, limit=None, plot=True)[source]

Polar plot stiffness body of laminate. This method should be used for laminate results for the Halpin-Tsai homogenization.

Parameters:

  • laminate_stiffness (ndarray of shape (3, 3)) – Planar stiffness matrix in Voigt or normalized Voigt notation.

  • o (int) – Number of discretization steps for first angle.

  • limit (float) – Limit of radial axis in polar plot.

  • plot (boolean) – Determines whether the plot will be displayed. If False, only the metadata of the plot will be returned.

Returns:

  • rad (ndarray of shape (n+1,)) – Angular positions for polar plot.

  • E (ndarray of shape (n+1,)) – Sitffness at corresponding angle.

get_E_laminate(C, phi)[source]

Return Young’s modulus of laminate as a function of angle omega.

Parameters:

  • C (ndarray of shape (3, 3)) – Stiffness of laminate in default (orthonormal) coordinate system.

  • phi (float) – Angle of orientation in radians.

Returns:

E (float) – Young’s modulus in angle direction