mods.strain_transformation

Module Contents

Functions

average_strain(epsilon_x, epsilon_y)

Calculates the average strain and returns the value.

normal_strain_transform(epsilon_x, epsilon_y, ...)

Applies a strain transformation to the given strains and returns the transformed strain value.

shear_strain_transform(epsilon_x, epsilon_y, gamma_xy, ...)

Applies a transformation to the given shear strain and returns the transformed shear strain value.

principal_strain(epsilon_x, epsilon_y, gamma_xy)

Calculates the principal strains and returns the values in a tuple.

principal_strain_angle(epsilon_x, epsilon_y, gamma_xy)

Calculates the principal directions and returns the values in a tuple.

maximum_in_plane_shear_strain(epsilon_x, epsilon_y, ...)

Calculates the maximum in-plane shear strain and returns the value.

maximum_in_plane_shear_strain_angle(epsilon_x, ...)

Calculates the angle of the maximum in-plane shear strain and returns the value.

mohrs_circle(epsilon_x, epsilon_y, gamma_xy)

Calculates the center and radius of the Mohr's circle and returns the values in a tuple.

mohrs_circle_plot(epsilon_x, epsilon_y, gamma_xy)

Plots the Mohr's circle and returns the plot.

mohrs_circle_strain(epsilon_x, epsilon_y, gamma_xy, theta)

Calculates the center and radius of the transformed Mohr's circle and returns the values in a tuple.

mohrs_circle_strain_plot(epsilon_x, epsilon_y, ...)

Plots the Mohr's circle and a point representing the transformed strain state and returns the plot.
mods.strain_transformation.average_strain(epsilon_x, epsilon_y)[source]

Calculates the average strain and returns the value.

Parameters:

  • epsilon_x (float) – Strain value in the x-direction

  • epsilon_y (float) – Strain value in the y-direction

Returns:

Average strain value

Return type:

float

mods.strain_transformation.normal_strain_transform(epsilon_x, epsilon_y, gamma_xy, theta)[source]

Applies a strain transformation to the given strains and returns the transformed strain value.

Parameters:

  • epsilon_x (float) – Strain value in the x-direction

  • epsilon_y (float) – Strain value in the y-direction

  • gamma_xy (float) – Shear strain value in the xy-plane

  • theta (float) – Angle of rotation in degrees

Returns:

Transformed strain value in the x’-direction and y’-direction

Return type:

tuple

mods.strain_transformation.shear_strain_transform(epsilon_x, epsilon_y, gamma_xy, theta)[source]

Applies a transformation to the given shear strain and returns the transformed shear strain value.

Parameters:

  • epsilon_x (float) – Strain value in the x-direction

  • epsilon_y (float) – Strain value in the y-direction

  • gamma_xy (float) – Shear strain value in the xy-plane

  • theta (float) – Angle of rotation in degrees

Returns:

Transformed shear strain value in the x’y’-plane

Return type:

float

mods.strain_transformation.principal_strain(epsilon_x, epsilon_y, gamma_xy)[source]

Calculates the principal strains and returns the values in a tuple.

Parameters:

  • epsilon_x (float) – Strain value in the x-direction

  • epsilon_y (float) – Strain value in the y-direction

  • gamma_xy (float) – Shear strain value in the xy-plane

Returns:

Principal strain values in the x’-direction and y’-direction

Return type:

tuple

mods.strain_transformation.principal_strain_angle(epsilon_x, epsilon_y, gamma_xy)[source]

Calculates the principal directions and returns the values in a tuple.

Parameters:

  • epsilon_x (float) – Strain value in the x-direction

  • epsilon_y (float) – Strain value in the y-direction

  • gamma_xy (float) – Shear strain value in the xy-plane

Returns:

Principal direction values in degrees

Return type:

tuple

mods.strain_transformation.maximum_in_plane_shear_strain(epsilon_x, epsilon_y, gamma_xy)[source]

Calculates the maximum in-plane shear strain and returns the value.

Parameters:

  • epsilon_x (float) – Strain value in the x-direction

  • epsilon_y (float) – Strain value in the y-direction

  • gamma_xy (float) – Shear strain value in the xy-plane

Returns:

Maximum in-plane shear strain value

Return type:

float

mods.strain_transformation.maximum_in_plane_shear_strain_angle(epsilon_x, epsilon_y, gamma_xy)[source]

Calculates the angle of the maximum in-plane shear strain and returns the value.

Parameters:

  • epsilon_x (float) – Strain value in the x-direction

  • epsilon_y (float) – Strain value in the y-direction

  • gamma_xy (float) – Shear strain value in the xy-plane

Returns:

Angle of the maximum in-plane shear strain value in degrees

Return type:

float

mods.strain_transformation.mohrs_circle(epsilon_x, epsilon_y, gamma_xy)[source]

Calculates the center and radius of the Mohr’s circle and returns the values in a tuple.

Parameters:

  • epsilon_x (float) – Strain value in the x-direction

  • epsilon_y (float) – Strain value in the y-direction

  • gamma_xy (float) – Shear strain value in the xy-plane

Returns:

Center and radius of the Mohr’s circle

Return type:

tuple

mods.strain_transformation.mohrs_circle_plot(epsilon_x, epsilon_y, gamma_xy)[source]

Plots the Mohr’s circle and returns the plot.

Parameters:

  • epsilon_x (float) – Strain value in the x-direction

  • epsilon_y (float) – Strain value in the y-direction

  • gamma_xy (float) – Shear strain value in the xy-plane

Returns:

Plot of the Mohr’s circle

Return type:

matplotlib.pyplot.plot

mods.strain_transformation.mohrs_circle_strain(epsilon_x, epsilon_y, gamma_xy, theta)[source]

Calculates the center and radius of the transformed Mohr’s circle and returns the values in a tuple.

Parameters:

  • epsilon_x (float) – Strain value in the x-direction

  • epsilon_y (float) – Strain value in the y-direction

  • gamma_xy (float) – Shear strain value in the xy-plane

  • theta (float) – Angle of rotation in degrees

Returns:

Center and radius of the transformed Mohr’s circle

Return type:

tuple

mods.strain_transformation.mohrs_circle_strain_plot(epsilon_x, epsilon_y, gamma_xy, theta)[source]

Plots the Mohr’s circle and a point representing the transformed strain state and returns the plot.

Parameters:

  • epsilon_x (float) – Strain value in the x-direction

  • epsilon_y (float) – Strain value in the y-direction

  • gamma_xy (float) – Shear strain value in the xy-plane

  • theta (float) – Plane inclination angle in degrees

Returns:

Plot of the Mohr’s circle and transformed strain state

Return type:

matplotlib.pyplot.plot