Plot Poisson ratio as 2D sections

This example shows how to plot the directional dependence of the Poisson ratio in XY, XZ and YZ planes.

Define the stiffness tensor for NiTi

We define the stiffness tensor for a monoclinic NiTi material using its elastic constants. They are taken from the Materials Project (mp-1048).

from elasticipy.tensors.elasticity import StiffnessTensor
C = StiffnessTensor.monoclinic(
    phase_name='TiNi',
    C11=231, C12=127, C13=104,
    C22=240, C23=131, C33=175,
    C44=81, C55=11, C66=85,
    C15=-18, C25=1, C35=-3, C46=3
)
print("Stiffness tensor for NiTi:\n", C)

Stiffness tensor for NiTi:
 Stiffness tensor (in Voigt mapping):
[[231. 127. 104.   0. -18.   0.]
 [127. 240. 131.   0.   1.   0.]
 [104. 131. 175.   0.  -3.   0.]
 [  0.   0.   0.  81.   0.   3.]
 [-18.   1.  -3.   0.  11.   0.]
 [  0.   0.   0.   3.   0.  85.]]
Phase: TiNi

Get the Poisson ratio from the stiffness tensor

nu = C.Poisson_ratio
print("Poisson ratio:")
print(nu)

Poisson ratio:
Hyperspherical function
Min=-0.550188605619326, Max=1.4394343811864985

Plot it as polar curves in planar sections

fig, ax = nu.plot_xyz_sections()