Scripts to plot Mohr circles.

mohr2d.py

"""
Mohr circle in 2D.

@author: Nicolás Guarín-Zapata
@date: May 2020
"""
import numpy as np
import matplotlib.pyplot as plt
from matplotlib import rcParams
rcParams['font.family'] = 'serif'
rcParams['font.size'] = 16 


def mohr(S):
    """Plot Mohr circle for a 2D tensor"""
    S11 = S[0][0] 
    S12 = S[0][1] 
    S22 = S[1][1] 
    center = [(S11 + S22)/2.0, 0.0]
    radius = np.sqrt((S11 - S22)**2/4.0 + S12**2)
    Smin = center[0] - radius
    Smax = center[0] + radius

    print("Minimum Normal Stress: %g" % Smin)
    print("Maximum Normal Stress: %g" % Smax)
    print("Average Normal Stress: %g" % center[0])
    print("Minimum Shear Stress: %g" % -radius)
    print("Maximum Shear Stress: %g" % radius)

    circ = plt.Circle((center[0],0), radius, facecolor='#cce885', lw=3,
    edgecolor='#5c8037') 
    plt.axis('image')
    ax = plt.gca() 
    ax.add_artist(circ)
    ax.set_xlim(Smin - .1*radius, Smax + .1*radius)
    ax.set_ylim(-1.1*radius, 1.1*radius)
    plt.plot([S22, S11], [S12, -S12], 'ko')
    plt.plot([S22, S11], [S12, -S12], 'k')
    plt.plot(center[0], center[1], 'o', mfc='w')
    plt.text(S22 + 0.1*radius, S12, 'A')
    plt.text(S11 + 0.1*radius, -S12, 'B')
    plt.xlabel(r"$\sigma$", size=18)
    plt.ylabel(r"$\tau$", size=18) 
    plt.show()
    return None


S = np.array([[1.0, 2.0],[2.0, -3.0]])
mohr(S)

plt.figure()
S2 = np.array([[2.0, 3.0],[3.0, 1.0]])
mohr(S2)
plt.show()

mohr3d.py

"""
Mohr circle in 3D.

@author: Nicolás Guarín-Zapata
@date: May 2020
"""
import numpy as np
import matplotlib.pyplot as plt
from scipy.linalg import eigvalsh
from matplotlib import rcParams
 
rcParams['font.family'] = 'serif'
rcParams['font.size'] = 16 


def plot_mohr3d(S):
    r"""Plot 3D Mohr circles."""
    
    S3, S2, S1 = eigvalsh(S)

    R_maj = 0.5*(S1 - S3)
    cent_maj = 0.5*(S1+S3)
    
    R_min = 0.5*(S2 - S3)
    cent_min = 0.5*(S2 + S3)
    
    R_mid = 0.5*(S1 - S2)
    cent_mid = 0.5*(S1 + S2)
    
    circ1 = plt.Circle((cent_maj,0), R_maj, facecolor='#cce885', lw=3,
                       edgecolor='#5c8037')
    circ2 = plt.Circle((cent_min,0), R_min, facecolor='w', lw=3,
                       edgecolor='#15a1bd')
    circ3 = plt.Circle((cent_mid,0), R_mid, facecolor='w', lw=3,
                       edgecolor='#e4612d')
    plt.axis('image')
    ax = plt.gca()
    ax.add_artist(circ1)
    ax.add_artist(circ2)
    ax.add_artist(circ3)
    ax.set_xlim(S3 - .1*R_maj, S1 + .1*R_maj)
    ax.set_ylim(-1.1*R_maj, 1.1*R_maj)
    plt.xlabel(r"$\sigma$", size=18)
    plt.ylabel(r"$\tau$", size=18)
    #plt.savefig('Mohr_circle_3D.svg')
    plt.show()

    
S = np.array([
    [90,0,95],
    [0,96,0],
    [95,0,-50]])    

plt.figure()
plot_mohr3d(S)

S2 = np.array([
    [1,0,0],
    [0,2,0],
    [0,0,4]])  

plt.figure()
plot_mohr3d(S2)
plt.show()