G2 Example 4

G2Example4.py

# ------------------------------------------------------------------------
# The following Python code is implemented by Professor Terje Haukaas at
# the University of British Columbia in Vancouver, Canada. It is made
# freely available online at terje.civil.ubc.ca together with notes,
# examples, and additional Python code. Please be cautious when using
# this code; it may contain bugs and comes without warranty of any kind.
# ------------------------------------------------------------------------

import matplotlib.pyplot as plt
from G2MaterialPlasticity import *
from G2MaterialBilinear import *
from G2MaterialBoucWen import *

# ------------------------------------------------------------------------
# INPUT
# ------------------------------------------------------------------------

# Applied strain history
strain0 = 0.005       # Magnitude of sin(x) strain history
nsine = 1.02           # Number of sine waves of length 2*pi
nsteps = 100          # Number of time steps from 0 to 2*pi

# Material parameters
E = 200000.0          # Young's modulus
fy = 350.0            # Yield stress
alpha = 0.01          # Second-slope stiffness factor
eta = 3               # Bouc-Wen sharpness
gamma = 0.5           # Bouc-Wen parameter
beta = 0.5            # Bouc-Wen parameter
tolerance = 1e-3      # Newton-Raphson within Bouc-Wen
maxNumIter = 100      # Newton-Raphson within Bouc-Wen
H = alpha*E/(1-alpha) # Kinematic hardening parameter
K = 1                 # Linear isotropic hardening parameter
delta = 0             # Saturation isotropic hardening parameter
fy_inf = 100.0        # Asymptotic yield stress for saturation isotropic hardening

# ------------------------------------------------------------------------
# RESPONSE TO sin(x) STRAIN HISTORY
# ------------------------------------------------------------------------

# Create the plot
plt.clf()
plt.ion()
plt.title('Stress-strain curve')
plt.grid(True)
plt.autoscale(True)
plt.ylabel('Stress')
plt.xlabel('Strain')

# Create storage for results
pseudoTime = []
strainArray = []
bilinearStressArray = []
plasticStressArray = []
boucWenStressArray = []

# Start at zero
pseudoTime.append(0.0)
strainArray.append(0.0)
bilinearStressArray.append(0.0)
plasticStressArray.append(0.0)
boucWenStressArray.append(0.0)

# Create the material objects
thePlasticityMaterial = plasticityMaterial(['Plasticity', E, fy, H, K, delta, fy_inf])
theBilinearMaterial = bilinearMaterial(['Bilinear', E, fy, alpha])
theBoucWenMaterial = boucWenMaterial(['BoucWen', E, fy, alpha, eta, beta, gamma, tolerance, maxNumIter])

# Walk along the sine function
previousStrain = 0.0
for n in range(int(nsine*float(nsteps))):

    # Compute value of strain driving the problem
    totalStrain = strain0 * np.sin(n * 2 * np.pi / nsteps)
    strainIncrement = totalStrain - previousStrain
    previousStrain = totalStrain

    # Material state determination (give strain in U-vector format)
    [plasticStress, stiffness] = thePlasticityMaterial.state([totalStrain, 0.0, 0.0])
    [bilinearStress, stiffness] = theBilinearMaterial.state([totalStrain, strainIncrement, 0.0])
    [boucWenStress, stiffness] = theBoucWenMaterial.state([totalStrain, strainIncrement, 0.0])

    # Commit the state
    thePlasticityMaterial.commit()
    theBilinearMaterial.commit()
    theBoucWenMaterial.commit()

    # Add results to storage
    pseudoTime.append(n+1)
    strainArray.append(totalStrain)
    bilinearStressArray.append(bilinearStress)
    plasticStressArray.append(plasticStress)
    boucWenStressArray.append(boucWenStress)

    # Add points to plot
    plt.plot(strainArray, bilinearStressArray, 'bo-', linewidth=1.0, markersize=5, label='Bilinear')
    plt.plot(strainArray, plasticStressArray, 'ro-', linewidth=1.0, markersize=2, label='Plasticity')
    plt.plot(strainArray, boucWenStressArray, 'ko-', linewidth=1.0, markersize=2, label='Bouc-Wen')
    if n == 0:
        plt.legend()
    plt.pause(0.001)

# Pause and view the plot
print('\n'"Click somewhere in the plot to continue...")
#plt.savefig('Figure.pdf', format='pdf')
plt.waitforbuttonpress()