Initial commits to calculate non-linear material response using the t…

…rained ML function to reconstruct stress strain curves.

examples/data_6d/Stress_Strain_Calculation.py

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+"""
+Use trained ML yield function tos calculate the elastic-plastic behavior of  the material
+This example is for a simple monotonic loading in x-direction
+Authors:  Ronak Shoghi, Alexander Hartmaier
+ICAMS/Ruhr University Bochum, Germany
+October 2023
+"""
+
+import pylabfea as FE
+import numpy as np
+import matplotlib.pyplot as plt
+import src.pylabfea.training as CTD
+import math
+from matplotlib.lines import Line2D
+import matplotlib.lines as mlines
+
+def construct_CV(C11, C12, C44):
+    """
+    Construct the elastic stiffness matrix in Voigt notation for a cubic crystal.
+
+    Parameters:
+    - C11, C12, C44: Material's elastic constants
+
+    Returns:
+    - CV: Elastic stiffness matrix
+    """
+    return np.array([
+        [C11, C12, C12, 0, 0, 0],
+        [C12, C11, C12, 0, 0, 0],
+        [C12, C12, C11, 0, 0, 0],
+        [0, 0, 0, C44, 0, 0],
+        [0, 0, 0, 0, C44, 0],
+        [0, 0, 0, 0, 0, C44]
+    ])
+
+# Import Data
+db = FE.Data("Data_Base_Updated_Final_Rotated_Train.JSON", wh_data=True)
+mat_ref = FE.Material(name="reference")  # define reference material, J2 plasticity, linear w.h.
+mat_ref.elasticity(E=db.mat_data['E_av'], nu=db.mat_data['nu_av'])
+mat_ref.plasticity(sy=db.mat_data['sy_av'], khard=4.5e3)
+mat_ref.calc_properties(verb=False, eps=0.03, sigeps=True)
+
+# db.plot_yield_locus(db =db, mat_data= db.mat_data, active ='flow_stress')
+print(f'Successfully imported data for {db.mat_data["Nlc"]} load cases')
+mat_ml = FE.Material(db.mat_data['Name'], num=1)  # define material
+mat_ml.from_data(db.mat_data)  # data-based definition of material
+
+# Train SVC with data from all microstructures
+mat_ml.train_SVC(C=1, gamma=0.4, Fe=0.7, Ce=0.9, Nseq=2, gridsearch=False, plot=False)
+print(f'Training successful.\nNumber of support vectors: {len(mat_ml.svm_yf.support_vectors_)}')
+
+# Define elastic stiffness tensor
+CV = construct_CV(170, 124, 75)
+sig = np.zeros(6)
+epl = np.zeros(6)
+strains = [0]
+stresses = [0]
+
+# Strain increments to reach 3% strain in x-direction
+total_strain = 0.03
+n_increments = 100
+deps_increment = np.array([total_strain/n_increments, 0, 0, 0, 0, 0])
+
+for i in range(n_increments):
+    # Use the response function to calculate the material response for the given strain increment
+    fy1, sig, depl, grad_stiff = mat_ml.response(sig, epl, deps_increment, CV)
+    epl += depl
+
+    stresses.append(sig[0])
+    strains.append(strains[-1] + deps_increment[0])
+
+# Plot stress-strain curve
+plt.scatter(strains, stresses)
+plt.xlabel("Strain")
+plt.ylabel("Stress")
+plt.show()