""" 304L bar calibration initial point estimation --------------------------------------------- In this example, we estimate an initial point for our full finite element model calibration to data from :cite:p:`laser_weld_paper`. We will use MatFit on the ASTME8 tension data to provide the initial point for the next example, :ref:`304L stainless steel viscoplastic calibration`. .. note:: Useful Documentation links: #. :ref:`Running MatFit` First, import all needed tools. We will be using tools from NumPy, MatPlotLib, MatFit and MatCal for this example. """ import numpy as np from matcal import * from matfit.models import Voce from matfit.fitting import MatFit import matplotlib.pyplot as plt plt.rc('text', usetex=True) plt.rc('font', family='serif') plt.rc('font', size=12) figsize = (4,3) #%% # We import the data using the # :class:`~matcal.core.data_importer.BatchDataImporter` tension_data = BatchDataImporter("ductile_failure_ASTME8_304L_data/*.dat", file_type="csv").batch #%% # To use MatFit, we need to extract certain quantities of interest (QoIs) # from each engineering stress strain curve. We need # the yield stress, ultimate stress, strain at ultimate stress and # the elongation strain for each test. We extract those from the # :class:`~matcal.core.data.DataCollection` below and store each # QoI set in a list to be used with MatFit. We use NumPy and # MatCal's :class:`~matcal.core.data_analysis.determine_pt2_offset_yield` # to determine these QoIs from the data. qoi_sets = [] steel_elastic_mod = 29e3 for state, data_sets in tension_data.items(): for data in data_sets: yield_pt = determine_pt2_offset_yield(data, steel_elastic_mod) yield_stress = yield_pt[1] ultimate_stress = np.max(data["engineering_stress"]) argmax = np.argmax(data["engineering_stress"]) strain_at_ultimate = data["engineering_strain"][argmax] elongation_strain = np.max(data["engineering_strain"]) qoi_sets.append([yield_stress, ultimate_stress, strain_at_ultimate, elongation_strain]) #%% # Next, we write a function that will take those QoIs and provide # an estimate for a Voce material model :cite:p:`voce1948relationship` using MatFit. # The function returns the Voce material parameters of # saturation stress (:math:`A`) and Voce exponent (:math:`b`) in a solution dictionary. # Since we already have an estimate for the yield, we will only be calibrating # :math:`A` and :math:`b` with MatFit. MatFit requires specific formatting # of input parameters. See the MatFit documentation for more information # :cite:p:`matfit`. The bounds for our two calibrated parameters are estimated # from the stress-strain curves and previous experience with the model # for austenitic stainless steels. def get_voce_params(yield_stress, ultimate_stress, strain_at_ultimate, elongation_strain): material_specification = dict( ultimate_strength = ultimate_stress, strain_at_ultimate = strain_at_ultimate, elongation = elongation_strain, yield_stress = yield_stress, youngs_modulus=steel_elastic_mod, poissons_ratio=0.27, density=7.41e-4) voce_parameters = dict( hardening_modulus=dict(value=200, lower=0, upper=1e3, calibrate=True), exponential_coefficient=dict(value=2.0, lower=0.0, upper=5, calibrate=True), ) voce_model = Voce(material_specification, voce_parameters, name='Voce') MF = MatFit(voce_model) MF.fit(solver_settings=dict(method='trf')) solution = MF.get_solution() return solution #%% # Next, we write another function to take the QoIs and calculate our # Voce material parameters. We will store those in a dictionary for # further analysis. voce_params = {"Ys":[], "As":[], "bs":[]} for qoi_set in qoi_sets: voce_params["Ys"].append(qoi_set[0]) solution = get_voce_params(*qoi_set) voce_params["As"].append(solution['hardening_modulus']) voce_params["bs"].append(solution['exponential_coefficient']) #%% # First, we make histograms of each parameter. # We want to ensure the parameters are as expected and # try to understand the cause of any multi-modal behavior. figsize=[4,3] plt.figure("Ys", figsize, constrained_layout=True) plt.hist(voce_params["Ys"], density=True, alpha=0.8) plt.xlabel("Y (ksi)") plt.ylabel("PDF") plt.figure("As", figsize, constrained_layout=True) plt.hist(voce_params["As"], density=True, alpha=0.8) plt.xlabel("A (Ksi)") plt.ylabel("PDF") plt.figure("bs", figsize, constrained_layout=True) plt.hist(voce_params["bs"], density=True, alpha=0.8) plt.xlabel("b") plt.ylabel("PDF") #%% # From these plots there is some slight grouping. However, # the parameter values are not spread out over a large range # indicating MatFit has provided a good initial guess for the parameters. # We can plot the data collection and verify that two groupings of the data are # present. We do this with MatCal's :meth:`~matcal.core.data.DataCollection.plot` # method for :class:`~matcal.core.data.DataCollection` objects. tension_fig = plt.figure("data", (5,4), constrained_layout=True) tension_data.plot("engineering_strain", "engineering_stress", figure=tension_fig, labels='ASTME8 data', color="#bdbdbd") plt.xlabel("engineering strain") plt.ylabel("engineering stress (ksi)") #%% # In this plot, two groupings of the data can be seen since there are two # groups with different elongation strains. This verifies the # results seen in the histograms. Since these tension specimens were # extracted from a large diameter bar, the different groupings likely # correspond to extraction location and the resulting groupings in stress-strain # behavior are expected. # # Since we are ignoring any material inhomogeneity for this calibration, # we will take the average of all calculated values and save that # as the initial point for our full finite element model calibration. voce_initial_point = {} voce_initial_point["Y_0"] = np.average(voce_params["Ys"]) voce_initial_point["A"] = np.average(voce_params["As"]) voce_initial_point["b"] = np.average(voce_params["bs"]) print(voce_initial_point) matcal_save("voce_initial_point.serialized", voce_initial_point)