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PlottingUtils.py
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PlottingUtils.py
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import numpy as np
import matplotlib.pyplot as plt
from MicroMesh import MicroMesh, MicroSolver, circles_microstructure
from tqdm import tqdm
from scipy.stats import multivariate_normal
from VoigtReussSens import get_VR_sens
def int_logscale(max_n):
init_scale = np.logspace(np.log10(3), np.log10(max_n), num=30)
return np.unique(init_scale.astype(int))
def Converge(mat_1_params=[10E9, 0.32], mat_2_params=[80E9, 0.22], rel_conc=0.55, nxs=np.array([3, 5, 6, 7,8,9,10,11, 13, 16, 21]), num_candidates=4):
E_1, nu_1 = mat_1_params
E_2, nu_2 = mat_2_params
Cs = np.zeros((nxs.shape[0], 3, 3))
C_errs = np.zeros_like(Cs)
temp_Cs = np.zeros((num_candidates, 3, 3))
real_concs = np.zeros((nxs.shape[0]))
nnodes = np.zeros_like(real_concs)
Es = np.zeros_like(nnodes)
E_errs = np.zeros_like(nnodes)
E_tmp = np.zeros((num_candidates))
nus = np.zeros_like((Es))
nu_errs = np.zeros_like((nus))
nu_tmp = np.zeros_like(E_tmp)
print(f"Using nx values of {nxs}")
for i in tqdm(range(len(nxs)), desc="Running through nx values"):
nx = nxs[i]
for j in tqdm(range(num_candidates), desc="Testing ensemble of Meshes", leave=False):
mesh = MicroMesh(nx, nx, E_1, E_2, nu_1, nu_2, rel_conc)#, micro_fun=circles_microstructure)
solver = MicroSolver(mesh)
temp_Cs[j, :, :] = solver.homogenize()
E_tmp[j], nu_tmp[j] = solver.infer_props()
Cs[i, :, :] = np.average(temp_Cs, axis=0)
C_errs[i, :, :] = np.average((temp_Cs - Cs[i, :, :])**2, axis=0)
Es[i] = np.average(E_tmp)
E_errs[i] = np.average((E_tmp - Es[i])**2)
nus[i] = np.average(nu_tmp)
nu_errs[i] = np.average((nu_tmp - nus[i])**2)
real_concs[i] = np.sum([el.E == E_1 for el in mesh.ELS])/mesh.ELS.shape[0]
nnodes[i] = mesh.nnodes
C_errs = np.sqrt(C_errs)
E_errs = np.sqrt(E_errs)
nu_errs = np.sqrt(nu_errs)
return Cs, C_errs, Es, E_errs, nus, nu_errs, real_concs, nnodes
def plot_c_converge(Cs, C_errs, Es, E_errs, nus, nu_errs, real_concs, nnodes, mat_1_params=[10E9, 0.32], mat_2_params=[80E9, 0.22], rel_conc=0.55):
E_1, nu_1 = mat_1_params
E_2, nu_2 = mat_2_params
mesh = MicroMesh(3, 3, E_1, E_2, nu_1, nu_2, rel_conc)
solver = MicroSolver(mesh)
voigt_C = solver.Voigt()/1E9
reuss_C = solver.Reuss()/1E9
C_1 = solver.elasticity(E_1, nu_1)/1E9
C_2 = solver.elasticity(E_2, nu_2)/1E9
Cs = Cs.copy()/1E9
C_errs = C_errs.copy()/1E9
Es = Es.copy()/1E9
E_errs = E_errs/1E9
fig, ax = plt.subplots(3, 3, figsize=(14.0, 14.0))
font_size=20
for i in range(3):
for j in range(3):
ax[i, j].plot(nnodes, Cs[:, i, j], label="Homogenized", color='k')
ax[i, j].fill_between(nnodes, Cs[:, i, j] + 2*C_errs[:, i, j], Cs[:, i, j] - 2*C_errs[:, i, j], color='C3', alpha=0.3)
ax[i, j].hlines(voigt_C[i, j], 0, np.max(nnodes), label='Voigt bound', color='C1', linestyle='dashed')
ax[i, j].hlines(reuss_C[i, j], 0, np.max(nnodes), label='Reuss bound', color='C2', linestyle='dashed')
#ax[i, j].hlines(C_1[i, j], 0, np.max(nnodes), label='Material 1', color='C3', linestyle='dashed')
#ax[i, j].hlines(C_2[i, j], 0, np.max(nnodes), label='Material 2', color='C4', linestyle='dashed')
ax[i, j].set_title(f"Convergence of $C_{{{i + 1},{j + 1}}}$")
ax[i, j].set_xlabel("Total Number of Nodes")
ax[i, j].set_ylabel("Estimated Elastic Property/GPa")
ax[i, j].set_xscale('log')
# if (i<2 and j<2) or (i==2 and j==2):
# ax[i, j].set_yscale("log")
ax[i, j].legend()
plt.tight_layout()
plt.savefig("C_convergence.png")
E_voigt, nu_voigt = solver.infer_props(voigt_C*1E9)
E_reuss, nu_reuss = solver.infer_props(reuss_C*1E9)
E_voigt /= 1E9
E_reuss /= 1E9
fig, ax = plt.subplots(nrows=3, figsize=(14.0, 7.0))
ax[0].plot(nnodes, Es, label="Homogenized", color='k')
ax[0].fill_between(nnodes, Es + 2*E_errs, Es - 2*E_errs, color='C3', alpha=0.3)
ax[0].hlines(E_voigt, 0, np.max(nnodes), label='Voigt bound', color='C1', linestyle='dashed')
ax[0].hlines(E_reuss, 0, np.max(nnodes), label='Reuss bound', color='C2', linestyle='dashed')
ax[0].set_title("Convergence of $E_{eff}$")
ax[0].set_xlabel("Total Number of Nodes")
ax[0].set_ylabel("Estimated\nYoung's Modulus/GPa")
ax[0].set_xscale('log')
ax[0].legend()
ax[1].plot(nnodes, nus, label="Homogenized", color='k')
ax[1].fill_between(nnodes, nus + 2*nu_errs, nus - 2*nu_errs, color='C3', alpha=0.3)
ax[1].hlines(nu_voigt, 0, np.max(nnodes), label='Voigt bound', color='C1', linestyle='dashed')
ax[1].hlines(nu_reuss, 0, np.max(nnodes), label='Reuss bound', color='C2', linestyle='dashed')
ax[1].set_title(r"Convergence of $\nu_{eff}$")
ax[1].set_xlabel("Total Number of Nodes")
ax[1].set_ylabel("Estimated\nPoisson's Ratio")
ax[1].set_xscale('log')
ax[1].legend()
ax[2].plot(nnodes, real_concs, label="Simulated", color='k')
ax[2].hlines(rel_conc, 0, np.max(nnodes), label='Target', color='C1', linestyle='dashed')
ax[2].set_title("Convergence of Relative Concentration")
ax[2].set_xlabel("Total Number of Nodes")
ax[2].set_ylabel("Relative Concentration\nof Materials")
ax[2].set_xscale('log')
ax[2].legend()
plt.tight_layout()
plt.savefig("E_convergence.png")
def sens_analysis(n=33, steps=np.array([10E7, 80E7, 0.0032, 0.0022, 0.0055]), x_opt=np.array([10E9, 80E9, 0.32, 0.22, 0.55]), candidates = 10):
def central_difference(Q_1, Q_2, step):
return (Q_2 - Q_1)/(2*step)
Q_grads = np.zeros((steps.shape[0], 3, 3))
for c in tqdm(range(candidates), desc="Running an Ensemble"):
for i in tqdm(range(steps.shape[0]), desc="Generating Sens for parameters", leave=False):
x = x_opt
x[i] -= steps[i]
mesh = MicroMesh(n, n, *x)
solver = MicroSolver(mesh)
Q_1 = solver.homogenize()
x = x_opt
x[i] += steps[i]
mesh = MicroMesh(n, n, *x)
solver = MicroSolver(mesh)
Q_2 = solver.homogenize()
Q_grads[i, :, :] += np.abs(central_difference(Q_1, Q_2, steps[i]) * x_opt[i]) # Absolute Scaled Sensitivities
return Q_grads/candidates
def plot_sens(Q_grads):
fig, ax = plt.subplots(3, 3, figsize=(10.0, 10.0))
Q_grads = np.abs(Q_grads.copy()/1E9)
v_sens, r_sens = get_VR_sens()
v_sens = np.abs(v_sens/1E9)
r_sens = np.abs(r_sens/1E9)
width = 0.3
labels=[r"E$_1$", r"E$_2$", r"$\nu_1$", r"$\nu_2$", r"$\phi_A$"]
for i in range(3):
for j in range(3):
ax[i, j].bar((3.5*np.array(range(Q_grads.shape[0])))*width, v_sens[:, i, j], label="Voigt Sensitivities", width=width)
ax[i, j].bar((3.5*np.array(range(Q_grads.shape[0]))+1)*width, Q_grads[:, i, j], label="True Sensitivities", width=width)
ax[i, j].bar((3.5*np.array(range(Q_grads.shape[0]))+2)*width, r_sens[:, i, j], label="Reuss Sensitivities", width=width)
ax[i, j].set_xticks((3.5*np.array(range(Q_grads.shape[0])) + 1)*width)
ax[i, j].set_xticklabels(labels)
ax[i, j].set_xlabel("Parameter")
ax[i, j].set_ylabel("Scaled Sensitivity/GPa")
ax[i, j].set_title(f"Sensitivity of $C_{{{i + 1},{j + 1}}}$")
ax[i, j].legend()
plt.tight_layout()
plt.savefig("Sensitivities.png")
def RVE_analysis(num_circs=np.arange(1, 5)**2, num_candidates=5, shifts=0.01):
mat_1_params=[10E9, 0.32]
mat_2_params=[80E9, 0.22]
rel_conc=0.55
E_1, nu_1 = mat_1_params
E_2, nu_2 = mat_2_params
C_tmp = np.zeros((num_candidates, 3, 3))
Cs = np.zeros((num_circs.shape[0], 3, 3))
C_errs = np.zeros_like(Cs)
x0 = np.array([E_1/1E9, E_2/1E9, nu_1, nu_2])
cov = np.diag(shifts*x0)
dist = multivariate_normal(x0, cov)
for j in tqdm(range(num_circs.shape[0]), desc="Running over RVE size"):
for i in tqdm(range(num_candidates), desc="Testing ensemble of Meshes", leave=False):
x = dist.rvs()
x[0:2] *= 1E9
mesh = MicroMesh(35, 35, *x, rel_conc, micro_fun=circles_microstructure, num_circ=int(num_circs[j]))
solver = MicroSolver(mesh)
C_tmp[i, :, :] = solver.homogenize()
Cs[j, :, :] = np.average(C_tmp, axis=0)
C_errs[j, :, :] = np.average((C_tmp - Cs[j, :, :])**2, axis=0)
voigt_C = solver.Voigt()
reuss_C = solver.Reuss()
return Cs, C_errs, num_circs, voigt_C, reuss_C
def plot_RVE(Cs, C_errs, num_circs, voigt_C, reuss_C):
Cs = Cs.copy()/1E9
C_errs = C_errs.copy()/1E9
voigt_C = voigt_C.copy()/1E9
reuss_C = reuss_C.copy()/1E9
fig, ax = plt.subplots(3, 3, figsize=(14.0, 14.0))
for i in range(3):
for j in range(3):
ax[i, j].plot(num_circs, Cs[:, i, j], label="Homogenized", color='k')
ax[i, j].fill_between(num_circs, Cs[:, i, j] + 2*C_errs[:, i, j], Cs[:, i, j] - 2*C_errs[:, i, j], color='C3', alpha=0.3)
ax[i, j].hlines(voigt_C[i, j], 0, np.max(num_circs), label='Voigt bound', color='C1', linestyle='dashed')
ax[i, j].hlines(reuss_C[i, j], 0, np.max(num_circs), label='Reuss bound', color='C2', linestyle='dashed')
#ax[i, j].hlines(C_1[i, j], 0, np.max(nnodes), label='Material 1', color='C3', linestyle='dashed')
#ax[i, j].hlines(C_2[i, j], 0, np.max(nnodes), label='Material 2', color='C4', linestyle='dashed')
ax[i, j].set_title(f"Convergence of $C_{{{i + 1},{j + 1}}}$")
ax[i, j].set_xlabel("Number of Circular Regions")
ax[i, j].set_ylabel("Estimated Elastic Property/GPa")
ax[i, j].set_xticks(num_circs)
#ax[i, j].set_xscale('log')
# if (i<2 and j<2) or (i==3 and j==3):
# ax[i, j].set_yscale("log")
ax[i, j].legend()
plt.tight_layout()
plt.savefig("RVE_converge.png")
para_1 = [8E9, 0.34]
para_2 = [48E9, 0.24]
vol_frac = 0.65
# props = Converge(para_1, para_2, vol_frac)
# plot_c_converge(*props, para_1, para_2, vol_frac)
props = Converge()
plot_c_converge(*props)
# Q_grad = sens_analysis()
# plot_sens(Q_grad)
# props = RVE_analysis()
# plot_RVE(*props)