Truncate NTFA modes

Felix Fritzen fritzen@simtech.uni-stuttgart.de, Julius Herb julius.herb@mib.uni-stuttgart.de, Shadi Sharba shadi.sharba@isc.fraunhofer.de

University of Stuttgart, Institute of Applied Mechanics, Chair for Data Analytics in Engineering

Funding acknowledgment The IGF-Project no.: 21.079 N / DVS-No.: 06.3341 of the “Forschungsvereinigung Schweißen und verwandte Verfahren e.V.” of the German Welding Society (DVS), Aachener Str. 172, 40223 Düsseldorf, Germany, was funded by the Federal Ministry for Economic Affairs and Climate Action (BMWK) via the German Federation of Industrial Research Associations (AiF) in accordance with the policy to support the Industrial Collective Research (IGF) on the orders of the German Bundestag.

Felix Fritzen is funded by the German Research Foundation (DFG) – 390740016 (EXC-2075); 406068690 (FR2702/8-1); 517847245 (FR2702/10-1).

This notebook exemplifies how the NTFA modes can be truncated after computation.

Imports

import h5py
import numpy as np
import os

from material_parameters import *

data_path = "../data"

fname = os.path.join(data_path, "rve", "rve_thermoplastic_6loadings_10samples.h5")
basename = "/ms_9p/dset0_ntfa/"

F = h5py.File(fname, "r")
A_bar = np.array(F[basename + "A_bar"])
A0 = np.array(F[basename + "A0"])
A1 = np.array(F[basename + "A1"])
C0 = np.array(F[basename + "C0"])
C1 = np.array(F[basename + "C1"])
C_bar = np.array(F[basename + "C_bar"])
D_theta = np.array(F[basename + "D_theta"])
D_xi = np.array(F[basename + "D_xi"])
tau_theta = np.array(F[basename + "tau_theta"])
tau_xi = np.array(F[basename + "tau_xi"])
temperatures = np.array(F[basename + "temperatures"])
vol_frac = np.array(F["ms_9p/dset0_ntfa"].attrs["combo_volume_fraction"])
# vol_frac = np.zeros(2)
# vol_frac[1] = np.mean(F["ms_1p/dset0_sim/mat_id"])
# vol_frac[0] = 1. - vol_frac[1]
# print(vol_frac)
mu = np.array(F["/ms_9p/dset0_sim/plastic_modes"])
mu_eff = np.linalg.norm(mu, axis=2).sum(axis=0)
# print(mu_eff/vol_frac[0])
print(np.mean(mu[:, :12, :], axis=0))
F.close()

[[-4.81957192e-03 -1.87528725e-03  6.69485918e-03 -2.51804015e-01
  -2.52646652e-01 -2.52964984e-01]
 [ 1.45886310e-03 -6.41553815e-04 -8.17309288e-04 -1.99404954e-01
  -1.58046155e-01  3.56296561e-01]
 [-8.78852426e-05  1.26334860e-03 -1.17546336e-03 -2.99336425e-01
   3.22711105e-01 -2.43784261e-02]
 [-2.80818244e-01 -9.75181120e-02  3.78336356e-01  4.02089368e-03
   6.01847530e-03  6.82159257e-03]
 [ 2.75147501e-01 -3.81194901e-01  1.06047400e-01 -2.82880727e-04
   1.71243014e-03 -1.01420933e-03]
 [-4.12447345e-02 -1.57588433e-02  5.70035778e-02 -1.04866728e-02
  -1.03093058e-02 -1.02459260e-02]
 [-7.86225341e-04 -1.96939329e-03  2.75561863e-03  1.27961341e-01
  -8.91150551e-02 -3.90480145e-02]
 [-2.50104340e-03  1.99375768e-03  5.07285721e-04  2.86961002e-02
   9.63577684e-02 -1.25873730e-01]
 [-8.39072811e-03 -3.99626799e-03  1.23869961e-02  1.00012553e-01
   1.00066432e-01  9.95045543e-02]
 [-4.14913018e-03 -1.52616497e-01  1.56765628e-01 -3.64521611e-03
  -6.63791917e-03 -5.17289708e-03]
 [-1.91486891e-01  1.01497428e-01  8.99894627e-02 -1.87006015e-03
  -1.68134243e-03 -8.04254774e-03]
 [-1.21860436e-04 -1.82412608e-03  1.94598651e-03 -1.20850520e-01
   1.16432336e-01  4.61590318e-03]]

Ntemp = temperatures.size
Nmax = 24
# truncate and change order of the data
# print(A_bar.shape)
# phase average stress localization
A0 = np.transpose(A0[:, : Nmax + 7, :], axes=[2, 0, 1])
A1 = np.transpose(A1[:, : Nmax + 7, :], axes=[2, 0, 1])

sig_ph = np.zeros((2,) + A0.shape)
sig_ph[0] = A0
sig_ph[1] = A1

# phase stiffness tensors at the different temperatures
C0 = np.transpose(C0, axes=[2, 0, 1])
C1 = np.transpose(C1, axes=[2, 0, 1])

C_ph = np.zeros((2,) + C0.shape)
C_ph[0] = C0
C_ph[1] = C1

eps_th_ph = np.zeros((2, Ntemp, 6))
eps_th_ph[0, :, :] = eps_th_cu(temperatures)[:, None] * I2[None, :]
eps_th_ph[1, :, :] = eps_th_wsc(temperatures)[:, None] * I2[None, :]

A_bar = -np.transpose(A_bar[:, :Nmax, :], axes=[2, 1, 0])
# print(A_bar.shape)
D_xi = -np.transpose(D_xi[:Nmax, :Nmax, :], axes=[2, 0, 1])
# print(np.linalg.eigvals(D_xi[0,:3,:3]))
tau_xi = -np.transpose(tau_xi[:Nmax, :], axes=[1, 0])
tau_theta = np.transpose(tau_theta)
C_bar = np.transpose(C_bar, axes=[2, 0, 1])
A = A_bar[0]
XX = A.T @ np.linalg.pinv(A @ A.T) @ A
print(XX)

[[ 1.00000000e+00 -1.83013327e-16 -2.70616862e-16  0.00000000e+00
   2.91433544e-16 -3.07046055e-16]
 [-3.93782229e-16  1.00000000e+00 -2.64545330e-16 -1.47451495e-16
   1.64798730e-16 -8.41340886e-17]
 [ 1.43982049e-16  4.88758339e-16  1.00000000e+00 -3.41740525e-16
   6.34041430e-16 -2.46330734e-16]
 [ 2.76037873e-16  5.25079112e-16  1.72821826e-16  1.00000000e+00
  -2.83193607e-16  2.42427606e-16]
 [-2.25514052e-16 -5.44215280e-16 -2.50017021e-16 -1.92987987e-17
   1.00000000e+00 -1.72604986e-16]
 [-4.94396191e-17  1.68051337e-17  1.25984292e-16  2.04697370e-16
   2.87096735e-16  1.00000000e+00]]

# print(( vol_frac[1]*A1[0,:,:7]+vol_frac[0]*A0[0,:,:7]) )
x = C_bar[0, :, :].flatten()
x0 = A0[0, :, :6].flatten()
x1 = A1[0, :, :6].flatten()

alpha = np.dot(x - x1, x0 - x1) / np.dot(x0 - x1, x0 - x1)
# print(alpha, vol_frac)
alpha = 37 / 64
print("c_Bar:")
print(C_bar[0, :, :])

c_Bar:
[[2.83544622e+08 1.30812412e+08 1.30812412e+08 1.24569387e+05
  1.24569387e+05 7.44890553e+04]
 [1.30812412e+08 2.83544622e+08 1.30812412e+08 1.24569387e+05
  7.44890553e+04 1.24569387e+05]
 [1.30812412e+08 1.30812412e+08 2.83544622e+08 7.44890553e+04
  1.24569387e+05 1.24569387e+05]
 [1.24569387e+05 1.24569387e+05 7.44890553e+04 1.55475051e+08
  1.67818031e+05 1.67818031e+05]
 [1.24569387e+05 7.44890553e+04 1.24569387e+05 1.67818031e+05
  1.55475051e+08 1.67818031e+05]
 [7.44890553e+04 1.24569387e+05 1.24569387e+05 1.67818031e+05
  1.67818031e+05 1.55475051e+08]]

xx = alpha * x0 + (1 - alpha) * x1
# print(xx.reshape((6,6))-C_bar[0,:,:])
print("error:", xx / np.linalg.norm(x))

error: [4.44244702e-01 2.03578631e-01 2.03578631e-01 2.26026406e-04
 2.26026406e-04 1.38090640e-04 2.03578631e-01 4.44244702e-01
 2.03578631e-01 2.26026406e-04 1.38090640e-04 2.26026406e-04
 2.03578631e-01 2.03578631e-01 4.44244702e-01 1.38090640e-04
 2.26026406e-04 2.26026406e-04 2.18730561e-04 2.18730561e-04
 1.30794698e-04 2.45482202e-01 2.94670288e-04 2.94670288e-04
 2.18730561e-04 1.30794698e-04 2.18730561e-04 2.94670288e-04
 2.45482202e-01 2.94670288e-04 1.30794698e-04 2.18730561e-04
 2.18730561e-04 2.94670288e-04 2.94670288e-04 2.45482202e-01]

# print((C_bar[0,:,:]), tau_theta[0,:])
fname = os.path.join(data_path, "ntfa", f"ntfa_6loadings_10samples_N{Nmax}.h5")
F = h5py.File(fname, "w")
F.create_dataset("SIG_phases", data=sig_ph)
F.create_dataset("C_phases", data=C_ph)
F.create_dataset("eps_th_phases", data=eps_th_ph)
F.create_dataset("A_bar", data=A_bar)
F.create_dataset("v_frac", data=vol_frac)
F.create_dataset("C_bar", data=C_bar)
F.create_dataset("D_xi", data=D_xi)
F.create_dataset("D_theta", data=D_theta)
F.create_dataset("tau_xi", data=tau_xi)
F.create_dataset("tau_theta", data=tau_theta)
F.create_dataset("temperatures", data=temperatures)
F.close()
eps_th_500 = np.linalg.solve(C_bar[20, :, :], tau_theta[20, :])
print(eps_th_500)
print(tau_theta)

[-2.91058179e-04 -2.91058179e-04 -2.91058179e-04  7.56424908e-07
  7.56424908e-07  7.56424908e-07]
[[-4.09384219e+04 -4.09384219e+04 -4.09384219e+04  5.84757940e+00
   5.84757940e+00  5.84757940e+00]
 [-4.67906106e+04 -4.67906106e+04 -4.67906106e+04  6.68330174e+00
   6.68330174e+00  6.68330174e+00]
 [-5.26422371e+04 -5.26422371e+04 -5.26422371e+04  7.51886249e+00
   7.51886249e+00  7.51886249e+00]
 ...
 [-4.58740710e+05 -4.58740710e+05 -4.58740712e+05 -1.14949438e+03
  -1.14949447e+03 -1.14949439e+03]
 [-4.43545699e+05 -4.43545699e+05 -4.43545699e+05 -1.12134182e+03
  -1.12134185e+03 -1.12134183e+03]
 [-4.28268141e+05 -4.28268141e+05 -4.28268141e+05 -1.09241643e+03
  -1.09241643e+03 -1.09241643e+03]]