def test_main(self):
with h5py.File('Cartesian3d_random.hdf5', 'r') as data:
shape = data['/shape'][...]
i = np.eye(3)
I = np.einsum('xy,ij', np.ones(shape), i)
I4 = np.einsum('xy,ijkl->xyijkl', np.ones(shape),
np.einsum('il,jk', i, i))
I4rt = np.einsum('xy,ijkl->xyijkl', np.ones(shape),
np.einsum('ik,jl', i, i))
I4s = (I4 + I4rt) / 2.0
mat = GMat.Matrix(shape[0], shape[1])
I = data['/LinearHardening/I'][...]
idx = data['/LinearHardening/idx'][...]
K = data['/LinearHardening/K'][...]
G = data['/LinearHardening/G'][...]
tauy0 = data['/LinearHardening/tauy0'][...]
H = data['/LinearHardening/H'][...]
mat.setLinearHardening(I, idx, K, G, tauy0, H)
I = data['/Elastic/I'][...]
idx = data['/Elastic/idx'][...]
K = data['/Elastic/K'][...]
G = data['/Elastic/G'][...]
mat.setElastic(I, idx, K, G)
for i in range(20):
mat.increment()
F = data['/random/{0:d}/F'.format(i)][...]
self.assertTrue(
np.allclose(mat.Stress(F),
data['/random/{0:d}/Stress'.format(i)][...],
1e-3))
self.assertTrue(
np.allclose(
mat.Tangent(F)[1],
data['/random/{0:d}/Tangent'.format(i)][...], 1e-3))
self.assertTrue(
np.allclose(mat.Epsp(),
data['/random/{0:d}/Epsp'.format(i)][...],
1e-3))
def StressStrain(mat, plastic):
ninc = 301
epseq = np.zeros(ninc)
sigeq = np.zeros(ninc)
for ilam, lam in enumerate(np.linspace(0.0, 1.0, ninc)):
if plastic:
mat.increment()
F = np.array([
[1.0 + lam, 0.0, 0.0],
[0.0, 1.0 / (1.0 + lam), 0.0],
[0.0, 0.0, 1.0],
])
mat.setDefGrad(F)
epseq[ilam] = gmat.Epseq(gmat.Strain(F))
sigeq[ilam] = gmat.Sigeq(mat.Stress())
return (epseq, sigeq)
def test_Elastic(self):
K = 12.3
G = 45.6
gamma = 0.02
F = np.array([
[1.0 + gamma, 0.0, 0.0],
[0.0, 1.0 / (1.0 + gamma), 0.0],
[0.0, 0.0, 1.0]])
Sig = np.array([
[G * 2.0 * np.log(1.0 + gamma), 0.0, 0.0],
[0.0, - G * 2.0 * np.log(1.0 + gamma), 0.0],
[0.0, 0.0, 0.0]])
mat = GMat.Elastic(K, G)
mat.setDefGrad(F)
Sig = mat.Stress()
self.assertTrue(np.allclose(mat.Stress(), Sig))
def test_Array2d(self):
K = 12.3
G = 45.6
gamma = 0.02
F = np.array([
[1.0 + gamma, 0.0, 0.0],
[0.0, 1.0 / (1.0 + gamma), 0.0],
[0.0, 0.0, 1.0]])
Sig = np.array([
[G * 2.0 * np.log(1.0 + gamma), 0.0, 0.0],
[0.0, - G * 2.0 * np.log(1.0 + gamma), 0.0],
[0.0, 0.0, 0.0]])
nelem = 3
nip = 2
mat = GMat.Array2d([nelem, nip])
ndim = 3
I = np.ones([nelem, nip], dtype='int')
mat.setElastic(I, K, G)
f = np.zeros((nelem, nip, ndim, ndim))
sig = np.zeros((nelem, nip, ndim, ndim))
for e in range(nelem):
for q in range(nip):
f[e, q, :, :] = F
sig[e, q, :, :] = Sig
mat.setDefGrad(f)
self.assertTrue(np.allclose(mat.Stress(), sig))
Tau = Sig * np.linalg.det(F)
P = A2_dot_B2(Tau, np.linalg.inv(F).T)
dP = P - P0
y[i] = norm(dP - (A4_ddot_B2(K, dF.T)).T) / norm(dP)
return (x, y)
# Plot
fig, ax = plt.subplots()
ax.plot(*consistency(gmat.Elastic(10.0, 1.0), False), c='b', label=r'Elastic')
ax.plot(*consistency(gmat.LinearHardening(10.0, 1.0, 1.0, 1.0), True),
c='r',
label=r'LinearHardening')
ax.set_xscale('log')
ax.set_yscale('log')
ax.set_xlim([1e-16, 1e0])
ax.set_ylim([1e-16, 1e0])
ax.set_xlabel(r'$|| \delta \bm{\varepsilon} ||$')
ax.set_ylabel(r'$\eta$')
gplt.plot_powerlaw(
[0.0, 0.0, 1.0],
])
mat.setDefGrad(F)
epseq[ilam] = gmat.Epseq(gmat.Strain(F))
sigeq[ilam] = gmat.Sigeq(mat.Stress())
return (epseq, sigeq)
# Plot
fig, ax = plt.subplots()
elas = gmat.Elastic(10.0, 1.0)
plas = gmat.LinearHardening(10.0, 1.0, 1.0, 1.0)
ax.plot(*StressStrain(elas, False), c='b', label=r'Elastic')
ax.plot(*StressStrain(plas, True), c='r', label=r'LinearHardening')
ax.plot(ax.get_xlim(), plas.tauy0() * np.ones(2), c='r', ls='--', lw=1.)
ax.plot(plas.tauy0() / (3.0 * plas.G()) * np.ones(2),
ax.get_ylim(),
c='r',
ls='--',
lw=1.)
ax.set_xlabel(r'$\varepsilon_\mathrm{eq}$')
ax.set_ylabel(r'$\sigma_\mathrm{eq}$')
import GMatElastoPlasticFiniteStrainSimo.Cartesian3d as GMat
with h5py.File('Cartesian3d_random.hdf5', 'w') as data:
nelem = 1000
nip = 4
iden = 2.0 * np.random.random([nelem, nip])
iden = np.where(iden < 1.0, 0.0, iden)
iden = np.where(iden >= 1.0, 1.0, iden)
iden = iden.astype(np.int)
shape = np.array([nelem, nip], np.int)
data['/shape'] = shape
mat = GMat.Array2d(shape)
I = np.where(iden == 0, 1, 0).astype(np.int)
n = np.sum(I)
idx = np.zeros(I.size, np.int)
idx[np.argwhere(I.ravel() == 1).ravel()] = np.arange(n)
idx = idx.reshape(I.shape)
K = np.ones(n)
G = np.ones(n)
tauy0 = 0.1 * np.ones(n)
H = np.ones(n)
data['/LinearHardening/I'] = I
data['/LinearHardening/idx'] = idx
data['/LinearHardening/K'] = K
data['/LinearHardening/G'] = G
phase[1, 0, 0] = 1.
# function to convert material parameters to grid of scalars
param = lambda M0,M1: M0*np.ones([Nx,Ny,Nz])*(1.-phase)+\
M1*np.ones([Nx,Ny,Nz])* phase
# material parameters
K = param(0.833, 0.833) # bulk modulus
mu = param(0.386, 0.386) # shear modulus
H = param(0.004, 0.008) # hardening modulus
tauy0 = param(1000., 0.003) # initial yield stress
# --------------------------------------- C++ IMPLEMENTATION ---------------------------------------
Isoft = (1. - phase).astype(np.uint).reshape(2, 1)
Ihard = (phase).astype(np.uint).reshape(2, 1)
mat = GMat.Array2d([2, 1])
mat.setElastic(Isoft, K[0, 0, 0], mu[0, 0, 0])
mat.setLinearHardening(Ihard, K[1, 0, 0], mu[1, 0, 0], tauy0[1, 0, 0], H[1, 0,
0])
# -------------------------------------------- LOADING ---------------------------------------------
# stress, deformation gradient, plastic strain, elastic Finger tensor
# NB "_t" signifies that it concerns the value at the previous increment
ep_t = np.zeros([Nx, Ny, Nz])
P = np.zeros([3, 3, Nx, Ny, Nz])
F = np.array(I, copy=True)
F_t = np.array(I, copy=True)
be_t = np.array(I, copy=True)
# initialize macroscopic incremental loading