def test_main(self):
with h5py.File("Cartesian2d_random.hdf5", "r") as data:
mat = GMat.Array2d(data["/shape"][...])
I = data["/cusp/I"][...]
idx = data["/cusp/idx"][...]
K = data["/cusp/K"][...]
G = data["/cusp/G"][...]
epsy = data["/cusp/epsy"][...]
mat.setCusp(I, idx, K, G, epsy)
I = data["/smooth/I"][...]
idx = data["/smooth/idx"][...]
K = data["/smooth/K"][...]
G = data["/smooth/G"][...]
epsy = data["/smooth/epsy"][...]
mat.setSmooth(I, idx, K, G, epsy)
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):
GradU = data[f"/random/{i:d}/GradU"][...]
Eps = np.einsum("...ijkl,...lk->...ij", mat.I4s(), GradU)
mat.setStrain(Eps)
self.assertTrue(
np.allclose(mat.Stress(),
data[f"/random/{i:d}/Stress"][...]))
self.assertTrue(
np.allclose(mat.Tangent(),
data[f"/random/{i:d}/Tangent"][...]))
self.assertTrue(
np.allclose(
mat.CurrentYieldLeft(),
data[f"/random/{i:d}/CurrentYieldLeft"][...],
))
self.assertTrue(
np.allclose(
mat.CurrentYieldRight(),
data[f"/random/{i:d}/CurrentYieldRight"][...],
))
self.assertTrue(
np.all(mat.CurrentIndex() ==
data[f"/random/{i:d}/CurrentIndex"][...]))
def test_Array2d(self):
K = 12.3
G = 45.6
gamma = 0.02
epsm = 0.12
Eps = np.array([[epsm, gamma], [gamma, epsm]])
Sig_elas = np.array([[K * epsm, G * gamma], [G * gamma, K * epsm]])
Sig_plas = np.array([[K * epsm, 0.0], [0.0, K * epsm]])
nelem = 3
nip = 2
mat = GMat.Array2d([nelem, nip])
ndim = 2
I = np.zeros([nelem, nip], dtype="int")
I[0, :] = 1
mat.setElastic(I, K, G)
I = np.zeros([nelem, nip], dtype="int")
I[1, :] = 1
mat.setCusp(I, K, G, 0.01 + 0.02 * np.arange(100))
I = np.zeros([nelem, nip], dtype="int")
I[2, :] = 1
mat.setSmooth(I, K, G, 0.01 + 0.02 * np.arange(100))
eps = np.zeros((nelem, nip, ndim, ndim))
sig = np.zeros((nelem, nip, ndim, ndim))
epsp = np.zeros((nelem, nip))
for e in range(nelem):
for q in range(nip):
fac = float((e + 1) * nip + (q + 1))
eps[e, q, :, :] = fac * Eps
if e == 0:
sig[e, q, :, :] = fac * Sig_elas
epsp[e, q] = 0.0
else:
sig[e, q, :, :] = fac * Sig_plas
epsp[e, q] = fac * gamma
mat.setStrain(eps)
self.assertTrue(np.allclose(mat.Stress(), sig))
self.assertTrue(np.allclose(mat.Epsp(), epsp))
def test_Array2d_refModel(self):
K = 12.3
G = 45.6
gamma = 0.02
epsm = 0.12
Eps = np.array([[epsm, gamma], [gamma, epsm]])
Sig_elas = np.array([[K * epsm, G * gamma], [G * gamma, K * epsm]])
Sig_plas = np.array([[K * epsm, 0.0], [0.0, K * epsm]])
nelem = 3
nip = 2
mat = GMat.Array2d([nelem, nip])
I = np.zeros([nelem, nip], dtype="int")
I[0, :] = 1
mat.setElastic(I, K, G)
I = np.zeros([nelem, nip], dtype="int")
I[1, :] = 1
mat.setCusp(I, K, G, 0.01 + 0.02 * np.arange(100))
I = np.zeros([nelem, nip], dtype="int")
I[2, :] = 1
mat.setSmooth(I, K, G, 0.01 + 0.02 * np.arange(100))
for e in range(nelem):
for q in range(nip):
fac = float((e + 1) * nip + (q + 1))
if e == 0:
model = mat.refElastic([e, q])
model.setStrain(fac * Eps)
self.assertTrue(np.allclose(model.Stress(),
fac * Sig_elas))
elif e == 1:
model = mat.refCusp([e, q])
model.setStrain(fac * Eps)
self.assertTrue(np.allclose(model.Stress(),
fac * Sig_plas))
self.assertTrue(np.allclose(model.epsp(), fac * gamma))
elif e == 2:
model = mat.refSmooth([e, q])
model.setStrain(fac * Eps)
self.assertTrue(np.allclose(model.Stress(),
fac * Sig_plas))
self.assertTrue(np.allclose(model.epsp(), fac * gamma))
# nodal quantities disp = np.zeros(coor.shape) fint = np.zeros(coor.shape) fext = np.zeros(coor.shape) fres = np.zeros(coor.shape) # element/material definition # --------------------------- # element definition quad = GooseFEM.Element.Quad4.Quadrature(vector.AsElement(coor)) nip = quad.nip() # material definition mat = GMat.Array2d([nelem, nip]) iden = np.zeros(mat.shape(), dtype="int") iden[elastic, :] = 1 mat.setElastic(iden, 10.0, 1.0) iden = np.zeros(mat.shape(), dtype="int") iden[plastic, :] = 1 mat.setElastic(iden, 10.0, 1.0) # solve # ----- # strain, stress, tangent ue = vector.AsElement(disp) Eps = quad.SymGradN_vector(ue)
with h5py.File("Cartesian2d_random.hdf5", "w") as data:
nelem = 1000
nip = 4
iden = 3.0 * np.random.random([nelem, nip])
iden = np.where(iden < 1.0, 0.0, iden)
iden = np.where((iden >= 1.0) * (iden < 2.0), 1.0, iden)
iden = np.where(iden >= 2.0, 2.0, 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)
epsy = np.cumsum(np.random.random([n, 500]), 1)
K = np.ones(n)
G = np.ones(n)
data["/cusp/I"] = I
data["/cusp/idx"] = idx
data["/cusp/K"] = K
data["/cusp/G"] = G
data["/cusp/epsy"] = epsy
def ComputePerturbation(sigma_star_test):
# mesh
# ----
# define mesh
mesh = GooseFEM.Mesh.Quad4.FineLayer(13, 13)
# mesh dimensions
nelem = mesh.nelem()
# mesh definitions
coor = mesh.coor()
conn = mesh.conn()
dofs = mesh.dofs()
# node sets
nodesLft = mesh.nodesLeftOpenEdge()
nodesRgt = mesh.nodesRightOpenEdge()
nodesTop = mesh.nodesTopEdge()
nodesBot = mesh.nodesBottomEdge()
# element sets
plastic = mesh.elementsMiddleLayer()
elastic = np.setdiff1d(np.arange(nelem), plastic)
# periodicity and fixed displacements DOFs
# ----------------------------------------
dofs[nodesRgt, :] = dofs[nodesLft, :]
dofs = GooseFEM.Mesh.renumber(dofs)
iip = np.concatenate(
(dofs[nodesBot, 0], dofs[nodesBot, 1], dofs[nodesTop,
0], dofs[nodesTop, 1]))
# simulation variables
# --------------------
# vector definition
vector = GooseFEM.VectorPartitioned(conn, dofs, iip)
# allocate system matrix
K = GooseFEM.MatrixPartitioned(conn, dofs, iip)
Solver = GooseFEM.MatrixPartitionedSolver()
# nodal quantities
disp = np.zeros(coor.shape)
fint = np.zeros(coor.shape)
fext = np.zeros(coor.shape)
fres = np.zeros(coor.shape)
# element/material definition
# ---------------------------
# element definition
quad = GooseFEM.Element.Quad4.Quadrature(vector.AsElement(coor))
nip = quad.nip()
# material definition
mat = GMat.Array2d([nelem, nip])
iden = np.zeros(mat.shape(), dtype="int")
iden[elastic, :] = 1
mat.setElastic(iden, 10.0, 1.0)
iden = np.zeros(mat.shape(), dtype="int")
iden[plastic, :] = 1
mat.setElastic(iden, 10.0, 1.0)
# solve
# -----
# strain
ue = vector.AsElement(disp)
Eps = quad.SymGradN_vector(ue)
# pre-stress
trigger = plastic[int(len(plastic) / 2.0)]
Sigstar = quad.AllocateQtensor(2, 0.0)
for q in range(nip):
Sigstar[trigger, q, :, :] = sigma_star_test
Sigstar[trigger, q, :, :] = sigma_star_test
# stress & tangent
mat.setStrain(Eps)
Sig = mat.Stress() - Sigstar
C = mat.Tangent()
# stiffness matrix
Ke = quad.Int_gradN_dot_tensor4_dot_gradNT_dV(C)
K.assemble(Ke)
# residual force
fe = quad.Int_gradN_dot_tensor2_dV(Sig)
fint = vector.AssembleNode(fe)
fext = vector.Copy_p(fint, fext)
fres = fext - fint
# solve
disp = Solver.Solve(K, fres, disp)
# post-process
# ------------
ue = vector.AsElement(disp)
Eps = quad.SymGradN_vector(ue)
return (
GMat.Deviatoric(Eps[trigger, 0]),
trigger,
disp,
coor,
conn,
vector,
quad,
mat,
)