def __call__(self, mat, virtual, state, **kwargs):
"""
Doubled out-of-diagonal strain entries!
"""
rindx = virtual.get_component_indices()
cindx = state.get_component_indices()
kindx = lindx = get_range_indices(state.dim)
fi = nm.array(get_full_indices(state.dim))
val = virtual.get_element_zeros()
for ir, irs in rindx:
for ik, iks in kindx:
irk = fi[ir, ik]
irks = slice(irk, irk + 1)
erk = virtual.grad(ir, ik)
for ic, ics in cindx:
for il, ils in lindx:
icl = fi[ic, il]
icls = slice(icl, icl + 1)
ecl = state.grad(ic, il)
val += mat[..., irks, icls] * erk * ecl
return val
def __call__(self, mat, virtual, state, **kwargs):
"""
Doubled out-of-diagonal strain entries!
"""
rindx = virtual.get_component_indices()
cindx = state.get_component_indices()
kindx = lindx = get_range_indices(state.dim)
fi = nm.array(get_full_indices(state.dim))
val = virtual.get_element_zeros()
for ir, irs in rindx:
for ik, iks in kindx:
irk = fi[ir, ik]
irks = slice(irk, irk + 1)
erk = virtual.grad(ir, ik)
for ic, ics in cindx:
for il, ils in lindx:
icl = fi[ic, il]
icls = slice(icl, icl + 1)
ecl = state.grad(ic, il)
val += mat[..., irks, icls] * erk * ecl
return val
def eval_force(region_name):
strain = problem.evaluate(
'ev_cauchy_strain.i.%s(u)' % region_name,
mode='qp',
verbose=False,
)
D = problem.evaluate(
'ev_integrate_mat.i.%s(solid.D, u)' % region_name,
mode='qp',
verbose=False,
)
normal = nm.array([1, 0, 0], dtype=nm.float64)
s2f = get_full_indices(len(normal))
stress = nm.einsum('cqij,cqjk->cqik', D, strain)
# Full (matrix) form of stress.
mstress = stress[..., s2f, 0]
# Force in normal direction.
force = nm.einsum('cqij,i,j->cq', mstress, normal, normal)
def get_force(ts, coors, mode=None, **kwargs):
if mode == 'qp':
return {'force': force.reshape(coors.shape[0], 1, 1)}
aux = Material('aux', function=Function('get_force', get_force))
middle_force = -problem.evaluate(
'ev_integrate_mat.i.%s(aux.force, u)' % region_name,
aux=aux,
verbose=False,
)
output('%s section axial force:' % region_name, middle_force)
def test_transform_data4(self):
import numpy as nm
import sfepy.mechanics.tensors as tn
ok = True
if not hasattr(nm, 'einsum'):
self.report('no numpy.einsum(), skipping!')
return ok
expected = nm.zeros((6, 6), dtype=nm.float64)
expected[0, 0] = expected[1, 1] = 1.0
phi = nm.deg2rad(30.)
dr, v1, v2, om1, om2 = get_ortho_d(phi, phi + nm.deg2rad(90.))
# Rotate coordinate system by phi.
mtx = tn.make_axis_rotation_matrix([0., 0., 1.], phi)
do = tn.transform_data(dr[None, ...], mtx=mtx[None, ...])
_ok = nm.allclose(do, expected, rtol=0.0, atol=1e-14)
self.report('sym. 4th-th order tensor rotation: %s' % _ok)
ok = ok and _ok
dt, vt1, vt2, omt1, omt2 = get_ortho_d(0, nm.deg2rad(90.))
expected1 = nm.zeros((3, 3), dtype=nm.float64)
expected1[0, 0] = 1.0
expected2 = nm.zeros((3, 3), dtype=nm.float64)
expected2[1, 1] = 1.0
omr1 = nm.einsum('pq,ip,jq->ij', om1, mtx, mtx)
omr2 = nm.einsum('pq,ip,jq->ij', om2, mtx, mtx)
ii = tn.get_sym_indices(3)
jj = tn.get_full_indices(3)
o1 = om1.flat[ii]
o2 = om2.flat[ii]
omr12 = tn.transform_data(o1[None,...], mtx=mtx[None, ...])[0, jj]
omr22 = tn.transform_data(o2[None,...], mtx=mtx[None, ...])[0, jj]
_ok1 = nm.allclose(omr1, expected1, rtol=0.0, atol=1e-14)
_ok2 = nm.allclose(omr12, expected1, rtol=0.0, atol=1e-14)
self.report('einsum-transform_data compatibility 1: %s %s'
% (_ok1, _ok2))
ok = ok and _ok1 and _ok2
_ok1 = nm.allclose(omr2, expected2, rtol=0.0, atol=1e-14)
_ok2 = nm.allclose(omr22, expected2, rtol=0.0, atol=1e-14)
self.report('einsum-transform_data compatibility 2: %s %s'
% (_ok1, _ok2))
ok = ok and _ok1 and _ok2
return ok
def test_transform_data4(self):
import numpy as nm
import sfepy.mechanics.tensors as tn
ok = True
if not hasattr(nm, 'einsum'):
self.report('no numpy.einsum(), skipping!')
return ok
expected = nm.zeros((6, 6), dtype=nm.float64)
expected[0, 0] = expected[1, 1] = 1.0
phi = nm.deg2rad(30.)
dr, v1, v2, om1, om2 = get_ortho_d(phi, phi + nm.deg2rad(90.))
# Rotate coordinate system by phi.
mtx = tn.make_axis_rotation_matrix([0., 0., 1.], phi)
do = tn.transform_data(dr[None, ...], mtx=mtx[None, ...])
_ok = nm.allclose(do, expected, rtol=0.0, atol=1e-14)
self.report('sym. 4th-th order tensor rotation: %s' % _ok)
ok = ok and _ok
dt, vt1, vt2, omt1, omt2 = get_ortho_d(0, nm.deg2rad(90.))
expected1 = nm.zeros((3, 3), dtype=nm.float64)
expected1[0, 0] = 1.0
expected2 = nm.zeros((3, 3), dtype=nm.float64)
expected2[1, 1] = 1.0
omr1 = nm.einsum('pq,ip,jq->ij', om1, mtx, mtx)
omr2 = nm.einsum('pq,ip,jq->ij', om2, mtx, mtx)
ii = tn.get_sym_indices(3)
jj = tn.get_full_indices(3)
o1 = om1.flat[ii]
o2 = om2.flat[ii]
omr12 = tn.transform_data(o1[None,...], mtx=mtx[None, ...])[0, jj]
omr22 = tn.transform_data(o2[None,...], mtx=mtx[None, ...])[0, jj]
_ok1 = nm.allclose(omr1, expected1, rtol=0.0, atol=1e-14)
_ok2 = nm.allclose(omr12, expected1, rtol=0.0, atol=1e-14)
self.report('einsum-transform_data compatibility 1: %s %s'
% (_ok1, _ok2))
ok = ok and _ok1 and _ok2
_ok1 = nm.allclose(omr2, expected2, rtol=0.0, atol=1e-14)
_ok2 = nm.allclose(omr22, expected2, rtol=0.0, atol=1e-14)
self.report('einsum-transform_data compatibility 2: %s %s'
% (_ok1, _ok2))
ok = ok and _ok1 and _ok2
return ok
def d_fun(out, traction, val, grad_mv, div_mv, sg):
tdim, tdim2 = (None, None) if traction is None else traction.shape[2:]
dim = val.shape[2]
sym = (dim + 1) * dim // 2
n_el, n_qp = div_mv.shape[:2]
val2 = sg.normal
if tdim is None:
trac = nm.tile(nm.eye(dim), (n_el, n_qp, 1, 1))
elif tdim == 1:
trac = nm.tile(nm.eye(dim), (n_el, n_qp, 1, 1)) * traction
elif tdim == dim and tdim2 == 1: # Traction vector
trac = nm.tile(nm.eye(dim), (n_el, n_qp, 1, 1))
val2 = traction
elif tdim == dim and tdim2 == dim: # Traction tensor - nonsymmetric
trac = traction
elif tdim == sym: # Traction tensor
remap = nm.array(get_full_indices(dim)).flatten()
trac = traction[..., remap, :].reshape((-1, n_qp, dim, dim))
sa_trac = trac * div_mv
sa_trac -= nm.einsum('qpik,qpkj->qpij',
trac,
grad_mv,
optimize='greedy')
aux = dot_sequences(val, sa_trac, 'ATB')
aux = dot_sequences(aux, val2, 'AB')
status = sg.integrate(out, aux)
return status
