import numpy as nm
from sfepy.linalg import dot_sequences
from sfepy.terms.terms import Term, terms
from sfepy.terms.terms_th import THTerm, ETHTerm
from sfepy.terms.terms_elastic import CauchyStressTerm
[docs]
class BiotTerm(Term):
r"""
Biot coupling term with :math:`\alpha_{ij}` given in:
* vector form exploiting symmetry - in 3D it has the
indices ordered as :math:`[11, 22, 33, 12, 13, 23]`, in 2D it has
the indices ordered as :math:`[11, 22, 12]`,
* matrix form - non-symmetric coupling parameter.
Corresponds to weak forms of Biot gradient and divergence terms.
Can be evaluated. Can use derivatives.
:Definition:
.. math::
\int_{\Omega} p\ \alpha_{ij} e_{ij}(\ul{v}) \mbox{ , } \int_{\Omega}
q\ \alpha_{ij} e_{ij}(\ul{u})
:Arguments 1:
- material : :math:`\alpha_{ij}`
- virtual : :math:`\ul{v}`
- state : :math:`p`
:Arguments 2:
- material : :math:`\alpha_{ij}`
- state : :math:`\ul{u}`
- virtual : :math:`q`
:Arguments 3:
- material : :math:`\alpha_{ij}`
- parameter_v : :math:`\ul{u}`
- parameter_s : :math:`p`
"""
name = 'dw_biot'
arg_types = (('material', 'virtual', 'state'),
('material', 'state', 'virtual'),
('material', 'parameter_v', 'parameter_s'))
arg_shapes = [{'material' : 'S, 1',
'virtual/grad' : ('D', None), 'state/grad' : 1,
'virtual/div' : (1, None), 'state/div' : 'D',
'parameter_v' : 'D', 'parameter_s' : 1},
{'material' : 'D, D'}]
modes = ('grad', 'div', 'eval')
[docs]
def get_fargs(self, mat, vvar, svar,
mode=None, term_mode=None, diff_var=None, **kwargs):
sym_mode = False if mat.shape[-2] == mat.shape[-1] > 1 else True
if not sym_mode:
sh = mat.shape
# the gradient given by 'self.get' is transposed
mat = nm.swapaxes(mat, 2, 3)
mat = mat.reshape(sh[:2] + (sh[2]**2, 1))
if self.mode == 'grad':
qp_var, qp_name = svar, 'val'
else:
if sym_mode:
qp_var, qp_name = vvar, 'cauchy_strain'
else:
qp_var, qp_name = vvar, 'grad'
if mode == 'weak':
vvg, _ = self.get_mapping(vvar)
svg, _ = self.get_mapping(svar)
if diff_var is None:
val_qp = self.get(qp_var, qp_name)
if qp_name == 'grad':
sh = val_qp.shape
val_qp = val_qp.reshape(sh[:2] + (sh[2]**2, 1))
fmode = 0
else:
val_qp = nm.array([0], ndmin=4, dtype=nm.float64)
fmode = 1
return 1.0, val_qp, mat, svg, vvg, fmode
elif mode == 'eval':
vvg, _ = self.get_mapping(vvar)
if sym_mode:
strain = self.get(vvar, 'cauchy_strain')
else:
strain = self.get(vvar, 'grad')
sh = strain.shape
strain = strain.reshape(sh[:2] + (sh[2]**2, 1))
pval = self.get(svar, 'val')
return 1.0, pval, strain, mat, vvg
else:
raise ValueError('unsupported evaluation mode in %s! (%s)'
% (self.name, mode))
[docs]
def get_eval_shape(self, mat, vvar, svar,
mode=None, term_mode=None, diff_var=None, **kwargs):
n_el, n_qp, dim, n_en, n_c = self.get_data_shape(vvar)
return (n_el, 1, 1, 1), vvar.dtype
[docs]
def set_arg_types(self):
self.function = {
'grad' : terms.dw_biot_grad,
'div' : terms.dw_biot_div,
'eval' : terms.d_biot_div,
}[self.mode]
[docs]
class BiotStressTerm(CauchyStressTerm):
r"""
Evaluate Biot stress tensor.
It is given in the usual vector form exploiting symmetry: in 3D it has 6
components with the indices ordered as :math:`[11, 22, 33, 12, 13, 23]`, in
2D it has 3 components with the indices ordered as :math:`[11, 22, 12]`.
Supports 'eval', 'el_avg' and 'qp' evaluation modes.
:Definition:
.. math::
- \int_{\Omega} \alpha_{ij} p
:Arguments:
- material : :math:`\alpha_{ij}`
- parameter : :math:`p`
"""
name = 'ev_biot_stress'
arg_types = ('material', 'parameter')
arg_shapes = {'material' : 'S, 1', 'parameter' : 1}
integration = 'cell'
[docs]
@staticmethod
def function(out, val_qp, mat, vg, fmode):
if fmode == 2:
out[:] = dot_sequences(mat, val_qp)
status = 0
else:
status = terms.de_cauchy_stress(out, val_qp, mat, vg.cmap, fmode)
out *= -1.0
return status
[docs]
def get_fargs(self, mat, parameter,
mode=None, term_mode=None, diff_var=None, **kwargs):
vg, _ = self.get_mapping(parameter)
val_qp = self.get(parameter, 'val')
fmode = {'eval' : 0, 'el_avg' : 1, 'qp' : 2}.get(mode, 1)
return val_qp, mat, vg, fmode
[docs]
class BiotTHTerm(BiotTerm, THTerm):
r"""
Fading memory Biot term. Can use derivatives.
:Definition:
.. math::
\begin{array}{l}
\int_{\Omega} \left [\int_0^t \alpha_{ij}(t-\tau)\,p(\tau)) \difd{\tau}
\right]\,e_{ij}(\ul{v}) \mbox{ ,} \\
\int_{\Omega} \left [\int_0^t
\alpha_{ij}(t-\tau) e_{kl}(\ul{u}(\tau)) \difd{\tau} \right] q
\end{array}
:Arguments 1:
- ts : :class:`TimeStepper` instance
- material : :math:`\alpha_{ij}(\tau)`
- virtual : :math:`\ul{v}`
- state : :math:`p`
:Arguments 2:
- ts : :class:`TimeStepper` instance
- material : :math:`\alpha_{ij}(\tau)`
- state : :math:`\ul{u}`
- virtual : :math:`q`
"""
name = 'dw_biot_th'
arg_types = (('ts', 'material', 'virtual', 'state'),
('ts', 'material', 'state', 'virtual'))
arg_shapes = {'material' : '.: N, S, 1',
'virtual/grad' : ('D', None), 'state/grad' : 1,
'virtual/div' : (1, None), 'state/div' : 'D'}
modes = ('grad', 'div')
[docs]
def get_fargs(self, ts, mats, vvar, svar,
mode=None, term_mode=None, diff_var=None, **kwargs):
if self.mode == 'grad':
qp_var, qp_name = svar, 'val'
else:
qp_var, qp_name = vvar, 'cauchy_strain'
n_el, n_qp, dim, n_en, n_c = self.get_data_shape(svar)
if mode == 'weak':
vvg, _ = self.get_mapping(vvar)
svg, _ = self.get_mapping(svar)
if diff_var is None:
def iter_kernel():
for ii, mat in enumerate(mats):
val_qp = self.get(qp_var, qp_name, step=-ii)
mat = nm.tile(mat, (n_el, n_qp, 1, 1))
yield ii, (ts.dt, val_qp, mat, svg, vvg, 0)
fargs = iter_kernel
else:
val_qp = nm.array([0], ndmin=4, dtype=nm.float64)
mat = nm.tile(mats[0], (n_el, n_qp, 1, 1))
fargs = ts.dt, val_qp, mat, svg, vvg, 1
return fargs
else:
raise ValueError('unsupported evaluation mode in %s! (%s)'
% (self.name, mode))
[docs]
class BiotETHTerm(BiotTerm, ETHTerm):
r"""
This term has the same definition as dw_biot_th, but assumes an
exponential approximation of the convolution kernel resulting in much
higher efficiency. Can use derivatives.
:Definition:
.. math::
\begin{array}{l}
\int_{\Omega} \left [\int_0^t \alpha_{ij}(t-\tau)\,p(\tau)) \difd{\tau}
\right]\,e_{ij}(\ul{v}) \mbox{ ,} \\
\int_{\Omega} \left [\int_0^t
\alpha_{ij}(t-\tau) e_{kl}(\ul{u}(\tau)) \difd{\tau} \right] q
\end{array}
:Arguments 1:
- ts : :class:`TimeStepper` instance
- material_0 : :math:`\alpha_{ij}(0)`
- material_1 : :math:`\exp(-\lambda \Delta t)` (decay at :math:`t_1`)
- virtual : :math:`\ul{v}`
- state : :math:`p`
:Arguments 2:
- ts : :class:`TimeStepper` instance
- material_0 : :math:`\alpha_{ij}(0)`
- material_1 : :math:`\exp(-\lambda \Delta t)` (decay at :math:`t_1`)
- state : :math:`\ul{u}`
- virtual : :math:`q`
"""
name = 'dw_biot_eth'
arg_types = (('ts', 'material_0', 'material_1', 'virtual', 'state'),
('ts', 'material_0', 'material_1', 'state', 'virtual'))
arg_shapes = {'material_0' : 'S, 1', 'material_1' : '1, 1',
'virtual/grad' : ('D', None), 'state/grad' : 1,
'virtual/div' : (1, None), 'state/div' : 'D'}
modes = ('grad', 'div')
[docs]
def get_fargs(self, ts, mat0, mat1, vvar, svar,
mode=None, term_mode=None, diff_var=None, **kwargs):
if self.mode == 'grad':
qp_var, qp_name, iv = svar, 'val', 4
else:
qp_var, qp_name, iv = vvar, 'cauchy_strain', 3
if mode == 'weak':
vvg, _, key = self.get_mapping(vvar, return_key=True)
svg, _ = self.get_mapping(svar)
if diff_var is None:
val_qp = self.get(qp_var, qp_name)
key += tuple(self.arg_names[ii] for ii in [1, 2, iv])
data = self.get_eth_data(key, qp_var, mat1, val_qp)
val = data.history + data.values
fargs = (ts.dt, val, mat0, svg, vvg, 0)
else:
val_qp = nm.array([0], ndmin=4, dtype=nm.float64)
fargs = (ts.dt, val_qp, mat0, svg, vvg, 1)
return fargs
else:
raise ValueError('unsupported evaluation mode in %s! (%s)'
% (self.name, mode))