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Remove SolidBody._area_change #970

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Jul 14, 2025
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Remove SolidBody._area_change #970

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54 changes: 44 additions & 10 deletions src/felupe/mechanics/_solidbody.py
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Original file line number Diff line number Diff line change
Expand Up @@ -22,7 +22,6 @@
import numpy as np

from ..assembly import IntegralForm
from ..constitution import AreaChange
from ..math import det, dot, transpose
from ..view import ViewSolid
from ._helpers import Assemble, Evaluate, Results
Expand Down Expand Up @@ -174,8 +173,7 @@ class SolidBody(Solid):

Notes
-----
The total potential energy of internal forces is given in Eq.
:eq:`solidbody`
The total potential energy of internal forces is given in Eq. :eq:`solidbody`

.. math::
:label: solidbody
Expand Down Expand Up @@ -269,11 +267,20 @@ def __init__(
self.results.kinematics = self._extract(self.field)

if statevars is not None:
# state variables are located in the results
self.results.statevars = statevars

else:
# init the shape of the state variables
statevars_shape = (0,)

# take the shape of the last item of the list if the provided umat has an
# x-attribute
if hasattr(umat, "x"):
statevars_shape = umat.x[-1].shape

# create and fill the array of state variables with zeros
# state variables are located in the results
self.results.statevars = np.zeros(
(
*statevars_shape,
Expand All @@ -296,10 +303,6 @@ def __init__(
kirchhoff_stress=self._kirchhoff_stress,
)

self._area_change = AreaChange()

self._form = IntegralForm

def _vector(
self,
field=None,
Expand All @@ -322,13 +325,18 @@ def _vector(
if apply is None:
apply = self.apply

# evaluate the (first Piola-Kirchhoff) stress tensor and store it in the results
self.results.stress = self._gradient(field, args=args, kwargs=kwargs)
self.results.force = self._form(

# assemble the internal force vector
# optionally, use only the first n items for mixed-field formulations
self.results.force = IntegralForm(
fun=self.results.stress[slice(items)],
v=self.field,
dV=self.field.region.dV,
).assemble(parallel=parallel, block=block)

# apply a callback on the assembled internal force vector
if apply is not None:
self.results.force = apply(self.results.force)

Expand Down Expand Up @@ -356,29 +364,43 @@ def _matrix(
if apply is None:
apply = self.apply

# evaluate the fourth-order elasticity tensor and store it in the results
# (associated to the first Piola-Kirchhoff stress tensor, i.e. the partial
# derivative of the first Piola-Kirchhoff stress tensor w.r.t. the deformation
# gradient tensor)
self.results.elasticity = self._hessian(field, args=args, kwargs=kwargs)

form = self._form(
# assemble the (sparse) tangent stiffness matrix
# optionally, use only the first n items for mixed-field formulations
form = IntegralForm(
fun=self.results.elasticity[slice(items)],
v=self.field,
u=self.field,
dV=self.field.region.dV,
)

# in a first step, integrate the weak-form and store the stiffness values
# (this dense array is only allocated once and will be re-used in all following
# evaluations)
self.results.stiffness_values = form.integrate(
parallel=parallel, out=self.results.stiffness_values
)

# finally, the dense array of stiffness-values is assembled into the sparse
# matrix
self.results.stiffness = form.assemble(
values=self.results.stiffness_values, block=block
)

# apply a callback on the assembled tangent stiffness matrix
if apply is not None:
self.results.stiffness = apply(self.results.stiffness)

return self.results.stiffness

def _extract(self, field):
"Evaluate and return the kinematics (the deformation gradient tensor)."

self.field = field
self.results.kinematics = self.field.extract(out=self.results.kinematics)

Expand All @@ -388,18 +410,25 @@ def _gradient(self, field=None, args=(), kwargs=None):
if kwargs is None:
kwargs = {}

# update the deformation gradient
if field is not None:
self.field = field
self.results.kinematics = self._extract(self.field)

if "out" in inspect.signature(self.umat.gradient).parameters:
kwargs["out"] = self.results.gradient

# evaluate the partial derivative of the strain energy density w.r.t. the
# deformation gradient
gradient = self.umat.gradient(
[*self.results.kinematics, self.results.statevars], *args, **kwargs
)
# store the first Piola-Kirchhoff stress tensor in the results
self.results.gradient = gradient[0]

# store all gradients and the temporary state variables in the results
# the state variables are only updated to the public results-attribute if the
# solution is valid
self.results.stress, self.results._statevars = gradient[:-1], gradient[-1]

return self.results.stress
Expand All @@ -415,9 +444,14 @@ def _hessian(self, field=None, args=(), kwargs=None):
if "out" in inspect.signature(self.umat.hessian).parameters:
kwargs["out"] = self.results.hessian

# evaluate the second partial derivative of the strain energy density w.r.t. the
# deformation gradient
self.results.elasticity = self.umat.hessian(
[*self.results.kinematics, self.results.statevars], *args, **kwargs
)

# store the partial derivative of the first Piola-Kirchhoff stress tensor w.r.t.
# the deformation gradient in the results
self.results.hessian = self.results.elasticity[0]

return self.results.elasticity
Expand Down Expand Up @@ -458,7 +492,7 @@ def _mass(self, density=None):
field = self.field[0].as_container()
dim = field[0].dim

form = self._form(
form = IntegralForm(
fun=[density * np.eye(dim).reshape(dim, dim, 1, 1)],
v=field,
u=field,
Expand Down
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