def _external_work(self, u, v):
F = dolfin.variable(kinematics.DeformationGradient(u))
N = self.geometry.facet_normal
ds = self.geometry.ds
dx = self.geometry.dx
external_work = []
for neumann in self.bcs.neumann:
n = neumann.traction * ufl.cofac(F) * N
external_work.append(dolfin.inner(v, n) * ds(neumann.marker))
for robin in self.bcs.robin:
external_work.append(
dolfin.inner(robin.value * u, v) * ds(robin.marker))
for body_force in self.bcs.body_force:
external_work.append(
-dolfin.derivative(dolfin.inner(body_force, u) * dx, u, v), )
if len(external_work) > 0:
return list_sum(external_work)
return None
def V0constrainedE(self,inverse=False): mesh = self.parameters["mesh"] u = self.parameters["displacement_variable"] ds = dolfin.ds(subdomain_data=self.parameters["facetboundaries"]) dsendo = ds(self.parameters["endoid"], domain = self.parameters["mesh"], subdomain_data = self.parameters["facetboundaries"]) pendo = self.parameters["volconst_variable"] V0= self.parameters["constrained_vol"] X = SpatialCoordinate(mesh) x = u + X F = self.Fmat() N = self.parameters["facet_normal"] n = cofac(F)*N area = assemble(Constant(1.0) * dsendo) if inverse: V_u = - Constant(0.0/3.0) * inner(x, n) Wvol = (Constant(0.0/area) * pendo * V0 * dsendo) - (pendo * V_u *dsendo) else: V_u = - Constant(1.0/3.0) * inner(x, n) Wvol = (Constant(1.0/area) * pendo * V0 * dsendo) - (pendo * V_u *dsendo) return Wvol
###############################################################
# Invariants of deformation tensors (media)
I_m = tr(C_m)
Ie_m = tr(Ce_m)
J_m = det(Fe_m) #Jacobian of F or Fe?
###############################################################
# Invariants of deformation tensors (Adventitia)
I_a = tr(C_a)
Ie_a = tr(Ce_a)
J_a = det(Fe_a)
###############################################################
#deformed normal vector
NansonOp = cofac(F)
deformed_N = dot(NansonOp, n)
###############################################################
# Stored strain energy density (neo-Hookean Hopzafel model)
psi_i = (mu_i / 2) * (Ie_i - 3) + (eta_i / beta_i) * (
exp(beta_i *
(rho_i * (I4_i - 1)**2 + (1 - rho_i) * (Ie_i - 3)**2)) - 1) + (
(mu_i * nu_i) / (1 - 2 * nu_i)) * (J_i - 1)**2 - mu_i * ln(J_i)
psi_m = (mu_m / 2) * (Ie_m - 3) + (eta_m / beta_m) * (
exp(beta_m *
(rho_m * (I4_m - 1)**2 + (1 - rho_m) * (Ie_m - 3)**2)) - 1) + (
(mu_m * nu_m) / (1 - 2 * nu_m)) * (J_m - 1)**2 - mu_m * ln(J_m)
psi_a = (mu_a / 2) * (Ie_a - 3) + (eta_a / beta_a) * (
exp(beta_a *
(rho_a * (I4_a - 1)**2 + (1 - rho_a) * (Ie_a - 3)**2)) - 1) + (