def solve(self):
"""Solve for and return the computed displacement field, u"""
# Create solver
formulation = self.parameters['solver_parameters']['problem_formulation']
if formulation == 'displacement':
self.solver = StaticMomentumBalanceSolver_U(self, self.parameters["solver_parameters"],\
self.coordinate_system)
elif formulation == 'mixed_up':
self.solver = StaticMomentumBalanceSolver_UP(self, self.parameters['solver_parameters'],\
self.coordinate_system)
# Call solver
return self.solver.solve()
class StaticHyperelasticity(CBCProblem):
"""Base class for all static hyperelasticity problems"""
def __init__(self, coordinate_system = None):
"""Create the static hyperelasticity problem"""
# Set up parameters
self.parameters = Parameters("problem_parameters")
self.parameters.add(solver_parameters())
self.coordinate_system = coordinate_system
def solve(self):
"""Solve for and return the computed displacement field, u"""
# Create solver
formulation = self.parameters['solver_parameters']['problem_formulation']
if formulation == 'displacement':
self.solver = StaticMomentumBalanceSolver_U(self, self.parameters["solver_parameters"],\
self.coordinate_system)
elif formulation == 'mixed_up':
self.solver = StaticMomentumBalanceSolver_UP(self, self.parameters['solver_parameters'],\
self.coordinate_system)
# Call solver
return self.solver.solve()
def body_force(self):
"""Return body force, B"""
return []
def body_force_u(self, u):
# FIXME: This is currently only implemented for the cG(1) solver
"""Return body force, B, depending on displacement u"""
return []
def dirichlet_values(self):
"""Return Dirichlet boundary conditions for the displacment
field"""
return []
def dirichlet_boundaries(self):
"""Return boundaries over which Dirichlet conditions act"""
return []
def neumann_conditions(self):
"""Return Neumann boundary conditions for the stress field"""
return []
def neumann_boundaries(self):
"""Return boundaries over which Neumann conditions act"""
return []
def periodic_boundaries(self):
""" Return periodic boundaries """
return []
def material_model(self):
pass
def first_pk_stress(self, u):
"""Return the first Piola-Kirchhoff stress tensor, P, given a
displacement field, u"""
material_model = self.material_model()
if isinstance(material_model, tuple):
fpk_list = []
material_list, subdomains_list = material_model
for material in material_list:
fpk_list.append(material.FirstPiolaKirchhoffStress(u, self.coordinate_system))
return (fpk_list, subdomains_list)
else:
return material_model.FirstPiolaKirchhoffStress(u, self.coordinate_system)
def second_pk_stress(self, u):
"""Return the second Piola-Kirchhoff stress tensor, S, given a
displacement field, u"""
material_model = self.material_model()
if isinstance(material_model, tuple):
spk_list = []
material_list, subdomains_list = material_model
for material in material_list:
spk_list.append(material.SecondPiolaKirchhoffStress(u, self.coordinate_system))
return (spk_list, subdomains_list)
else:
return self.material_model().SecondPiolaKirchhoffStress(u, self.coordinate_system)
def strain_energy(self, u):
"""Return the strain (potential) energy density given a displacement
field, u"""
S = self.second_pk_stress(u)
E = GreenLagrangeStrain(u)
if isinstance(S, tuple):
S_list, subdomains_list = S
V = FunctionSpace(u.function_space().mesh(), 'DG', 0)
temp = Function(V)
psi = Function(V)
subdomains = subdomains_list[0]
for cell_no in range(len(subdomains[0].array())):
subdomain_no = subdomains[0].array()[cell_no]
temp = project(0.5*inner(S_list[int(subdomain_no - 1)], E), V)
psi.vector()[cell_no] = temp.vector()[cell_no][0]
else:
psi = 0.5*inner(S, E)
return psi
def functional(self, u):
"""Return value of goal functional"""
return None
def reference(self):
"""Return reference value for the goal functional"""
return None
def __str__(self):
"""Return a short description of the problem"""
return "Static hyperelasticity problem"