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"])
elif formulation == 'mixed_up':
self.solver = StaticMomentumBalanceSolver_UP(self, self.parameters['solver_parameters'])
elif formulation == 'incompressible':
self.solver = StaticMomentumBalanceSolver_Incompressible(self, self.parameters['solver_parameters'])
# Call solver
return self.solver.solve()
class StaticHyperelasticity(CBCProblem):
"""Base class for all static hyperelasticity problems"""
def __init__(self):
"""Create the static hyperelasticity problem"""
# Set up parameters
self.parameters = Parameters("problem_parameters")
self.parameters.add(solver_parameters())
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"])
elif formulation == 'mixed_up':
self.solver = StaticMomentumBalanceSolver_UP(self, self.parameters['solver_parameters'])
elif formulation == 'incompressible':
self.solver = StaticMomentumBalanceSolver_Incompressible(self, self.parameters['solver_parameters'])
# 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 material_model(self):
pass
def first_pk_stress(self, u):
"""Return the first Piola-Kirchhoff stress tensor, P, given a
displacement field, u"""
return self.material_model().FirstPiolaKirchhoffStress(u)
def second_pk_stress(self, u):
"""Return the second Piola-Kirchhoff stress tensor, S, given a
displacement field, u"""
return self.material_model().SecondPiolaKirchhoffStress(u)
def strain_energy(self, u):
"""Return the strain (potential) energy given a displacement
field, u"""
S = self.material_model().SecondPiolaKirchhoffStress(u)
E = GreenLagrangeStrain(u)
psi = assemble(0.5*inner(S, E)*dx, mesh=u.function_space().mesh())
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"
