def test_save_1d_tensor(tempfile, file_options):
mesh = UnitIntervalMesh(MPI.COMM_WORLD, 32)
u = Function(TensorFunctionSpace(mesh, ("Lagrange", 2)))
u.vector.set(1)
VTKFile(tempfile + "u.pvd").write(u)
for file_option in file_options:
VTKFile(tempfile + "u.pvd", file_option).write(u)
def test_save_3d_tensor(tempdir, encoding, cell_type):
filename = os.path.join(tempdir, "u3t.xdmf")
mesh = UnitCubeMesh(MPI.comm_world, 4, 4, 4, cell_type)
u = Function(TensorFunctionSpace(mesh, ("Lagrange", 2)))
u.vector.set(1.0 + (1j if has_petsc_complex else 0))
with XDMFFile(mesh.mpi_comm(), filename, encoding=encoding) as file:
file.write(u)
def test_save_2d_tensor(tempdir, encoding, cell_type):
filename = os.path.join(tempdir, "tensor.xdmf")
mesh = UnitSquareMesh(MPI.COMM_WORLD, 16, 16, cell_type)
u = Function(TensorFunctionSpace(mesh, ("Lagrange", 2)))
u.vector.set(1.0 + (1j if has_petsc_complex else 0))
with XDMFFile(mesh.mpi_comm(), filename, "w", encoding=encoding) as file:
file.write_mesh(mesh)
file.write_function(u)
def test_save_3d_tensor(tempdir):
mesh = UnitCubeMesh(MPI.COMM_WORLD, 8, 8, 8)
u = Function(TensorFunctionSpace(mesh, ("Lagrange", 2)))
with u.vector.localForm() as loc:
loc.set(1.0)
filename = os.path.join(tempdir, "u.pvd")
with VTKFile(mesh.mpi_comm(), filename, "w") as vtk:
vtk.write_function(u, 0.)
def test_save_3d_tensor(tempfile, file_options):
mesh = UnitCubeMesh(MPI.COMM_WORLD, 8, 8, 8)
u = Function(TensorFunctionSpace(mesh, ("Lagrange", 2)))
u.vector.set(1)
VTKFile(tempfile + "u.pvd").write(u)
f = VTKFile(tempfile + "u.pvd")
f.write(u, 0.)
f.write(u, 1.)
for file_option in file_options:
VTKFile(tempfile + "u.pvd", file_option).write(u)
def test_save_2d_tensor(tempfile, file_options):
mesh = UnitSquareMesh(MPI.comm_world, 16, 16)
u = Function(TensorFunctionSpace(mesh, ("Lagrange", 2)))
u.vector.set(1)
VTKFile(tempfile + "u.pvd").write(u)
f = VTKFile(tempfile + "u.pvd")
f.write(u, 0.)
f.write(u, 1.)
for file_option in file_options:
VTKFile(tempfile + "u.pvd", file_option).write(u)
def Q(mesh):
return TensorFunctionSpace(mesh, ('CG', 1))
def __init__(self, io_params, time_params, fem_params, constitutive_models, bc_dict, time_curves, io, comm=None):
problem_base.__init__(self, io_params, time_params, comm)
self.problem_physics = 'solid'
self.simname = io_params['simname']
self.io = io
# number of distinct domains (each one has to be assigned a own material model)
self.num_domains = len(constitutive_models)
self.order_disp = fem_params['order_disp']
try: self.order_pres = fem_params['order_pres']
except: self.order_pres = 1
self.quad_degree = fem_params['quad_degree']
self.incompressible_2field = fem_params['incompressible_2field']
self.fem_params = fem_params
self.constitutive_models = constitutive_models
# collect domain data
self.dx_, self.rho0, self.rayleigh, self.eta_m, self.eta_k = [], [], [False]*self.num_domains, [], []
for n in range(self.num_domains):
# integration domains
self.dx_.append(dx(subdomain_data=self.io.mt_d, subdomain_id=n+1, metadata={'quadrature_degree': self.quad_degree}))
# data for inertial and viscous forces: density and damping
if self.timint != 'static':
self.rho0.append(constitutive_models['MAT'+str(n+1)+'']['inertia']['rho0'])
if 'rayleigh_damping' in constitutive_models['MAT'+str(n+1)+''].keys():
self.rayleigh[n] = True
self.eta_m.append(constitutive_models['MAT'+str(n+1)+'']['rayleigh_damping']['eta_m'])
self.eta_k.append(constitutive_models['MAT'+str(n+1)+'']['rayleigh_damping']['eta_k'])
try: self.prestress_initial = fem_params['prestress_initial']
except: self.prestress_initial = False
# type of discontinuous function spaces
if str(self.io.mesh.ufl_cell()) == 'tetrahedron' or str(self.io.mesh.ufl_cell()) == 'triangle3D':
dg_type = "DG"
if (self.order_disp > 1 or self.order_pres > 1) and self.quad_degree < 3:
raise ValueError("Use at least a quadrature degree of 3 or more for higher-order meshes!")
elif str(self.io.mesh.ufl_cell()) == 'hexahedron' or str(self.io.mesh.ufl_cell()) == 'quadrilateral3D':
dg_type = "DQ"
if (self.order_disp > 1 or self.order_pres > 1) and self.quad_degree < 5:
raise ValueError("Use at least a quadrature degree of 5 or more for higher-order meshes!")
else:
raise NameError("Unknown cell/element type!")
# create finite element objects for u and p
P_u = VectorElement("CG", self.io.mesh.ufl_cell(), self.order_disp)
P_p = FiniteElement("CG", self.io.mesh.ufl_cell(), self.order_pres)
# function spaces for u and p
self.V_u = FunctionSpace(self.io.mesh, P_u)
self.V_p = FunctionSpace(self.io.mesh, P_p)
# Quadrature tensor, vector, and scalar elements
Q_tensor = TensorElement("Quadrature", self.io.mesh.ufl_cell(), degree=1, quad_scheme="default")
Q_vector = VectorElement("Quadrature", self.io.mesh.ufl_cell(), degree=1, quad_scheme="default")
Q_scalar = FiniteElement("Quadrature", self.io.mesh.ufl_cell(), degree=1, quad_scheme="default")
# not yet working - we cannot interpolate into Quadrature elements with the current dolfinx version currently!
#self.Vd_tensor = FunctionSpace(self.io.mesh, Q_tensor)
#self.Vd_vector = FunctionSpace(self.io.mesh, Q_vector)
#self.Vd_scalar = FunctionSpace(self.io.mesh, Q_scalar)
# Quadrature function spaces (currently not properly functioning for higher-order meshes!!!)
self.Vd_tensor = TensorFunctionSpace(self.io.mesh, (dg_type, self.order_disp-1))
self.Vd_vector = VectorFunctionSpace(self.io.mesh, (dg_type, self.order_disp-1))
self.Vd_scalar = FunctionSpace(self.io.mesh, (dg_type, self.order_disp-1))
# functions
self.du = TrialFunction(self.V_u) # Incremental displacement
self.var_u = TestFunction(self.V_u) # Test function
self.dp = TrialFunction(self.V_p) # Incremental pressure
self.var_p = TestFunction(self.V_p) # Test function
self.u = Function(self.V_u, name="Displacement")
self.p = Function(self.V_p, name="Pressure")
# values of previous time step
self.u_old = Function(self.V_u)
self.v_old = Function(self.V_u)
self.a_old = Function(self.V_u)
self.p_old = Function(self.V_p)
# a setpoint displacement for multiscale analysis
self.u_set = Function(self.V_u)
self.p_set = Function(self.V_p)
self.tau_a_set = Function(self.Vd_scalar)
# initial (zero) functions for initial stiffness evaluation (e.g. for Rayleigh damping)
self.u_ini, self.p_ini, self.theta_ini, self.tau_a_ini = Function(self.V_u), Function(self.V_p), Function(self.Vd_scalar), Function(self.Vd_scalar)
self.theta_ini.vector.set(1.0)
self.theta_ini.vector.ghostUpdate(addv=PETSc.InsertMode.INSERT, mode=PETSc.ScatterMode.FORWARD)
# growth stretch
self.theta = Function(self.Vd_scalar, name="theta")
self.theta_old = Function(self.Vd_scalar)
self.growth_thres = Function(self.Vd_scalar)
# initialize to one (theta = 1 means no growth)
self.theta.vector.set(1.0), self.theta_old.vector.set(1.0)
self.theta.vector.ghostUpdate(addv=PETSc.InsertMode.INSERT, mode=PETSc.ScatterMode.FORWARD), self.theta_old.vector.ghostUpdate(addv=PETSc.InsertMode.INSERT, mode=PETSc.ScatterMode.FORWARD)
# active stress
self.tau_a = Function(self.Vd_scalar, name="tau_a")
self.tau_a_old = Function(self.Vd_scalar)
self.amp_old, self.amp_old_set = Function(self.Vd_scalar), Function(self.Vd_scalar)
self.amp_old.vector.set(1.0), self.amp_old_set.vector.set(1.0)
self.amp_old.vector.ghostUpdate(addv=PETSc.InsertMode.INSERT, mode=PETSc.ScatterMode.FORWARD), self.amp_old_set.vector.ghostUpdate(addv=PETSc.InsertMode.INSERT, mode=PETSc.ScatterMode.FORWARD)
# prestressing history defgrad and spring prestress
if self.prestress_initial:
self.F_hist = Function(self.Vd_tensor, name="Defgrad_hist")
self.u_pre = Function(self.V_u)
else:
self.F_hist = None
self.u_pre = None
self.internalvars = {"theta" : self.theta, "tau_a" : self.tau_a}
self.internalvars_old = {"theta" : self.theta_old, "tau_a" : self.tau_a_old}
# reference coordinates
self.x_ref = Function(self.V_u)
self.x_ref.interpolate(self.x_ref_expr)
if self.incompressible_2field:
self.ndof = self.u.vector.getSize() + self.p.vector.getSize()
else:
self.ndof = self.u.vector.getSize()
# initialize solid time-integration class
self.ti = timeintegration.timeintegration_solid(time_params, fem_params, time_curves, self.t_init, self.comm)
# check for materials that need extra treatment (anisotropic, active stress, growth, ...)
have_fiber1, have_fiber2 = False, False
self.have_active_stress, self.active_stress_trig, self.have_frank_starling, self.have_growth = False, 'ode', False, False
self.mat_active_stress, self.mat_growth, self.mat_remodel, self.mat_growth_dir, self.mat_growth_trig, self.mat_growth_thres = [False]*self.num_domains, [False]*self.num_domains, [False]*self.num_domains, [None]*self.num_domains, [None]*self.num_domains, []*self.num_domains
self.localsolve, growth_dir = False, None
self.actstress = []
for n in range(self.num_domains):
if 'holzapfelogden_dev' in self.constitutive_models['MAT'+str(n+1)+''].keys() or 'guccione_dev' in self.constitutive_models['MAT'+str(n+1)+''].keys():
have_fiber1, have_fiber2 = True, True
if 'active_fiber' in self.constitutive_models['MAT'+str(n+1)+''].keys():
have_fiber1 = True
self.mat_active_stress[n], self.have_active_stress = True, True
# if one mat has a prescribed active stress, all have to be!
if 'prescribed_curve' in self.constitutive_models['MAT'+str(n+1)+'']['active_fiber']:
self.active_stress_trig = 'prescribed'
if 'prescribed_multiscale' in self.constitutive_models['MAT'+str(n+1)+'']['active_fiber']:
self.active_stress_trig = 'prescribed_multiscale'
if self.active_stress_trig == 'ode':
act_curve = self.ti.timecurves(self.constitutive_models['MAT'+str(n+1)+'']['active_fiber']['activation_curve'])
self.actstress.append(activestress_activation(self.constitutive_models['MAT'+str(n+1)+'']['active_fiber'], act_curve))
if self.actstress[-1].frankstarling: self.have_frank_starling = True
if self.active_stress_trig == 'prescribed':
self.ti.funcs_to_update.append({self.tau_a : self.ti.timecurves(self.constitutive_models['MAT'+str(n+1)+'']['active_fiber']['prescribed_curve'])})
if 'active_iso' in self.constitutive_models['MAT'+str(n+1)+''].keys():
self.mat_active_stress[n], self.have_active_stress = True, True
# if one mat has a prescribed active stress, all have to be!
if 'prescribed_curve' in self.constitutive_models['MAT'+str(n+1)+'']['active_iso']:
self.active_stress_trig = 'prescribed'
if 'prescribed_multiscale' in self.constitutive_models['MAT'+str(n+1)+'']['active_iso']:
self.active_stress_trig = 'prescribed_multiscale'
if self.active_stress_trig == 'ode':
act_curve = self.ti.timecurves(self.constitutive_models['MAT'+str(n+1)+'']['active_iso']['activation_curve'])
self.actstress.append(activestress_activation(self.constitutive_models['MAT'+str(n+1)+'']['active_iso'], act_curve))
if self.active_stress_trig == 'prescribed':
self.ti.funcs_to_update.append({self.tau_a : self.ti.timecurves(self.constitutive_models['MAT'+str(n+1)+'']['active_iso']['prescribed_curve'])})
if 'growth' in self.constitutive_models['MAT'+str(n+1)+''].keys():
self.mat_growth[n], self.have_growth = True, True
self.mat_growth_dir[n] = self.constitutive_models['MAT'+str(n+1)+'']['growth']['growth_dir']
self.mat_growth_trig[n] = self.constitutive_models['MAT'+str(n+1)+'']['growth']['growth_trig']
# need to have fiber fields for the following growth options
if self.mat_growth_dir[n] == 'fiber' or self.mat_growth_trig[n] == 'fibstretch':
have_fiber1 = True
if self.mat_growth_dir[n] == 'radial':
have_fiber1, have_fiber2 = True, True
# in this case, we have a theta that is (nonlinearly) dependent on the deformation, theta = theta(C(u)),
# therefore we need a local Newton iteration to solve for equilibrium theta (return mapping) prior to entering
# the global Newton scheme - so flag localsolve to true
if self.mat_growth_trig[n] != 'prescribed' and self.mat_growth_trig[n] != 'prescribed_multiscale':
self.localsolve = True
self.mat_growth_thres.append(self.constitutive_models['MAT'+str(n+1)+'']['growth']['growth_thres'])
else:
self.mat_growth_thres.append(as_ufl(0))
# for the case that we have a prescribed growth stretch over time, append curve to functions that need time updates
# if one mat has a prescribed growth model, all have to be!
if self.mat_growth_trig[n] == 'prescribed':
self.ti.funcs_to_update.append({self.theta : self.ti.timecurves(self.constitutive_models['MAT'+str(n+1)+'']['growth']['prescribed_curve'])})
if 'remodeling_mat' in self.constitutive_models['MAT'+str(n+1)+'']['growth'].keys():
self.mat_remodel[n] = True
else:
self.mat_growth_thres.append(as_ufl(0))
# full linearization of our remodeling law can lead to excessive compiler times for ffcx... :-/
# let's try if we might can go without one of the critial terms (derivative of remodeling fraction w.r.t. C)
try: self.lin_remod_full = fem_params['lin_remodeling_full']
except: self.lin_remod_full = True
# growth threshold (as function, since in multiscale approach, it can vary element-wise)
if self.have_growth and self.localsolve:
growth_thres_proj = project(self.mat_growth_thres, self.Vd_scalar, self.dx_)
self.growth_thres.vector.ghostUpdate(addv=PETSc.InsertMode.ADD, mode=PETSc.ScatterMode.REVERSE)
self.growth_thres.interpolate(growth_thres_proj)
# read in fiber data
if have_fiber1:
fibarray = ['fiber']
if have_fiber2: fibarray.append('sheet')
# fiber function space - vector defined on quadrature points
V_fib = self.Vd_vector
self.fib_func = self.io.readin_fibers(fibarray, V_fib, self.dx_)
else:
self.fib_func = None
# for multiscale G&R analysis
self.tol_stop_large = 0
# initialize kinematics class
self.ki = solid_kinematics_constitutive.kinematics(fib_funcs=self.fib_func, F_hist=self.F_hist)
# initialize material/constitutive class
self.ma = []
for n in range(self.num_domains):
self.ma.append(solid_kinematics_constitutive.constitutive(self.ki, self.constitutive_models['MAT'+str(n+1)+''], self.incompressible_2field, mat_growth=self.mat_growth[n], mat_remodel=self.mat_remodel[n]))
# initialize solid variational form class
self.vf = solid_variationalform.variationalform(self.var_u, self.du, self.var_p, self.dp, self.io.n0, self.x_ref)
# initialize boundary condition class
self.bc = boundaryconditions.boundary_cond_solid(bc_dict, self.fem_params, self.io, self.ki, self.vf, self.ti)
if self.prestress_initial:
# initialize prestressing history deformation gradient
Id_proj = project(Identity(len(self.u)), self.Vd_tensor, self.dx_)
self.F_hist.interpolate(Id_proj)
self.bc_dict = bc_dict
# Dirichlet boundary conditions
if 'dirichlet' in self.bc_dict.keys():
self.bc.dirichlet_bcs(self.V_u)
self.set_variational_forms_and_jacobians()
def Q(mesh):
return TensorFunctionSpace(mesh, ('Lagrange', 1))
def __init__(self,
io_params,
time_params,
fem_params,
constitutive_models,
bc_dict,
time_curves,
io,
comm=None):
problem_base.__init__(self, io_params, time_params, comm)
self.problem_physics = 'fluid'
self.simname = io_params['simname']
self.io = io
# number of distinct domains (each one has to be assigned a own material model)
self.num_domains = len(constitutive_models)
self.order_vel = fem_params['order_vel']
self.order_pres = fem_params['order_pres']
self.quad_degree = fem_params['quad_degree']
# collect domain data
self.dx_, self.rho = [], []
for n in range(self.num_domains):
# integration domains
self.dx_.append(
dx(subdomain_data=self.io.mt_d,
subdomain_id=n + 1,
metadata={'quadrature_degree': self.quad_degree}))
# data for inertial forces: density
self.rho.append(constitutive_models['MAT' + str(n + 1) +
'']['inertia']['rho'])
self.incompressible_2field = True # always true!
self.localsolve = False # no idea what might have to be solved locally...
self.prestress_initial = False # guess prestressing in fluid is somehow senseless...
self.p11 = as_ufl(
0
) # can't think of a fluid case with non-zero 11-block in system matrix...
# type of discontinuous function spaces
if str(self.io.mesh.ufl_cell()) == 'tetrahedron' or str(
self.io.mesh.ufl_cell()) == 'triangle3D':
dg_type = "DG"
if (self.order_vel > 1
or self.order_pres > 1) and self.quad_degree < 3:
raise ValueError(
"Use at least a quadrature degree of 3 or more for higher-order meshes!"
)
elif str(self.io.mesh.ufl_cell()) == 'hexahedron' or str(
self.io.mesh.ufl_cell()) == 'quadrilateral3D':
dg_type = "DQ"
if (self.order_vel > 1
or self.order_pres > 1) and self.quad_degree < 5:
raise ValueError(
"Use at least a quadrature degree of 5 or more for higher-order meshes!"
)
else:
raise NameError("Unknown cell/element type!")
# create finite element objects for v and p
self.P_v = VectorElement("CG", self.io.mesh.ufl_cell(), self.order_vel)
self.P_p = FiniteElement("CG", self.io.mesh.ufl_cell(),
self.order_pres)
# function spaces for v and p
self.V_v = FunctionSpace(self.io.mesh, self.P_v)
self.V_p = FunctionSpace(self.io.mesh, self.P_p)
# a discontinuous tensor, vector, and scalar function space
self.Vd_tensor = TensorFunctionSpace(self.io.mesh,
(dg_type, self.order_vel - 1))
self.Vd_vector = VectorFunctionSpace(self.io.mesh,
(dg_type, self.order_vel - 1))
self.Vd_scalar = FunctionSpace(self.io.mesh,
(dg_type, self.order_vel - 1))
# functions
self.dv = TrialFunction(self.V_v) # Incremental velocity
self.var_v = TestFunction(self.V_v) # Test function
self.dp = TrialFunction(self.V_p) # Incremental pressure
self.var_p = TestFunction(self.V_p) # Test function
self.v = Function(self.V_v, name="Velocity")
self.p = Function(self.V_p, name="Pressure")
# values of previous time step
self.v_old = Function(self.V_v)
self.a_old = Function(self.V_v)
self.p_old = Function(self.V_p)
self.ndof = self.v.vector.getSize() + self.p.vector.getSize()
# initialize fluid time-integration class
self.ti = timeintegration.timeintegration_fluid(
time_params, fem_params, time_curves, self.t_init, self.comm)
# initialize kinematics_constitutive class
self.ki = fluid_kinematics_constitutive.kinematics()
# initialize material/constitutive class
self.ma = []
for n in range(self.num_domains):
self.ma.append(
fluid_kinematics_constitutive.constitutive(
self.ki, constitutive_models['MAT' + str(n + 1) + '']))
# initialize fluid variational form class
self.vf = fluid_variationalform.variationalform(
self.var_v, self.dv, self.var_p, self.dp, self.io.n0)
# initialize boundary condition class
self.bc = boundaryconditions.boundary_cond_fluid(
bc_dict, fem_params, self.io, self.ki, self.vf, self.ti)
self.bc_dict = bc_dict
# Dirichlet boundary conditions
if 'dirichlet' in self.bc_dict.keys():
self.bc.dirichlet_bcs(self.V_v)
self.set_variational_forms_and_jacobians()