nonlinear_problem.py 7.69 KB
 Jeremy BLEYER committed Feb 24, 2020 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 ``````from dolfin import * from mfront_wrapper.utils import * import mgis.behaviour as mgis_bv class MFrontNonlinearProblem(NonlinearProblem): def __init__(self, u, material, quadrature_degree=2): NonlinearProblem.__init__(self) self.u = u self.V = self.u.function_space() self.u_ = TestFunction(self.V) self.du = TrialFunction(self.V) self.mesh = self.V.mesh() self.material = material # print(self.material.hypothesis) self.axisymmetric = self.material.hypothesis==mgis_bv.Hypothesis.Axisymmetrical `````` Jeremy BLEYER committed Feb 24, 2020 16 `````` self.integration_type = mgis_bv.IntegrationType.IntegrationWithConsistentTangentOperator `````` Jeremy BLEYER committed Feb 24, 2020 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 `````` self.quadrature_degree = quadrature_degree self.set_quadrature_function_spaces() self.bc = [] self.dx = Measure("dx", metadata={"quadrature_degree": self.quadrature_degree, "quadrature_scheme": "default"}) if self.axisymmetric: x = SpatialCoordinate(self.mesh) measure = 2*pi*abs(x[0]) else: measure = 1 self.initialize_fields() # tangent bilinear form self.a = inner(self.strain_variation(self.du), dot(self.Ct, self.strain_variation(self.u_)))*measure*self.dx # residual form (internal forces) self.L = inner(self.strain_variation(self.u_), self.stress)*measure*self.dx self.solver = NewtonSolver() self.state_variables = [] def set_loading(self, Fext): # adds external forces to residual form self.L -= ufl.replace(Fext, {self.u: self.u_}) def set_quadrature_function_spaces(self): cell = self.mesh.ufl_cell() W0e = get_quadrature_element(cell, self.quadrature_degree) # scalar quadrature space self.W0 = FunctionSpace(self.mesh, W0e) # compute Gauss points numbers self.ngauss = self.W0.dim() # Set data manager self.material.set_data_manager(self.ngauss) self.finite_strain = self.material.behaviour.getBehaviourType()=="StandardFiniteStrainBehaviour" if self.material.hypothesis == mgis_bv.Hypothesis.Tridimensional: assert self.u.geometric_dimension()==3, "Conflicting geometric dimension and material hypothesis" else: assert self.u.geometric_dimension()==2, "Conflicting geometric dimension and material hypothesis" # Get strain measure dimension self.strain_dim = ufl.shape(self.strain_measure(self.u))[0] # Define quadrature spaces for stress/strain and tangent matrix Wsige = get_quadrature_element(cell, self.quadrature_degree, self.strain_dim) # stress/strain quadrature space self.Wsig = FunctionSpace(self.mesh, Wsige) Wce = get_quadrature_element(cell, self.quadrature_degree, (self.strain_dim, self.strain_dim)) # tangent matrix quadrature space self.WCt = FunctionSpace(self.mesh, Wce) def strain_measure(self, v): """ Strain measure associated with stress measure: * small strain behaviour: linearized strain tensor epsilon = sym(grad(u)) * finite strain behaviour: transformation gradient F = Id + grad(u) """ if self.axisymmetric: r = abs(SpatialCoordinate(self.mesh)[0]) g = axi_grad(r, v) E = symmetric_tensor_to_vector(sym(g)) if v.geometric_dimension()==2: return as_vector([E[i] for i in range(4)]) else: g = grad(v) if self.finite_strain: return transformation_gradient(g, dim=v.geometric_dimension()) else: return symmetric_gradient(g) def strain_variation(self, v): """ Variation of strain measure associated with stress measure: * small strain behaviour: linearized strain tensor d_epsilon = sym(grad(du)) * finite strain behaviour: displacement gradient d_F = grad(du) """ if self.axisymmetric: r = abs(SpatialCoordinate(self.mesh)[0]) g = axi_grad(r, v) E = symmetric_tensor_to_vector(sym(g)) if v.geometric_dimension()==2: return as_vector([E[i] for i in range(4)]) else: g = grad(v) if self.finite_strain: return gradient(g) else: return symmetric_gradient(g) def initialize_fields(self): self.stress = Function(self.Wsig, name="Current stress") self.strain = Function(self.Wsig, name="Current strain increment") self.Ct = Function(self.WCt, name="Consistent tangent operator") `````` Jeremy BLEYER committed Feb 24, 2020 110 111 `````` mgis_bv.integrate(self.material.data_manager, self.integration_type, 0, 0, self.material.data_manager.n); `````` Jeremy BLEYER committed Feb 24, 2020 112 113 114 115 116 117 118 119 120 121 122 123 `````` if self.finite_strain: local_project(self.strain_measure(self.u), self.Wsig, self.dx, self.strain) # copy the strain values to `MGIS` self.material.data_manager.s0.gradients[:, :] = self.strain.vector().get_local().reshape((self.material.data_manager.n, self.strain_dim)) else: self.Ct.vector().set_local(self.material.data_manager.K.flatten()) def update_constitutive_law(self, u): local_project(self.strain_measure(u), self.Wsig, self.dx, self.strain) # copy the strain values to `MGIS` self.material.data_manager.s1.gradients[:, :] = self.strain.vector().get_local().reshape((self.material.data_manager.n, self.strain_dim)) # integrate the behaviour `````` Jeremy BLEYER committed Feb 24, 2020 124 125 `````` mgis_bv.integrate(self.material.data_manager, self.integration_type, 0, 0, self.material.data_manager.n); `````` Jeremy BLEYER committed Feb 24, 2020 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 `````` # getting the stress and consistent tangent operator back to # the FEniCS world. if self.finite_strain: pk1v = self.stress.vector().get_local() mgis_bv.convertFiniteStrainStress(pk1v, self.material.data_manager, mgis_bv.FiniteStrainStress.PK1) self.stress.vector().set_local(pk1v) Ctv = self.Ct.vector().get_local() mgis_bv.convertFiniteStrainTangentOperator(Ctv, self.material.data_manager, mgis_bv.FiniteStrainTangentOperator.DPK1_DF) self.Ct.vector().set_local(Ctv) else: self.stress.vector().set_local(self.material.data_manager.s1.thermodynamic_forces.flatten()) self.Ct.vector().set_local(self.material.data_manager.K.flatten()) sizes = self.material.get_state_variable_sizes() for (s, i) in self.state_variables: size = sizes[i] s.vector().set_local(self.material.data_manager.s1.internal_state_variables[:, i:(i+size)].flatten()) def get_state_variable(self, name=None, position=None): if name is not None: position = self.material.get_state_variable_names().index(name) elif position is not None: name = self.material.get_state_variable_names()[position] else: raise ValueError("Name or position of state variable must be specified.") shape = self.material.get_state_variable_sizes()[position] We = get_quadrature_element(self.mesh.ufl_cell(), self.quadrature_degree, shape) W = FunctionSpace(self.mesh, We) self.state_variables.append([Function(W, name=name), position]) return self.state_variables[-1][0] def form(self, A, P, b, x): self.update_constitutive_law(self.u) assemble_system(self.a, self.L, A_tensor=A, b_tensor=b, bcs=self.bc, x0=x) def F(self,b,x): pass def J(self,A,x): pass def solve(self, x): self.solver.solve(self, x) mgis_bv.update(self.material.data_manager) ``````