Merge pull request #91 from sandialabs/ralberd/add_snap_example

Snap through example

Author: ralberd

examples/snap_through_cell/plot_results.py

@@ -0,0 +1,75 @@
+from matplotlib import pyplot as plt
+import numpy as np
+
+# Plotting settings
+legendFontSize = 14
+axisFontSize = 14
+lineWidth = 3.0
+
+def plot_total_work(fileName, linestyle='-'):
+    energies = np.load(fileName)
+    totalWork = energies['totalWork']
+    if 'time' in energies:
+        time = np.cumsum(energies['time'])
+        plt.plot(time, totalWork, linestyle=linestyle, linewidth=lineWidth)
+    else:
+        plt.plot(totalWork, linestyle=linestyle, linewidth=lineWidth)
+
+def plot_strain_energy(fileName, linestyle='-'):
+    energies = np.load(fileName)
+    strainEnergy = energies['strainEnergy']
+    if 'time' in energies:
+        time = np.cumsum(energies['time'])
+        plt.plot(time, strainEnergy, linestyle=linestyle, linewidth=lineWidth)
+    else:
+        plt.plot(strainEnergy, linestyle=linestyle, linewidth=lineWidth)
+
+def plot_dissipated_energy(fileName, linestyle='-'):
+    energies = np.load(fileName)
+    dissipatedEnergy = energies['dissipatedEnergy']
+    if 'time' in energies:
+        time = np.cumsum(energies['time'])
+        plt.plot(time, dissipatedEnergy, linestyle=linestyle, linewidth=lineWidth)
+    else:
+        plt.plot(dissipatedEnergy, linestyle=linestyle, linewidth=lineWidth)
+
+def plot_force_disp(fileName, linestyle='-'):
+    norm_x = -1.0
+    norm_y = -1.0
+    histories = np.load(fileName)
+    forces = norm_x*histories['force']
+    disps = norm_y*histories['displacement']
+    plt.plot(disps, forces, linestyle=linestyle, linewidth=lineWidth)
+
+# plot files
+energyPrefix = "energy_histories"
+forceDispPrefix = "force_control_response"
+fileType = ".npz"
+
+# plot force-displacement
+forceDispFile = forceDispPrefix + fileType
+plot_force_disp(forceDispFile, '-')
+
+plt.xlabel('Displacement (mm)', fontsize=axisFontSize)
+plt.ylabel('Force (N)', fontsize=axisFontSize)
+plt.xticks(fontsize=axisFontSize)
+plt.yticks(fontsize=axisFontSize)
+plt.savefig('force_disp.png')
+
+# plot energy histories
+plt.figure()
+
+energyFile = energyPrefix + fileType
+plot_total_work(energyFile, '-')
+plot_strain_energy(energyFile, ':')
+plot_dissipated_energy(energyFile, '--')
+
+if 'time' in np.load(energyFile):
+    plt.xlabel('Time(s)', fontsize=axisFontSize)
+else:
+    plt.xlabel('Step', fontsize=axisFontSize)
+plt.ylabel('Energy (mJ)', fontsize=axisFontSize)
+plt.xticks(fontsize=axisFontSize)
+plt.yticks(fontsize=axisFontSize)
+plt.legend(["External Work", "Strain Energy", "Dissipated Energy"], loc=0, frameon=True, fontsize=legendFontSize)
+plt.savefig('energy_histories.png')

examples/snap_through_cell/snap_cell.exo

@@ -0,0 +1,237 @@
+from jax import jit
+from optimism import EquationSolver
+from optimism import VTKWriter
+from optimism import FunctionSpace
+from optimism import Interpolants
+from optimism import Mechanics
+from optimism import Mesh
+from optimism import Objective
+from optimism import QuadratureRule
+from optimism import ReadExodusMesh
+from optimism import SparseMatrixAssembler
+from optimism.FunctionSpace import DofManager
+from optimism.FunctionSpace import EssentialBC
+from optimism.material import Neohookean
+
+import jax.numpy as np
+from optimism.inverse import AdjointFunctionSpace
+from collections import namedtuple
+
+EnergyFunctions = namedtuple('EnergyFunctions',
+                            ['energy_function_coords'])
+
+# simulation parameterized on mesh node coordinates
+class CoordinateParameterizedSimulation:
+
+    def __init__(self):
+        self.writeOutput = True
+
+        self.quad_rule = QuadratureRule.create_quadrature_rule_on_triangle(degree=2)
+        self.lineQuadRule = QuadratureRule.create_quadrature_rule_1D(degree=2)
+
+        self.ebcs = [
+            EssentialBC(nodeSet='bottom_sideset', component=1),
+
+            EssentialBC(nodeSet='right_sideset', component=0),
+            EssentialBC(nodeSet='left_sideset', component=0),
+        ]
+
+        shearModulus = 0.855 # MPa
+        bulkModulus = 1000*shearModulus # MPa
+        youngModulus = 9.0*bulkModulus*shearModulus / (3.0*bulkModulus + shearModulus)
+        poissonRatio = (3.0*bulkModulus - 2.0*shearModulus) / 2.0 / (3.0*bulkModulus + shearModulus)
+        props = {
+            'elastic modulus': youngModulus,
+            'poisson ratio': poissonRatio,
+            'version': 'coupled'
+        }
+        self.mat_model = Neohookean.create_material_model_functions(props)
+
+        self.eq_settings = EquationSolver.get_settings(max_trust_iters=2500, use_preconditioned_inner_product_for_cg=True)
+
+        self.input_mesh = './snap_cell.exo'
+
+        self.maxForce = -3.0
+        self.plot_file = 'force_control_response.npz'
+        self.stages = 1
+        steps_per_stage = 65
+        self.steps = self.stages * steps_per_stage
+
+    def create_field(self, Uu):
+        def get_ubcs():
+            V = np.zeros(self.mesh.coords.shape)
+            return self.dof_manager.get_bc_values(V)
+
+        return self.dof_manager.create_field(Uu, get_ubcs())
+
+    def reload_mesh(self):
+        origMesh = ReadExodusMesh.read_exodus_mesh(self.input_mesh)
+        self.mesh = Mesh.create_higher_order_mesh_from_simplex_mesh(origMesh, order=2, createNodeSetsFromSideSets=True)
+
+        func_space = FunctionSpace.construct_function_space(self.mesh, self.quad_rule)
+        self.dof_manager = DofManager(func_space, 2, self.ebcs)
+
+        surfaceXCoords = self.mesh.coords[self.mesh.nodeSets['top_sideset']][:,0]
+        self.tractionArea = np.max(surfaceXCoords) - np.min(surfaceXCoords)
+
+        self.stateNotStored = True
+        self.state = []
+
+    def run_simulation(self):
+
+        func_space = FunctionSpace.construct_function_space(self.mesh, self.quad_rule)
+        mech_funcs = Mechanics.create_mechanics_functions(func_space, mode2D='plane strain', materialModel=self.mat_model)
+
+        # methods defined on the fly
+        def energy_function(Uu, p):
+            U = self.create_field(Uu)
+            internal_variables = p.state_data
+            strainEnergy = mech_funcs.compute_strain_energy(U, internal_variables)
+
+            F = p.bc_data
+            def force_function(x, n):
+                return np.array([0.0, F/self.tractionArea])
+
+            loadPotential = Mechanics.compute_traction_potential_energy(
+                func_space, U, self.lineQuadRule, self.mesh.sideSets['top_sideset'], 
+                force_function)
+
+            return strainEnergy + loadPotential
+
+        def assemble_sparse(Uu, p):
+            U = self.create_field(Uu)
+            internal_variables = p.state_data
+            element_stiffnesses = mech_funcs.compute_element_stiffnesses(U, internal_variables)
+            return SparseMatrixAssembler.\
+                assemble_sparse_stiffness_matrix(element_stiffnesses, func_space.mesh.conns, self.dof_manager)
+    
+        def store_force_displacement(Uu, force_val, force, disp):
+            U = self.create_field(Uu)
+
+            index = (self.mesh.nodeSets['top_sideset'], 1)
+
+            force.append( force_val )
+            disp.append(np.mean(U.at[index].get()))
+
+            with open(self.plot_file,'wb') as f:
+                np.savez(f, force=force, displacement=disp)
+
+        def write_vtk_output(Uu, p, step):
+            U = self.create_field(Uu)
+            plotName = 'output-'+str(step).zfill(3)
+            writer = VTKWriter.VTKWriter(self.mesh, baseFileName=plotName)
+
+            writer.add_nodal_field(name='displ', nodalData=U, fieldType=VTKWriter.VTKFieldType.VECTORS)
+
+            energyDensities = mech_funcs.compute_output_energy_densities_and_stresses(U, p.state_data)[0]
+            cellEnergyDensities = FunctionSpace.project_quadrature_field_to_element_field(func_space, energyDensities)
+            writer.add_cell_field(name='strain_energy_density',
+                                  cellData=cellEnergyDensities,
+                                  fieldType=VTKWriter.VTKFieldType.SCALARS)
+            writer.write()
+
+        # problem set up
+        Uu = self.dof_manager.get_unknown_values(np.zeros(self.mesh.coords.shape))
+        ivs = mech_funcs.compute_initial_state()
+        p = Objective.Params(bc_data=0., state_data=ivs)
+        precond_strategy = Objective.PrecondStrategy(assemble_sparse)
+        self.objective = Objective.Objective(energy_function, Uu, p, precond_strategy)
+
+        # loop over load steps
+        force = 0.
+        fd_force = []
+        fd_disp = []
+
+        store_force_displacement(Uu, force, fd_force, fd_disp)
+        self.state.append((Uu, p))
+
+        steps_per_stage = int(self.steps / self.stages)
+        force_inc = self.maxForce / steps_per_stage
+        for step in range(1, steps_per_stage+1):
+            print('--------------------------------------')
+            print('LOAD STEP ', step)
+            force += force_inc
+            p = Objective.param_index_update(p, 0, force)
+            Uu, solverSuccess = EquationSolver.nonlinear_equation_solve(self.objective, Uu, p, self.eq_settings)
+
+            store_force_displacement(Uu, force, fd_force, fd_disp)
+            self.state.append((Uu, p))
+
+            if self.writeOutput:
+              write_vtk_output(Uu, p, step + 1)
+
+        self.stateNotStored = False
+
+    # energy functions for computing optimization quantities of interest
+    def setup_energy_functions(self):
+        shapeOnRef = Interpolants.compute_shapes(self.mesh.parentElement, self.quad_rule.xigauss)
+
+        def energy_function_all_dofs(U, p, coords):
+            adjoint_func_space = AdjointFunctionSpace.construct_function_space_for_adjoint(coords, shapeOnRef, self.mesh, self.quad_rule)
+            mech_funcs = Mechanics.create_mechanics_functions(adjoint_func_space, mode2D='plane strain', materialModel=self.mat_model)
+            ivs = p.state_data
+            return mech_funcs.compute_strain_energy(U, ivs)
+
+        def energy_function_coords(Uu, p, coords):
+            U = self.create_field(Uu)
+            return energy_function_all_dofs(U, p, coords)
+
+        return EnergyFunctions(energy_function_coords)
+
+    def compute_energy_quantities(self, uSteps, pSteps, coordinates, energy_function_coords):
+        index = (self.mesh.nodeSets['top_sideset'], 1)
+
+        totalWork = 0.0
+        complementaryWork = 0.0
+        totalWorkStored = []
+        complementaryWorkStored = []
+        strainEnergyStored = []
+        dissipatedEnergyStored = []
+        for step in range(1, self.steps+1):
+            Uu = uSteps[step]
+            p = pSteps[step]
+            U = self.create_field(Uu)
+            force = p.bc_data
+            disp = np.mean(U.at[index].get())
+
+            Uu_prev = uSteps[step-1]
+            p_prev = pSteps[step-1]
+            U_prev = self.create_field(Uu_prev)
+            force_prev = p_prev.bc_data
+            disp_prev = np.mean(U_prev.at[index].get())
+
+            totalWork += 0.5*(force + force_prev)*(disp - disp_prev)
+            complementaryWork += 0.5*(force - force_prev)*(disp + disp_prev)
+
+            totalWorkStored.append(totalWork)
+            complementaryWorkStored.append(complementaryWork)
+            strainEnergyStored.append(energy_function_coords(Uu, p, coordinates))
+            dissipatedEnergyStored.append(totalWork - energy_function_coords(Uu, p, coordinates))
+
+        print("\n Quantities of Interest:")
+        print(f"total work: {totalWork}")
+        print(f"complementary work: {complementaryWork}")
+        print(f"strain energy: {energy_function_coords(Uu, p, coordinates)}")
+        print(f"dissipated energy: {totalWork - energy_function_coords(Uu, p, coordinates)}")
+
+        with open("energy_histories.npz",'wb') as f:
+            np.savez(f, totalWork=totalWorkStored, complementaryWork=complementaryWorkStored, strainEnergy=strainEnergyStored, dissipatedEnergy=dissipatedEnergyStored)
+
+    def compute_qois(self):
+        if self.stateNotStored:
+            self.run_simulation()
+
+        parameters = self.mesh.coords
+        energyFuncs = self.setup_energy_functions()
+
+        uSteps = np.stack([self.state[i][0] for i in range(0, self.steps+1)], axis=0)
+        pSteps = [self.state[i][1] for i in range(0, self.steps+1)]
+
+        self.compute_energy_quantities(uSteps, pSteps, parameters, jit(energyFuncs.energy_function_coords)) 
+
+
+
+if __name__ == '__main__':
+    sim = CoordinateParameterizedSimulation()
+    sim.reload_mesh()
+    sim.compute_qois()