import pathlib
from optimism.JaxConfig import *
from optimism import FunctionSpace
from optimism.material import LinearElastic as MaterialModel
from optimism import Mesh
from optimism.Timer import Timer
from optimism.EquationSolver import newton_solve
from optimism import QuadratureRule
from optimism import Surface
from . import TestFixture
from optimism import ReadMesh
from optimism import Mechanics
TEST_FILE = pathlib.Path(__file__).parent.joinpath('patch.json')
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class TestMeshReadData(TestFixture.TestFixture):
# output from explore patch.g:
# Number of nodes = 36
# Number of elements = 50
# Number of element blocks = 1
# Number of nodal point sets = 5
# Length of node list = 30
# Length of distribution list = 30
# Number of element side sets = 5
# Length of element list = 25
# Length of node list = 50
# Length of distribution list = 50
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def setUp(self):
self.mesh = ReadMesh.read_json_mesh(TEST_FILE)
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def test_entity_counts(self):
readNodes = self.mesh.coords.shape[0]
self.assertEqual(readNodes, 36)
readElements = self.mesh.conns.shape[0]
self.assertEqual(readElements, 50)
readNodeSets = len(self.mesh.nodeSets)
self.assertEqual(readNodeSets, 5)
readSideSets = len(self.mesh.sideSets)
self.assertEqual(readSideSets, 5)
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def test_all_sets_named(self):
for ns in self.mesh.nodeSets:
self.assertGreater(len(ns), 0)
for ss in self.mesh.sideSets:
self.assertGreater(len(ss), 0)
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def interpolate_nodal_field_on_edge(mesh, U, quadRule, edge):
fieldIndex = Surface.get_field_index(edge, mesh.conns)
nodalValues = Surface.eval_field(U, fieldIndex)
return QuadratureRule.eval_at_iso_points(quadRule.xigauss, nodalValues)
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def compute_traction_potential_energy_on_edge(mesh, U, quadRule, edge, load):
uq = interpolate_nodal_field_on_edge(mesh, U, quadRule, edge)
Xq = interpolate_nodal_field_on_edge(mesh, mesh.coords, quadRule, edge)
tq = vmap(load)(Xq)
edgeCoords = Surface.get_coords(mesh, edge)
integrand = vmap(lambda u,t: u@t)(uq, tq)
return -Surface.integrate_values(quadRule, edgeCoords, integrand)
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def compute_traction_potential_energy(mesh, U, quadRule, edges, load):
return np.sum( vmap(compute_traction_potential_energy_on_edge, (None,None,None,0,None))(mesh, U, quadRule, edges, load) )
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class TestMeshReadPatchTest(TestFixture.TestFixture):
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def setUp(self):
self.mesh = ReadMesh.read_json_mesh(TEST_FILE)
quadRule = QuadratureRule.create_quadrature_rule_on_triangle(degree=1)
self.fs = FunctionSpace.construct_function_space(self.mesh, quadRule)
self.E = 1.0
self.nu = 0.3
props = {'elastic modulus': self.E,
'poisson ratio': self.nu}
materialModel = MaterialModel.create_material_model_functions(props)
self.props = MaterialModel.create_material_properties(props)
mechBvp = Mechanics.create_mechanics_functions(self.fs,
"plane strain",
materialModel)
self.compute_strain_energy = mechBvp.compute_strain_energy
self.internalVariables = mechBvp.compute_initial_state()
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def test_dirichlet_patch_test(self):
ebcs = [FunctionSpace.EssentialBC(nodeSet='left', component=0),
FunctionSpace.EssentialBC(nodeSet='left', component=1),
FunctionSpace.EssentialBC(nodeSet='bottom', component=0),
FunctionSpace.EssentialBC(nodeSet='bottom', component=1),
FunctionSpace.EssentialBC(nodeSet='right', component=0),
FunctionSpace.EssentialBC(nodeSet='right', component=1),
FunctionSpace.EssentialBC(nodeSet='top', component=0),
FunctionSpace.EssentialBC(nodeSet='top', component=1)]
targetDispGrad = np.array([[0.1, -0.2],[0.4, -0.1]])
U = self.mesh.coords@targetDispGrad.T
fieldDim = U.shape[1]
dofManager = FunctionSpace.DofManager(self.fs, fieldDim, ebcs)
# Uu is U_unconstrained
Ubc = dofManager.get_bc_values(U)
@jit
def objective(Uu):
U = dofManager.create_field(Uu, Ubc)
return self.compute_strain_energy(U, self.internalVariables, self.props)
grad_func = jit(grad(objective))
Uu, solverSuccess = newton_solve(objective, dofManager.get_unknown_values(U))
self.assertTrue(solverSuccess)
U = dofManager.create_field(Uu, Ubc)
dispGrads = FunctionSpace.compute_field_gradient(self.fs, U)
ne, nqpe = self.fs.vols.shape
for dg in dispGrads.reshape(ne*nqpe,2,2):
self.assertArrayNear(dg, targetDispGrad, 14)
self.assertNear(np.linalg.norm(grad_func(Uu)), 0.0, 14)
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def test_neumann_patch_test(self):
ebcs = [FunctionSpace.EssentialBC(nodeSet='left', component=0),
FunctionSpace.EssentialBC(nodeSet='bottom', component=1)]
U = np.zeros(self.mesh.coords.shape)
dofManager = FunctionSpace.DofManager(self.fs, dim=2, EssentialBCs=ebcs)
Ubc = dofManager.get_bc_values(U)
sigma11 = 1.0
sigma22 = 0.0
right_traction_func = lambda X: np.array([sigma11, 0.0])
top_traction_func = lambda X: np.array([0.0, sigma22])
quadRule = QuadratureRule.create_quadrature_rule_1D(degree=1)
@jit
def objective(Uu):
U = dofManager.create_field(Uu, Ubc)
internalPotential = self.compute_strain_energy(U, self.internalVariables, self.props)
loadPotential = compute_traction_potential_energy(self.mesh, U, quadRule, self.mesh.sideSets['right'], right_traction_func)
loadPotential += compute_traction_potential_energy(self.mesh, U, quadRule, self.mesh.sideSets['top'], top_traction_func)
return internalPotential + loadPotential
with Timer(name="NewtonSolve"):
Uu, solverSuccess = newton_solve(objective, dofManager.get_unknown_values(U))
self.assertTrue(solverSuccess)
U = dofManager.create_field(Uu, Ubc)
# exact solution
modulus1 = (1.0 - self.nu**2)/self.E
modulus2 = -self.nu*(1.0+self.nu)/self.E
UExact = np.column_stack( ((modulus1*sigma11 + modulus2*sigma22)*self.mesh.coords[:,0],
(modulus2*sigma11 + modulus1*sigma22)*self.mesh.coords[:,1]) )
self.assertArrayNear(U, UExact, 14)
if __name__ == '__main__':
TestFixture.unittest.main()