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bi-material.py
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Wed, Nov 6, 16:21

bi-material.py
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from __future__ import print_function
# ------------------------------------------------------------- #
import akantu as aka
import subprocess
import numpy as np
import time
# ------------------------------------------------------------- #
class LocalElastic:
# declares all the internals
def initMaterial(self, internals, params):
self.E = params['E']
self.nu = params['nu']
self.rho = params['rho']
# print(self.__dict__)
# First Lame coefficient
self.lame_lambda = self.nu * self.E / (
(1. + self.nu) * (1. - 2. * self.nu))
# Second Lame coefficient (shear modulus)
self.lame_mu = self.E / (2. * (1. + self.nu))
all_factor = internals['factor']
all_quad_coords = internals['quad_coordinates']
for elem_type in all_factor.keys():
factor = all_factor[elem_type]
quad_coords = all_quad_coords[elem_type]
factor[:] = 1.
factor[quad_coords[:, 1] < 0.5] = .5
# declares all the internals
@staticmethod
def registerInternals():
return ['potential', 'factor']
# declares all the internals
@staticmethod
def registerInternalSizes():
return [1, 1]
# declares all the parameters that could be parsed
@staticmethod
def registerParam():
return ['E', 'nu']
# declares all the parameters that are needed
def getPushWaveSpeed(self, params):
return np.sqrt((self.lame_lambda + 2 * self.lame_mu) / self.rho)
# compute small deformation tensor
@staticmethod
def computeEpsilon(grad_u):
return 0.5 * (grad_u + np.einsum('aij->aji', grad_u))
# constitutive law
def computeStress(self, grad_u, sigma, internals, params):
n_quads = grad_u.shape[0]
grad_u = grad_u.reshape((n_quads, 2, 2))
factor = internals['factor'].reshape(n_quads)
epsilon = self.computeEpsilon(grad_u)
sigma = sigma.reshape((n_quads, 2, 2))
trace = np.einsum('aii->a', grad_u)
sigma[:, :, :] = (
np.einsum('a,ij->aij', trace,
self.lame_lambda * np.eye(2))
+ 2. * self.lame_mu * epsilon)
# print(sigma.reshape((n_quads, 4)))
# print(grad_u.reshape((n_quads, 4)))
sigma[:, :, :] = np.einsum('aij, a->aij', sigma, factor)
# constitutive law tangent modulii
def computeTangentModuli(self, grad_u, tangent, internals, params):
n_quads = tangent.shape[0]
tangent = tangent.reshape(n_quads, 3, 3)
factor = internals['factor'].reshape(n_quads)
Miiii = self.lame_lambda + 2 * self.lame_mu
Miijj = self.lame_lambda
Mijij = self.lame_mu
tangent[:, 0, 0] = Miiii
tangent[:, 1, 1] = Miiii
tangent[:, 0, 1] = Miijj
tangent[:, 1, 0] = Miijj
tangent[:, 2, 2] = Mijij
tangent[:, :, :] = np.einsum('aij, a->aij', tangent, factor)
# computes the energy density
def getEnergyDensity(self, energy_type, energy_density,
grad_u, stress, internals, params):
nquads = stress.shape[0]
stress = stress.reshape(nquads, 2, 2)
grad_u = grad_u.reshape((nquads, 2, 2))
if energy_type != 'potential':
raise RuntimeError('not known energy')
epsilon = self.computeEpsilon(grad_u)
energy_density[:, 0] = (
0.5 * np.einsum('aij,aij->a', stress, epsilon))
# applies manually the boundary conditions
def applyBC(model):
nbNodes = model.getMesh().getNbNodes()
position = model.getMesh().getNodes()
displacement = model.getDisplacement()
blocked_dofs = model.getBlockedDOFs()
width = 1.
height = 1.
epsilon = 1e-8
for node in range(0, nbNodes):
if((np.abs(position[node, 0]) < epsilon) or # left side
(np.abs(position[node, 0] - width) < epsilon)): # right side
blocked_dofs[node, 0] = True
displacement[node, 0] = 0 * position[node, 0] + 0.
if(np.abs(position[node, 1]) < epsilon): # lower side
blocked_dofs[node, 1] = True
displacement[node, 1] = - 1.
if(np.abs(position[node, 1] - height) < epsilon): # upper side
blocked_dofs[node, 1] = True
displacement[node, 1] = 1.
# main parameters
spatial_dimension = 2
mesh_file = 'square.msh'
# call gmsh to generate the mesh
ret = subprocess.call(['gmsh', '-2', 'square.geo', '-optimize', 'square.msh'])
if ret != 0:
raise Exception(
'execution of GMSH failed: do you have it installed ?')
time.sleep(1)
# read mesh
mesh = aka.Mesh(spatial_dimension)
mesh.read(mesh_file)
# create the custom material
mat = LocalElastic()
aka.registerNewPythonMaterial(mat, "local_elastic")
# parse input file
aka.parseInput('material.dat')
# init the SolidMechanicsModel
model = aka.SolidMechanicsModel(mesh)
model.initFull(_analysis_method=aka._static)
# configure the solver
solver = model.getNonLinearSolver()
solver.set("max_iterations", 2)
solver.set("threshold", 1e-3)
solver.set("convergence_type", aka.SolveConvergenceCriteria__solution)
# prepare the dumper
model.setBaseName("bimaterial")
model.addDumpFieldVector("displacement")
model.addDumpFieldVector("internal_force")
model.addDumpFieldVector("external_force")
model.addDumpField("strain")
model.addDumpField("stress")
model.addDumpField("factor")
model.addDumpField("blocked_dofs")
# Boundary conditions
applyBC(model)
# solve the problem
model.solveStep()
# dump paraview files
model.dump()

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