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rAKA/examples/python/custom-material/custom-material.py
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custom-material.py
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#!/usr/bin/env python3
""" custom-material.py: Custom material example"""
__author__ = "Guillaume Anciaux"
__credits__ = [
"Guillaume Anciaux <guillaume.anciaux@epfl.ch>",
]
__copyright__ = "Copyright (©) 2016-2021 EPFL (Ecole Polytechnique Fédérale" \
" de Lausanne) Laboratory (LSMS - Laboratoire de Simulation" \
" en Mécanique des Solides)"
__license__ = "LGPLv3"
import numpy as np
import akantu as aka
# ------------------------------------------------------------------------------
class LocalElastic(aka.Material):
def __init__(self, model, _id):
super().__init__(model, _id)
super().registerParamReal('E',
aka._pat_readable | aka._pat_parsable,
'Youngs modulus')
super().registerParamReal('nu',
aka._pat_readable | aka._pat_parsable,
'Poisson ratio')
def initMaterial(self):
nu = self.getReal('nu')
E = self.getReal('E')
self.mu = E / (2 * (1 + nu))
self.lame_lambda = nu * E / (
(1. + nu) * (1. - 2. * nu))
# Second Lame coefficient (shear modulus)
self.lame_mu = E / (2. * (1. + nu))
super().initMaterial()
# declares all the parameters that are needed
def getPushWaveSpeed(self, element):
rho = self.getReal('rho')
return np.sqrt((self.lame_lambda + 2 * self.lame_mu) / 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, el_type, ghost_type):
grad_u = self.getGradU(el_type, ghost_type)
sigma = self.getStress(el_type, ghost_type)
n_quads = grad_u.shape[0]
grad_u = grad_u.reshape((n_quads, 2, 2))
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)
# constitutive law tangent modulii
def computeTangentModuli(self, el_type, tangent_matrix, ghost_type):
n_quads = tangent_matrix.shape[0]
tangent = tangent_matrix.reshape(n_quads, 3, 3)
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
# computes the energy density
def computePotentialEnergy(self, el_type):
sigma = self.getStress(el_type)
grad_u = self.getGradU(el_type)
nquads = sigma.shape[0]
stress = sigma.reshape(nquads, 2, 2)
grad_u = grad_u.reshape((nquads, 2, 2))
epsilon = self.computeEpsilon(grad_u)
energy_density = self.getPotentialEnergy(el_type)
energy_density[:, 0] = 0.5 * np.einsum('aij,aij->a', stress, epsilon)
# register material to the MaterialFactory
def allocator(_dim, unused, model, _id):
return LocalElastic(model, _id)
mat_factory = aka.MaterialFactory.getInstance()
mat_factory.registerAllocator("local_elastic", allocator)
# ------------------------------------------------------------------------------
# main
# ------------------------------------------------------------------------------
spatial_dimension = 2
aka.parseInput('material.dat')
mesh_file = 'bar.msh'
max_steps = 250
time_step = 1e-3
# ------------------------------------------------------------------------------
# Initialization
# ------------------------------------------------------------------------------
mesh = aka.Mesh(spatial_dimension)
mesh.read(mesh_file)
# parse input file
aka.parseInput('material.dat')
model = aka.SolidMechanicsModel(mesh)
model.initFull(_analysis_method=aka._explicit_lumped_mass)
model.setBaseName("waves")
model.addDumpFieldVector("displacement")
model.addDumpFieldVector("acceleration")
model.addDumpFieldVector("velocity")
model.addDumpFieldVector("internal_force")
model.addDumpFieldVector("external_force")
model.addDumpField("strain")
model.addDumpField("stress")
model.addDumpField("blocked_dofs")
# ------------------------------------------------------------------------------
# boundary conditions
# ------------------------------------------------------------------------------
model.applyBC(aka.FixedValue(0, aka._x), "XBlocked")
model.applyBC(aka.FixedValue(0, aka._y), "YBlocked")
# ------------------------------------------------------------------------------
# initial conditions
# ------------------------------------------------------------------------------
displacement = model.getDisplacement()
nb_nodes = mesh.getNbNodes()
position = mesh.getNodes()
pulse_width = 1
A = 0.01
for i in range(0, nb_nodes):
# Sinus * Gaussian
x = position[i, 0] - 5.
L = pulse_width
k = 0.1 * 2 * np.pi * 3 / L
displacement[i, 0] = A * \
np.sin(k * x) * np.exp(-(k * x) * (k * x) / (L * L))
# ------------------------------------------------------------------------------
# timestep value computation
# ------------------------------------------------------------------------------
time_factor = 0.8
stable_time_step = model.getStableTimeStep() * time_factor
print("Stable Time Step = {0}".format(stable_time_step))
print("Required Time Step = {0}".format(time_step))
time_step = stable_time_step * time_factor
model.setTimeStep(time_step)
# ------------------------------------------------------------------------------
# loop for evolution of motion dynamics
# ------------------------------------------------------------------------------
print("step,step * time_step,epot,ekin,epot + ekin")
for step in range(0, max_steps + 1):
model.solveStep()
if step % 10 == 0:
model.dump()
epot = model.getEnergy('potential')
ekin = model.getEnergy('kinetic')
# output energy calculation to screen
print("{0},{1},{2},{3},{4}".format(step, step * time_step,
epot, ekin,
(epot + ekin)))
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