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fragmentation.py
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Thu, May 2, 09:24

fragmentation.py
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#!/usr/bin/env python
# coding: utf-8
# import akantu
import subprocess
import akantu as aka
# import numpy for vector manipulation
import numpy as np
import matplotlib.pyplot as plt
# ## Setting up the geometry
#
# The above problem is modelled with the *BRep* representation in the GMsh format as follows.
# Please read and understand geoemtric details. Report your observations.
#
# The file *plate.geo* is:
L = 10
l = L/100
geometry_file = f"""
L = {L};
l = {l};
h = l;
"""
geometry_file += """
Point(1) = {0, 0, 0, h};
Point(2) = {L, 0, 0, h};
Point(3) = {L, l, 0, h};
Point(4) = {0, l, 0, h};
Line(1) = {1, 2};
Line(2) = {2, 3};
Line(3) = {3, 4};
Line(4) = {4, 1};
Line Loop(1) = {1, 2, 3, 4};
Plane Surface(1) = {1};
Transfinite Surface "*";
Physical Surface("bulk") = {1};
Physical Line("left") = {4};
Physical Line("bottom") = {1};
Physical Line("top") = {3};
Physical Line("right") = {2};
"""
with open('plate.geo', 'w') as f:
f.write(geometry_file)
ret = subprocess.run("gmsh -2 -order 1 -o plate.msh plate.geo", shell=True)
if ret.returncode:
print("Beware, gmsh could not run: mesh is not regenerated")
else:
print("Mesh generated")
# ## Regularization of the problem with cohesive element insertion
# In order the employ cohesive-zone modeling in **Akantu** with dynamical insersion, several changes must be made.
# ### Setting up the cohesive constitutive law
# We use a brittle material (same parameters as in the paper Zhou, Molinari, Ramesh 2007)
material_file = """
model solid_mechanics_model_cohesive [
cohesive_inserter [
bounding_box = [[0,10],[-10, 10]]
]
material elastic [
name = virtual
rho = 1 # density
E = 1 # young's modulus
nu = 0.3 # poisson's ratio
finite_deformation = true
]
material cohesive_linear [
name = cohesive
sigma_c = 0.1
G_c = 1e-2
beta = 1.
penalty = 10.
]
]
"""
with open('material.dat', 'w') as f:
f.write(material_file)
# ### Setting up the *SolidMechanicsModelCohesive*
# We need to read again the material file and the mesh
# Create the Solid Mechanics Cohesive Model in Akantu
# reading material file
aka.parseInput('material.dat')
# creating mesh
spatial_dimension = 2
mesh = aka.Mesh(spatial_dimension)
mesh.read('plate.msh')
# creates the model
model = aka.SolidMechanicsModelCohesive(mesh)
model.initFull(_analysis_method=aka._static, _is_extrinsic=True)
# Initialize the solver
# configures the static solver
solver = model.getNonLinearSolver('static')
solver.set('max_iterations', 100)
solver.set('threshold', 1e-10)
solver.set("convergence_type", aka.SolveConvergenceCriteria.residual)
# Initilize a new solver (explicit Newmark with lumped mass)
model.initNewSolver(aka._explicit_lumped_mass)
# Dynamic insertion of cohesive elements
model.updateAutomaticInsertion()
# Implement Boundary and initial conditions
# Dirichlet Boundary condition
#model.applyBC(aka.FixedValue(0., aka._x), 'left')
model.applyBC(aka.FixedValue(0., aka._y), 'bottom')
model.getExternalForce()[:] = 0
# ### Generate paraview files
# Initialization for bulk vizualisation
model.setBaseName('plate')
model.addDumpFieldVector('displacement')
model.addDumpFieldVector('velocity')
model.addDumpFieldVector('external_force')
model.addDumpField('strain')
model.addDumpField('stress')
model.addDumpField('blocked_dofs')
# Initialization of vizualisation for Cohesive model
model.setBaseNameToDumper('cohesive elements', 'cohesive')
model.addDumpFieldVectorToDumper('cohesive elements', 'displacement')
model.addDumpFieldToDumper('cohesive elements', 'damage')
model.addDumpFieldVectorToDumper('cohesive elements', 'tractions')
model.addDumpFieldVectorToDumper('cohesive elements', 'opening')
# Custom Dirichlet Boundary Condition to impose constant velocity
# Boundary functor fixing the displacement as it is
class FixedDisplacement (aka.DirichletFunctor):
'''
Fix the displacement at its current value
'''
def __init__(self, axis, vel):
super().__init__(axis)
self.axis = axis
self.time = 0
self.vel = vel
def set_time(self, t):
self.time = t
def __call__(self, node, flags, disp, coord):
# sets the blocked dofs vector to true in the desired axis
flags[int(self.axis)] = True
disp[int(self.axis)] = self.vel*self.time
functor_r = FixedDisplacement(aka._x, 1e-1)
model.applyBC(functor_r, 'right')
functor_l = FixedDisplacement(aka._x, -1e-1)
model.applyBC(functor_l, 'left')
# Initial condition : velocity gradient : in x = 0 we have -v and in x = L we have +v
nodes = model.getMesh().getNodes()
vel_field = np.zeros(nodes.shape)
vel_field[:, 0] = (2*nodes[:, 0]-L)/L*1e-1
model.getVelocity()[:] = vel_field
# ### Run the dynamical simulation
# Initialize data arrays
# Energies :
E_pot = []
E_kin = []
E_dis = []
E_rev = []
E_con = []
# Stress :
Stress = []
dt = model.getStableTimeStep()*0.1
# choose the timestep
model.setTimeStep(dt)
# set maximum number of iteration
maxsteps = 5000
# solve
for i in range(0, maxsteps):
time = dt*i
functor_r.set_time(time)
# fix displacements of the right boundary
model.applyBC(functor_r, 'right')
functor_l.set_time(time)
# fix displacements of the left boundary
model.applyBC(functor_l, 'left')
if i % 10 == 0:
model.dump()
model.dump('cohesive elements')
pass
if i % 50 == 0:
print('step {0}/{1}'.format(i, maxsteps))
model.checkCohesiveStress()
model.solveStep('explicit_lumped')
Ep = model.getEnergy("potential")
Ek = model.getEnergy("kinetic")
Ed = model.getEnergy("dissipated")
Er = model.getEnergy("reversible")
Ec = model.getEnergy("contact")
E_pot.append(Ep)
E_kin.append(Ek)
E_dis.append(Ed)
E_rev.append(Er)
E_con.append(Ec)
Stress_field = model.getMaterial(0).getStress(aka._triangle_3)
Stress_mean = np.mean(Stress_field)
Stress.append(Stress_mean)
# Use the fragment Manager
fragment_manager = aka.FragmentManager(model)
fragment_manager.computeAllData()
Nb_elem_per_frag = fragment_manager.getNbElementsPerFragment()
Nb_frag = fragment_manager.getNbFragment()
print('Nb_frag:', Nb_frag)
# Average number of elements per fragment
Nb_elem_mean = np.mean(Nb_elem_per_frag)
print('average Nb elem / fragment:', Nb_elem_mean)
# knowing the element size we can get the average fragment size
s_mean = Nb_elem_mean*l
print('average fragment size:', s_mean)
# ## Plots
# Plot stress as a function of time
Time = [i*dt for i in range(0, maxsteps)]
Stress_MPa = [x/10**6 for x in Stress]
plt.figure()
plt.plot(Time, Stress)
plt.xlabel("Time [s]")
plt.ylabel("Stress [Pa]")
plt.show()
# Plot the energies as a function of time
plt.figure()
plt.plot(Time, E_pot, label='Potential Energy')
plt.plot(Time, E_kin, label='Kinetic Energy')
plt.plot(Time, E_dis, label='Dissipated Energy')
plt.plot(Time, E_rev, label='Reversible Energy')
plt.plot(Time, E_con, label='Contact Energy')
plt.legend()
plt.show()

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