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custom_material.py
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Wed, Aug 14, 17:47

custom_material.py
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#!/usr/bin/env python3
# pylint: disable=missing-module-docstring
# pylint: disable=missing-function-docstring
__copyright__ = (
"Copyright (©) 2022-2023 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
spatial_dimension = 2
class LinearCohesive(aka.MaterialCohesive):
"""Material Cohesive Linear."""
def __init__(self, model, _id):
"""Construct the material and register the parameters to the parser."""
super().__init__(model, _id)
super().registerParamReal(
"G_c", aka._pat_readable | aka._pat_parsable, "Fracture energy"
)
super().registerParamReal(
"beta", aka._pat_readable | aka._pat_parsable, ""
)
self.registerInternalReal("delta_max", 1)
self.beta = 0.
self.sigma_c = 0.
self.delta_c = 0.
self.G_c = 0.
def initMaterial(self):
"""Initialize the parameters for the material."""
super().initMaterial()
self.sigma_c = self.getReal("sigma_c")
self.G_c = self.getReal("G_c")
self.beta = self.getReal("beta")
self.delta_c = 2 * self.G_c / self.sigma_c
def checkInsertion(self, _check_only):
"""Check if need to insert a cohesive element."""
model = self.getModel()
facets = self.getFacetFilter()
inserter = model.getElementInserter()
for type_facet in facets.elementTypes(dim=(spatial_dimension - 1)):
facet_filter = facets(type_facet)
nb_facet = facet_filter.shape[0]
if nb_facet == 0:
continue
fe_engine = model.getFEEngine("FacetsFEEngine")
facets_check = inserter.getCheckFacets(type_facet)
insertion = inserter.getInsertionFacets(type_facet)
nb_quad_facet = fe_engine.getNbIntegrationPoints(type_facet)
normals = fe_engine.getNormalsOnIntegrationPoints(type_facet)
facets_stresses = model.getStressOnFacets(type_facet)
tangents = model.getTangents(type_facet)
for facet in facet_filter:
if not facets_check[facet]:
continue
ref_stress = 0
for q in range(nb_quad_facet):
current_quad = facet * nb_quad_facet + q
normal = normals[current_quad, :].ravel()
tangent = tangents[current_quad, :].ravel()
quad_stresses = facets_stresses[current_quad, :].reshape(
2, spatial_dimension, spatial_dimension)
stress_1 = quad_stresses[0]
stress_2 = quad_stresses[1]
avg_stress = stress_1 + stress_2 / 2.0
traction = avg_stress.dot(normal)
n = traction.dot(normal)
n = max(0, n)
t = traction.dot(tangent)
ref_stress = max(
ref_stress, np.sqrt(n * n + t * t / (self.beta**2))
)
if ref_stress > self.sigma_c:
insertion[facet] = True
# constitutive law
def computeTraction(self, el_type, ghost_type):
"""Compute the traction for a given opening."""
normals = self.getNormals(el_type, ghost_type)
openings = self.getOpening(el_type, ghost_type)
tractions = self.getTraction(el_type, ghost_type)
delta_max = self.getInternalReal("delta_max")(el_type)
for el in range(normals.shape[0]):
normal = normals[el].ravel()
opening = openings[el].ravel()
delta_n = opening.dot(normal) * normal
delta_s = opening - delta_n
delta = self.beta * np.linalg.norm(delta_s) ** 2 + \
np.linalg.norm(delta_n) ** 2
delta_max[el] = max(delta, delta_max[el])
tractions[el, :] = (
(delta * delta_s + delta_n)
* self.sigma_c
/ delta
* (1 - delta / self.delta_c)
)
def allocator(_dim, _unused, model, _id): # NOQA
"""Register the material to the material factory."""
return LinearCohesive(model, _id)
mat_factory = aka.MaterialFactory.getInstance()
mat_factory.registerAllocator("local_cohesive", allocator)
# -------------------------------------------------------------------------
# Initialization
# -------------------------------------------------------------------------
aka.parseInput("local_material.dat")
mesh = aka.Mesh(spatial_dimension)
mesh.read("plate.msh")
model = aka.SolidMechanicsModelCohesive(mesh)
model.initFull(_analysis_method=aka._static, _is_extrinsic=True)
model.initNewSolver(aka._explicit_lumped_mass)
model.setBaseName("plate")
model.addDumpFieldVector("displacement")
model.addDumpFieldVector("external_force")
model.addDumpField("strain")
model.addDumpField("stress")
model.addDumpField("blocked_dofs")
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")
# -------------------------------------------------------------------------
# Boundary conditions
# -------------------------------------------------------------------------
model.applyBC(aka.FixedValue(0.0, aka._x), "XBlocked")
model.applyBC(aka.FixedValue(0.0, aka._y), "YBlocked")
trac = np.zeros(spatial_dimension)
traction = 0.095
trac[int(aka._y)] = traction
model.getExternalForce()[:] = 0
model.applyBC(aka.FromTraction(trac), "Traction")
print("Solve for traction ", traction)
solver = model.getNonLinearSolver("static")
solver.set("max_iterations", 100)
solver.set("threshold", 1e-10)
solver.set("convergence_type", aka.SolveConvergenceCriteria.residual)
model.solveStep("static")
model.dump()
model.dump("cohesive elements")
model.setTimeStep(model.getStableTimeStep() * 0.1)
maxsteps = 100
for i in range(0, maxsteps):
print("{0}/{1}".format(i, maxsteps))
model.checkCohesiveStress()
model.solveStep("explicit_lumped")
if i % 10 == 0:
model.dump()
model.dump("cohesive elements")

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