/usr/lib/python-escript-mpi/esys/modellib/mechanics.py is in python-escript-mpi 5.0-3.
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#
# Copyright (c) 2003-2016 by The University of Queensland
# http://www.uq.edu.au
#
# Primary Business: Queensland, Australia
# Licensed under the Apache License, version 2.0
# http://www.apache.org/licenses/LICENSE-2.0
#
# Development until 2012 by Earth Systems Science Computational Center (ESSCC)
# Development 2012-2013 by School of Earth Sciences
# Development from 2014 by Centre for Geoscience Computing (GeoComp)
#
##############################################################################
from __future__ import print_function, division
__copyright__="""Copyright (c) 2003-2016 by The University of Queensland
http://www.uq.edu.au
Primary Business: Queensland, Australia"""
__license__="""Licensed under the Apache License, version 2.0
http://www.apache.org/licenses/LICENSE-2.0"""
__url__="https://launchpad.net/escript-finley"
#from esys.escript import *
from esys.escript.modelframe import Model,IterationDivergenceError
from esys.escript.linearPDEs import LinearPDE
class Mechanics(Model):
"""
base class for mechanics models in updated lagrangean framework
:ivar domain: domain (in)
:ivar internal_force: =Data()
:ivar external_force: =Data()
:ivar prescribed_velocity: =Data()
:ivar location_prescribed_velocity: =Data()
:ivar temperature: = None
:ivar expansion_coefficient: = 0.
:ivar bulk_modulus: =1.
:ivar shear_modulus: =1.
:ivar rel_tol: =1.e-3
:ivar abs_tol: =1.e-15
:ivar max_iter: =10
:ivar displacement: =None
:ivar stress: =None
"""
SAFTY_FACTOR_ITERATION=1./100.
def __init__(self,**kwargs):
"""
set up the model
:keyword debug: debug flag
:type debug: ``bool``
"""
super(Mechanics, self).__init__(self,**kwargs)
self.declareParameter(domain=None, \
displacement=None, \
stress=None, \
velocity=None, \
internal_force=None, \
external_force=None, \
prescribed_velocity=None, \
location_prescribed_velocity=None, \
temperature = None, \
expansion_coefficient = 0., \
bulk_modulus=2., \
shear_modulus=1., \
rel_tol=1.e-3,abs_tol=1.e-15,max_iter=10)
self.__iter=0
def doInitialization(self):
"""
initialize model
"""
if not self.displacement: self.displacement=Vector(0.,ContinuousFunction(self.domain))
if not self.velocity: self.velocity=Vector(0.,ContinuousFunction(self.domain))
if not self.stress: self.stress=Tensor(0.,ContinuousFunction(self.domain))
if not self.internal_force: self.internal_force = Data()
if not self.external_force: self.external_force = Data()
if not self.prescribed_velocity: self.prescribed_velocity = Data()
if not self.location_prescribed_velocity: self.location_prescribed_velocity =Data()
# save the old values:
self.__stress_safe=self.stress
self.__temperature_safe=self.temperature
self.__displacement_safe=self.displacement
self.__velocity_safe=self.velocity
self.__velocity_old=None
self.__old_dt=None
self.__very_old_dt=None
# get node cooridnates and apply initial displacement
self.__x=self.domain.getX()
self.domain.setX(self.__x+self.displacement)
# open PDE:
self.__pde=LinearPDE(self.domain)
self.__pde.setSolverMethod(self.__pde.DIRECT)
self.__solver_options=self.__pde.getSolverOptions()
self.__solver_options.setSolverMethod(self.__solver_options.DIRECT)
self.__solver_options.setVerbosity(self.debug)
# self.__pde.setSymmetryOn()
def doStepPreprocessing(self,dt):
"""
step up pressure iteration
if run within a time dependend problem extrapolation of pressure from previous time steps is used to
get an initial guess (that needs some work!!!!!!!)
"""
# reset iteration counters:
self.__iter=0
self.__diff=self.UNDEF_DT
# set initial guesses for the iteration:
self.displacement=self.__displacement_safe
self.stress=self.__stress_safe
self.velocity=self.__velocity_safe
# update geometry
self.domain.setX(self.__x+self.displacement)
def doStep(self,dt):
"""
"""
self.__iter+=1
k3=kronecker(self.domain)
# set new thermal stress increment
if self.temperature == None:
self.deps_th=0.
else:
self.deps_th=self.expansion_coefficient*(self.temperature-self.__temperature_safe)
# set PDE coefficients:
self.__pde.setValue(A=self.S)
self.__pde.setValue(X=-self.stress-self.bulk_modulus*self.deps_th*k3)
if self.internal_force: self.__pde.setValue(Y=self.internal_force)
if self.external_force: self.__pde.setValue(y=self.external_force)
self.__pde.setValue(q=self.location_prescribed_velocity, \
r=Data())
if not self.prescribed_velocity.isEmpty() and self.__iter==1:
self.__pde.setValue(r=dt*self.prescribed_velocity)
# solve the PDE:
self.__solver_options.setTolerance(self.rel_tol**2)
self.du=self.__pde.getSolution()
# update geometry
self.displacement=self.displacement+self.du
self.domain.setX(self.__x+self.displacement)
self.velocity=(self.displacement-self.__displacement_safe)/dt
if self.debug:
for i in range(self.domain.getDim()):
self.trace("du %d range %e:%e"%(i,inf(self.du[i]),sup(self.du[i])))
for i in range(self.domain.getDim()):
self.trace("displacement %d range %e:%e"%(i,inf(self.displacement[i]),sup(self.displacement[i])))
for i in range(self.domain.getDim()):
self.trace("velocity %d range %e:%e"%(i,inf(self.velocity[i]),sup(self.velocity[i])))
self.__stress_last=self.stress
def terminateIteration(self):
"""iteration is terminateIterationd if relative pressure change is less than rel_tol"""
if self.__iter>self.max_iter:
raise IterationDivergenceError("Maximum number of iterations steps reached")
if self.__iter==0:
self.__diff=self.UNDEF_DT
else:
self.__diff,diff_safe=Lsup(self.stress-self.__stress_last),self.__diff
s_sup=Lsup(self.stress)
self.trace("stress max and increment :%e, %e"%(s_sup,self.__diff))
if self.__iter>2 and diff_safe<self.__diff:
raise IterationDivergenceError("no improvement in stress iteration")
return self.__diff<=self.rel_tol*self.SAFTY_FACTOR_ITERATION*s_sup+self.abs_tol
def doStepPostprocessing(self,dt):
"""
accept all the values:
"""
self.__displacement_safe=self.displacement
self.__temperature_safe=self.temperature
self.__stress_safe=self.stress
self.__velocity_safe=self.velocity
def getSafeTimeStepSize(self,dt):
"""
returns new step size
"""
a=sup(length(self.velocity)/self.domain.getSize())
if a>0:
return 1./a
else:
return self.UNDEF_DT
class DruckerPrager(Mechanics):
"""
"""
def __init__(self,**kwargs):
"""
set up model
"""
super(DruckerPrager, self).__init__(**kwargs)
self.declareParameter(plastic_stress=0.,
hardening=0.,
friction_parameter=0.,
dilatancy_parameter=0.,
shear_length=1.e15)
def doInitialization(self):
"""
"""
super(DruckerPrager, self).doInitialization()
self.__plastic_stress_safe=self.plastic_stress
self.__shear_length_safe=self.shear_length
self.__hardening_safe=self.hardening
self.__chi_safe=0
self.__tau_safe=0
def doStepPreprocessing(self,dt):
"""
"""
super(DruckerPrager, self).doStepPreprocessing(dt)
# set initial guess for iteration:
self.shear_length=self.__shear_length_safe
self.plastic_stress=self.__plastic_stress_safe
self.hardening=self.__hardening_safe
self.__chi=self.__chi_safe
self.__tau=self.__tau_safe
def doStep(self,dt):
# set new tangential operator:
self.setTangentialTensor()
# do the update step:
super(DruckerPrager, self).doStep(dt)
# update stresses:
self.setStress()
def doStepPostprocessing(self,dt):
super(DruckerPrager, self).doStepPostprocessing(dt)
self.__plastic_stress_safe=self.plastic_stress
self.__shear_length_safe=self.shear_length
self.__hardening_safe=self.hardening
self.__chi_safe=self.__chi
self.__tau_safe=self.__tau
def setStress(self):
d=self.domain.getDim()
G=self.shear_modulus
K=self.bulk_modulus
alpha=self.friction_parameter
beta=self.dilatancy_parameter
h=self.hardening
k3=kronecker(self.domain)
# elastic trial stress:
g=grad(self.du)
D=symmetric(g)
W=nonsymmetric(g)
s_e=self.stress+K*self.deps_th*k3+ \
2*G*D+(K-2./3*G)*trace(D)*k3 \
+2*symmetric(matrix_mult(W,self.stress))
p_e=-1./d*trace(s_e)
s_e_dev=s_e+p_e*k3
tau_e=sqrt(1./2*inner(s_e_dev,s_e_dev))
# yield conditon for elastic trial stress:
F=tau_e-alpha*p_e-self.shear_length
self.__chi=whereNonNegative(F+(self.rel_tol*(self.SAFTY_FACTOR_ITERATION)**2)*self.shear_length)
# plastic stress increment:
l=self.__chi*F/(h+G+beta*K)
self.__tau=tau_e-G*l
self.stress=self.__tau/(tau_e+self.abs_tol*whereZero(tau_e,self.abs_tol))*s_e_dev-(p_e+l*beta*K)*k3
self.plastic_stress=self.plastic_stress+l
# update hardening
self.hardening=(self.shear_length-self.__shear_length_safe)/(l+self.abs_tol*whereZero(l))
def setTangentialTensor(self):
d=self.domain.getDim()
G=self.shear_modulus
K=self.bulk_modulus
alpha=self.friction_parameter
beta=self.dilatancy_parameter
tau_Y=self.shear_length
chi=self.__chi
tau=self.__tau
h=self.hardening
k3=kronecker(Function(self.domain))
sXk3=outer(self.stress,k3)
k3Xk3=outer(k3,k3)
s_dev=self.stress-trace(self.stress)*(k3/d)
tmp=G*s_dev/(tau+self.abs_tol*whereZero(tau,self.abs_tol))
self.S=G*(swap_axes(k3Xk3,0,3)+swap_axes(k3Xk3,1,3)) \
+ (K-2./3*G)*k3Xk3 \
+ (sXk3-swap_axes(swap_axes(sXk3,1,2),2,3)) \
+ 1./2*(swap_axes(swap_axes(sXk3,0,2),2,3) \
-swap_axes(swap_axes(sXk3,0,3),2,3) \
-swap_axes(sXk3,1,2) \
+swap_axes(sXk3,1,3) ) \
- outer(chi/(h+G+alpha*beta*K)*(tmp+beta*K*k3),tmp+alpha*K*k3)
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