| 1 |
# |
| 2 |
# $Id$ |
| 3 |
# |
| 4 |
####################################################### |
| 5 |
# |
| 6 |
# Copyright 2003-2007 by ACceSS MNRF |
| 7 |
# Copyright 2007 by University of Queensland |
| 8 |
# |
| 9 |
# http://esscc.uq.edu.au |
| 10 |
# Primary Business: Queensland, Australia |
| 11 |
# Licensed under the Open Software License version 3.0 |
| 12 |
# http://www.opensource.org/licenses/osl-3.0.php |
| 13 |
# |
| 14 |
####################################################### |
| 15 |
# |
| 16 |
|
| 17 |
__copyright__=""" Copyright (c) 2006 by ACcESS MNRF |
| 18 |
http://www.access.edu.au |
| 19 |
Primary Business: Queensland, Australia""" |
| 20 |
__license__="""Licensed under the Open Software License version 3.0 |
| 21 |
http://www.opensource.org/licenses/osl-3.0.php""" |
| 22 |
|
| 23 |
from esys.escript import * |
| 24 |
from esys.escript.modelframe import Model,IterationDivergenceError |
| 25 |
from esys.escript.linearPDEs import LinearPDE |
| 26 |
|
| 27 |
class Mechanics(Model): |
| 28 |
""" |
| 29 |
base class for mechanics models in updated lagrangean framework |
| 30 |
|
| 31 |
@ivar domain: domain (in) |
| 32 |
@ivar internal_force: =Data() |
| 33 |
@ivar external_force: =Data() |
| 34 |
@ivar prescribed_velocity: =Data() |
| 35 |
@ivar location_prescribed_velocity: =Data() |
| 36 |
@ivar temperature: = None |
| 37 |
@ivar expansion_coefficient: = 0. |
| 38 |
@ivar bulk_modulus: =1. |
| 39 |
@ivar shear_modulus: =1. |
| 40 |
@ivar rel_tol: =1.e-3 |
| 41 |
@ivar abs_tol: =1.e-15 |
| 42 |
@ivar max_iter: =10 |
| 43 |
@ivar displacement: =None |
| 44 |
@ivar stress: =None |
| 45 |
""" |
| 46 |
SAFTY_FACTOR_ITERATION=1./100. |
| 47 |
def __init__(self,**kwargs): |
| 48 |
""" |
| 49 |
set up the model |
| 50 |
|
| 51 |
@param debug: debug flag |
| 52 |
@type debug: C{bool} |
| 53 |
""" |
| 54 |
super(Mechanics, self).__init__(self,**kwargs) |
| 55 |
self.declareParameter(domain=None, \ |
| 56 |
displacement=None, \ |
| 57 |
stress=None, \ |
| 58 |
velocity=None, \ |
| 59 |
internal_force=None, \ |
| 60 |
external_force=None, \ |
| 61 |
prescribed_velocity=None, \ |
| 62 |
location_prescribed_velocity=None, \ |
| 63 |
temperature = None, \ |
| 64 |
expansion_coefficient = 0., \ |
| 65 |
bulk_modulus=2., \ |
| 66 |
shear_modulus=1., \ |
| 67 |
rel_tol=1.e-3,abs_tol=1.e-15,max_iter=10) |
| 68 |
self.__iter=0 |
| 69 |
|
| 70 |
def doInitialization(self): |
| 71 |
""" |
| 72 |
initialize model |
| 73 |
""" |
| 74 |
if not self.displacement: self.displacement=Vector(0.,ContinuousFunction(self.domain)) |
| 75 |
if not self.velocity: self.velocity=Vector(0.,ContinuousFunction(self.domain)) |
| 76 |
if not self.stress: self.stress=Tensor(0.,ContinuousFunction(self.domain)) |
| 77 |
if not self.internal_force: self.internal_force = Data() |
| 78 |
if not self.external_force: self.external_force = Data() |
| 79 |
if not self.prescribed_velocity: self.prescribed_velocity = Data() |
| 80 |
if not self.location_prescribed_velocity: self.location_prescribed_velocity =Data() |
| 81 |
# save the old values: |
| 82 |
self.__stress_safe=self.stress |
| 83 |
self.__temperature_safe=self.temperature |
| 84 |
self.__displacement_safe=self.displacement |
| 85 |
self.__velocity_safe=self.velocity |
| 86 |
self.__velocity_old=None |
| 87 |
self.__old_dt=None |
| 88 |
self.__very_old_dt=None |
| 89 |
# get node cooridnates and apply initial displacement |
| 90 |
self.__x=self.domain.getX() |
| 91 |
self.domain.setX(self.__x+self.displacement) |
| 92 |
# open PDE: |
| 93 |
self.__pde=LinearPDE(self.domain) |
| 94 |
self.__pde.setSolverMethod(self.__pde.DIRECT) |
| 95 |
# self.__pde.setSymmetryOn() |
| 96 |
|
| 97 |
def doStepPreprocessing(self,dt): |
| 98 |
""" |
| 99 |
step up pressure iteration |
| 100 |
|
| 101 |
if run within a time dependend problem extrapolation of pressure from previous time steps is used to |
| 102 |
get an initial guess (that needs some work!!!!!!!) |
| 103 |
""" |
| 104 |
# reset iteration counters: |
| 105 |
self.__iter=0 |
| 106 |
self.__diff=self.UNDEF_DT |
| 107 |
# set initial guesses for the iteration: |
| 108 |
self.displacement=self.__displacement_safe |
| 109 |
self.stress=self.__stress_safe |
| 110 |
self.velocity=self.__velocity_safe |
| 111 |
# update geometry |
| 112 |
self.domain.setX(self.__x+self.displacement) |
| 113 |
|
| 114 |
def doStep(self,dt): |
| 115 |
""" |
| 116 |
""" |
| 117 |
self.__iter+=1 |
| 118 |
k3=kronecker(self.domain) |
| 119 |
# set new thermal stress increment |
| 120 |
if self.temperature == None: |
| 121 |
self.deps_th=0. |
| 122 |
else: |
| 123 |
self.deps_th=self.expansion_coefficient*(self.temperature-self.__temperature_safe) |
| 124 |
# set PDE coefficients: |
| 125 |
self.__pde.setValue(A=self.S) |
| 126 |
self.__pde.setValue(X=-self.stress-self.bulk_modulus*self.deps_th*k3) |
| 127 |
if self.internal_force: self.__pde.setValue(Y=self.internal_force) |
| 128 |
if self.external_force: self.__pde.setValue(y=self.external_force) |
| 129 |
self.__pde.setValue(q=self.location_prescribed_velocity, \ |
| 130 |
r=Data()) |
| 131 |
if not self.prescribed_velocity.isEmpty() and self.__iter==1: |
| 132 |
self.__pde.setValue(r=dt*self.prescribed_velocity) |
| 133 |
# solve the PDE: |
| 134 |
self.__pde.setTolerance(self.rel_tol**2) |
| 135 |
self.du=self.__pde.getSolution(verbose=self.debug) |
| 136 |
# update geometry |
| 137 |
self.displacement=self.displacement+self.du |
| 138 |
self.domain.setX(self.__x+self.displacement) |
| 139 |
self.velocity=(self.displacement-self.__displacement_safe)/dt |
| 140 |
|
| 141 |
if self.debug: |
| 142 |
for i in range(self.domain.getDim()): |
| 143 |
self.trace("du %d range %e:%e"%(i,inf(self.du[i]),sup(self.du[i]))) |
| 144 |
for i in range(self.domain.getDim()): |
| 145 |
self.trace("displacement %d range %e:%e"%(i,inf(self.displacement[i]),sup(self.displacement[i]))) |
| 146 |
for i in range(self.domain.getDim()): |
| 147 |
self.trace("velocity %d range %e:%e"%(i,inf(self.velocity[i]),sup(self.velocity[i]))) |
| 148 |
self.__stress_last=self.stress |
| 149 |
|
| 150 |
def terminateIteration(self): |
| 151 |
"""iteration is terminateIterationd if relative pressure change is less then rel_tol""" |
| 152 |
if self.__iter>self.max_iter: |
| 153 |
raise IterationDivergenceError,"Maximum number of iterations steps reached" |
| 154 |
if self.__iter==0: |
| 155 |
self.__diff=self.UNDEF_DT |
| 156 |
else: |
| 157 |
self.__diff,diff_safe=Lsup(self.stress-self.__stress_last),self.__diff |
| 158 |
s_sup=Lsup(self.stress) |
| 159 |
self.trace("stress max and increment :%e, %e"%(s_sup,self.__diff)) |
| 160 |
if self.__iter>2 and diff_safe<self.__diff: |
| 161 |
raise IterationDivergenceError,"no improvement in stress iteration" |
| 162 |
return self.__diff<=self.rel_tol*self.SAFTY_FACTOR_ITERATION*s_sup+self.abs_tol |
| 163 |
|
| 164 |
def doStepPostprocessing(self,dt): |
| 165 |
""" |
| 166 |
accept all the values: |
| 167 |
""" |
| 168 |
self.__displacement_safe=self.displacement |
| 169 |
self.__temperature_safe=self.temperature |
| 170 |
self.__stress_safe=self.stress |
| 171 |
self.__velocity_safe=self.velocity |
| 172 |
|
| 173 |
def getSafeTimeStepSize(self,dt): |
| 174 |
""" |
| 175 |
returns new step size |
| 176 |
""" |
| 177 |
a=sup(length(self.velocity)/self.domain.getSize()) |
| 178 |
if a>0: |
| 179 |
return 1./a |
| 180 |
else: |
| 181 |
return self.UNDEF_DT |
| 182 |
|
| 183 |
|
| 184 |
|
| 185 |
class DruckerPrager(Mechanics): |
| 186 |
""" |
| 187 |
|
| 188 |
""" |
| 189 |
|
| 190 |
def __init__(self,**kwargs): |
| 191 |
""" |
| 192 |
set up model |
| 193 |
""" |
| 194 |
super(DruckerPrager, self).__init__(**kwargs) |
| 195 |
self.declareParameter(plastic_stress=0., |
| 196 |
hardening=0., |
| 197 |
friction_parameter=0., |
| 198 |
dilatancy_parameter=0., |
| 199 |
shear_length=1.e15) |
| 200 |
def doInitialization(self): |
| 201 |
""" |
| 202 |
""" |
| 203 |
super(DruckerPrager, self).doInitialization() |
| 204 |
self.__plastic_stress_safe=self.plastic_stress |
| 205 |
self.__shear_length_safe=self.shear_length |
| 206 |
self.__hardening_safe=self.hardening |
| 207 |
self.__chi_safe=0 |
| 208 |
self.__tau_safe=0 |
| 209 |
|
| 210 |
def doStepPreprocessing(self,dt): |
| 211 |
""" |
| 212 |
""" |
| 213 |
super(DruckerPrager, self).doStepPreprocessing(dt) |
| 214 |
# set initial guess for iteration: |
| 215 |
self.shear_length=self.__shear_length_safe |
| 216 |
self.plastic_stress=self.__plastic_stress_safe |
| 217 |
self.hardening=self.__hardening_safe |
| 218 |
self.__chi=self.__chi_safe |
| 219 |
self.__tau=self.__tau_safe |
| 220 |
|
| 221 |
def doStep(self,dt): |
| 222 |
# set new tangential operator: |
| 223 |
self.setTangentialTensor() |
| 224 |
# do the update step: |
| 225 |
super(DruckerPrager, self).doStep(dt) |
| 226 |
# update stresses: |
| 227 |
self.setStress() |
| 228 |
|
| 229 |
def doStepPostprocessing(self,dt): |
| 230 |
super(DruckerPrager, self).doStepPostprocessing(dt) |
| 231 |
self.__plastic_stress_safe=self.plastic_stress |
| 232 |
self.__shear_length_safe=self.shear_length |
| 233 |
self.__hardening_safe=self.hardening |
| 234 |
self.__chi_safe=self.__chi |
| 235 |
self.__tau_safe=self.__tau |
| 236 |
|
| 237 |
def setStress(self): |
| 238 |
d=self.domain.getDim() |
| 239 |
G=self.shear_modulus |
| 240 |
K=self.bulk_modulus |
| 241 |
alpha=self.friction_parameter |
| 242 |
beta=self.dilatancy_parameter |
| 243 |
h=self.hardening |
| 244 |
k3=kronecker(self.domain) |
| 245 |
# elastic trial stress: |
| 246 |
g=grad(self.du) |
| 247 |
D=symmetric(g) |
| 248 |
W=nonsymmetric(g) |
| 249 |
s_e=self.stress+K*self.deps_th*k3+ \ |
| 250 |
2*G*D+(K-2./3*G)*trace(D)*k3 \ |
| 251 |
+2*symmetric(matrix_mult(W,self.stress)) |
| 252 |
p_e=-1./d*trace(s_e) |
| 253 |
s_e_dev=s_e+p_e*k3 |
| 254 |
tau_e=sqrt(1./2*inner(s_e_dev,s_e_dev)) |
| 255 |
# yield conditon for elastic trial stress: |
| 256 |
F=tau_e-alpha*p_e-self.shear_length |
| 257 |
self.__chi=whereNonNegative(F+(self.rel_tol*(self.SAFTY_FACTOR_ITERATION)**2)*self.shear_length) |
| 258 |
# plastic stress increment: |
| 259 |
l=self.__chi*F/(h+G+beta*K) |
| 260 |
self.__tau=tau_e-G*l |
| 261 |
self.stress=self.__tau/(tau_e+self.abs_tol*whereZero(tau_e,self.abs_tol))*s_e_dev-(p_e+l*beta*K)*k3 |
| 262 |
self.plastic_stress=self.plastic_stress+l |
| 263 |
# update hardening |
| 264 |
self.hardening=(self.shear_length-self.__shear_length_safe)/(l+self.abs_tol*whereZero(l)) |
| 265 |
|
| 266 |
def setTangentialTensor(self): |
| 267 |
d=self.domain.getDim() |
| 268 |
G=self.shear_modulus |
| 269 |
K=self.bulk_modulus |
| 270 |
alpha=self.friction_parameter |
| 271 |
beta=self.dilatancy_parameter |
| 272 |
tau_Y=self.shear_length |
| 273 |
chi=self.__chi |
| 274 |
tau=self.__tau |
| 275 |
h=self.hardening |
| 276 |
k3=kronecker(Function(self.domain)) |
| 277 |
|
| 278 |
sXk3=outer(self.stress,k3) |
| 279 |
k3Xk3=outer(k3,k3) |
| 280 |
s_dev=self.stress-trace(self.stress)*(k3/d) |
| 281 |
tmp=G*s_dev/(tau+self.abs_tol*whereZero(tau,self.abs_tol)) |
| 282 |
|
| 283 |
self.S=G*(swap_axes(k3Xk3,0,3)+swap_axes(k3Xk3,1,3)) \ |
| 284 |
+ (K-2./3*G)*k3Xk3 \ |
| 285 |
+ (sXk3-swap_axes(swap_axes(sXk3,1,2),2,3)) \ |
| 286 |
+ 1./2*(swap_axes(swap_axes(sXk3,0,2),2,3) \ |
| 287 |
-swap_axes(swap_axes(sXk3,0,3),2,3) \ |
| 288 |
-swap_axes(sXk3,1,2) \ |
| 289 |
+swap_axes(sXk3,1,3) ) \ |
| 290 |
- outer(chi/(h+G+alpha*beta*K)*(tmp+beta*K*k3),tmp+alpha*K*k3) |
Parent Directory
| 
Revision Log