/[escript]/trunk/modellib/py_src/mechanics.py
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Contents of /trunk/modellib/py_src/mechanics.py

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Revision 825 - (show annotations)
Tue Aug 29 06:59:27 2006 UTC (12 years, 9 months ago) by gross
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and more on Drucker Prager
1 # $Id:$
2
3 __copyright__=""" Copyright (c) 2006 by ACcESS MNRF
4 http://www.access.edu.au
5 Primary Business: Queensland, Australia"""
6 __license__="""Licensed under the Open Software License version 3.0
7 http://www.opensource.org/licenses/osl-3.0.php"""
8
9 from esys.escript import *
10 from esys.escript.modelframe import Model,IterationDivergenceError
11 from esys.escript.linearPDEs import LinearPDE
12
13 class Mechanics(Model):
14 """
15 base class for mechanics models in updated lagrangean framework
16
17 @ivar domain: domain (in)
18 @ivar internal_force: =Data()
19 @ivar external_force: =Data()
20 @ivar prescribed_velocity: =Data()
21 @ivar location_prescribed_velocity: =Data()
22 @ivar temperature: = None
23 @ivar expansion_coefficient: = 0.
24 @ivar bulk_modulus: =1.
25 @ivar shear_modulus: =1.
26 @ivar rel_tol: =1.e-3
27 @ivar abs_tol: =1.e-15
28 @ivar max_iter: =10
29 @ivar displacement: =None
30 @ivar stress: =None
31 @ivar velocity: =None
32 """
33 def __init__(self,debug=False):
34 """
35 set up the model
36
37 @param debug: debug flag
38 @type debug: C{bool}
39 """
40 super(Mechanics, self).__init__(self,debug=debug)
41 self.declareParameter(domain=None, \
42 displacement=None, \
43 stress=None, \
44 velocity=None, \
45 internal_force=Data(), \
46 external_force=Data(), \
47 prescribed_velocity=Data(), \
48 location_prescribed_velocity=Data(), \
49 temperature = None, \
50 expansion_coefficient = 0., \
51 bulk_modulus=2., \
52 shear_modulus=1., \
53 rel_tol=1.e-3,abs_tol=1.e-15,max_iter=10)
54 self.__iter=0
55
56 def doInitialization(self):
57 """
58 initialize model
59 """
60 if not self.displacement: self.displacement=Vector(0.,ContinuousFunction(self.domain))
61 if not self.velocity: self.velocity=Vector(0.,ContinuousFunction(self.domain))
62 if not self.stress: self.stress=Tensor(0.,ContinuousFunction(self.domain))
63 self.__pde=LinearPDE(self.domain)
64 self.__pde.setSymmetryOn()
65 self.__displacement_old=self.displacement
66 self.stress_old=self.stress
67 self.__velocity_old=self.velocity
68 self.__temperature_old=self.temperature
69
70 def doStepPreprocessing(self,dt):
71 """
72 step up pressure iteration
73
74 if run within a time dependend problem extrapolation of pressure from previous time steps is used to
75 get an initial guess (that needs some work!!!!!!!)
76 """
77 self.__iter=0
78 self.__diff=self.UNDEF_DT
79 # set new values:
80 self.displacement=self.__displacement_old
81 self.stress=self.stress_old
82 self.velocity=self.__velocity_old
83 self.temperature=self.__temperature_old
84 self.__velocity_last=self.velocity
85
86 def doStep(self,dt):
87 """
88
89 performs an iteration step of the penalty method.
90 IterationDivergenceError is raised if pressure error cannot be reduced or max_iter is reached.
91
92 requires self.S to be set
93 updates the thermal stress increment
94
95 """
96 k3=kronecker(self.domain)
97 # set new thermal stress increment
98 if self.temperature:
99 self.deps_therm=self.self.expansion_coefficient*(self.temperature-self.__temperature_old)
100 else:
101 self.deps_therm=0.
102 # set PDE coefficients:
103 self.__pde.setValue(A=self.S)
104 self.__pde.checkSymmetry()
105 self.__pde.setValue(X=self.stress_old-self.bulk_modulus*self.deps_therm*k3)
106 if self.internal_force: self.__pde.setValue(Y=self.internal_force)
107 if self.external_force: self.__pde.setValue(y=self.external_force)
108 self.__pde.setValue(r=self.prescribed_velocity, \
109 q=self.location_prescribed_velocity)
110 # solve the PDE:
111 self.__pde.setTolerance(self.rel_tol/100.)
112 self.velocity=self.__pde.getSolution(verbose=True)
113 # calculate convergence indicators:
114 self.__diff,diff_old=Lsup(self.velocity-self.__velocity_last),self.__diff
115 self.__velocity_last=self.velocity
116 self.displacement=self.__displacement_old+dt*self.velocity
117 self.__iter+=1
118 if self.debug:
119 for i in range(self.domain.getDim()):
120 self.trace("velocity %d range %e:%e"%(i,inf(self.velocity[i]),sup(self.velocity[i])))
121 self.trace("velocity increment %s"%self.__diff)
122 if self.__iter>2 and diff_old<self.__diff:
123 raise IterationDivergenceError,"no improvement in stress iteration"
124 if self.__iter>self.max_iter:
125 raise IterationDivergenceError,"Maximum number of iterations steps reached"
126
127 def terminateIteration(self):
128 """iteration is terminateIterationd if relative pressure change is less then rel_tol"""
129 return self.__diff<=self.rel_tol*Lsup(self.velocity)+self.abs_tol
130
131 def doStepPostprocessing(self,dt):
132 """
133 accept all the values:
134 """
135 self.__displacement_old=self.displacement
136 self.stress_old=self.stress
137 self.__velocity_old=self.velocity
138 self.__temperature_old=self.temperature
139
140 def getSafeTimeStepSize(self,dt):
141 """
142 returns new step size
143 """
144 d=Lsup(self.velocity-self.__velocity_old)/dt
145 if d>0:
146 return Lsup(self.displacement)/d
147 else:
148 return self.UNDEF_DT
149
150
151
152 class DruckerPrager(Mechanics):
153 """
154
155 """
156
157 def __init__(self,debug=False):
158 """
159 set up model
160 """
161 super(DruckerPrager, self).__init__(debug=debug)
162 self.declareParameter(plastic_stress=0.,
163 friction_parameter=0.,
164 dilatancy_parameter=0.,
165 shear_length=1.e15,
166 hardening=0.)
167
168 def doInitialization(self):
169 """
170 initialize model
171 """
172 super(DruckerPrager, self).doInitialization()
173 self.__plastic_stress_old=self.plastic_stress
174 self.__tau_y_old=self.shear_length
175 self.__hardening_old=self.hardening
176
177 def doStepPreprocessing(self,dt):
178 """
179 step up pressure iteration
180
181 if run within a time dependend problem extrapolation of pressure from previous time steps is used to
182 get an initial guess (that needs some work!!!!!!!)
183 """
184 super(DruckerPrager, self).doStepPreprocessing(dt)
185 self.plastic_stress=self.__plastic_stress_old
186 self.shear_length=self.__tau_y_old
187 self.hardening=self.__hardening_old
188
189 def doStep(self,dt):
190 G=self.shear_modulus
191 K=self.bulk_modulus
192 alpha=self.friction_parameter
193 beta=self.dilatancy_parameter
194 tau_Y=self.shear_length
195 h=self.hardening
196 # set new tangential operator:
197 self.S=self.getTangentialTensor(self.stress,
198 tau_Y,G,K,alpha,beta,h)
199 # do the update step:
200 super(DruckerPrager, self).doStep(dt)
201
202 # update stresses:
203 self.stress,self.plastic_stress=self.getNewStress(self.stress_old,self.__plastic_stress_old,
204 self.velocity*dt,
205 self.deps_therm,tau_Y,G,K,alpha,beta,h)
206 if self.__plastic_stress_old:
207 dps=self.plastic_stress-self.__plastic_stress_old
208 self.hardening=(tau_Y-self.__tau_y_old)/(dps+self.abs_tol*whereZero(dps))
209 else:
210 self.hardening=0
211
212 def doStepPostprocessing(self,dt):
213 super(DruckerPrager, self).doStepPostprocessing(dt)
214 self.__plastic_stress_old=self.plastic_stress
215 self.__tau_y_old=self.shear_length
216 self.__hardening_old=self.hardening
217
218 def getNewStress(self,s,gamma_p,du,deps_therm,tau_Y,G,K,alpha,beta,h):
219 k3=kronecker(self.domain)
220 dt=1.
221 g=grad(du)
222 D=symmetric(g)
223 W=nonsymmetric(g)
224 s_e=s+K*deps_therm*k3 +dt*(2*G*D+(K-2./3*G)*trace(D)*k3 \
225 +2*nonsymmetric(matrix_mult(W,s)))
226 p_e=-1./3*trace(s_e)
227 s_e_dev=s_e+p_e*k3
228 tau_e=sqrt(1./2*inner(s_e_dev,s_e_dev))
229 F=tau_e-alpha*p_e-tau_Y
230 chi=whereNonNegative(F)
231 l=chi*F/(h+G+beta*K)
232 s=(1.-l*G/tau_e)*s_e_dev+(p_e+l*beta*K)*k3
233 gamma_p=gamma_p+l
234 return s, gamma_p
235
236
237 def getTangentialTensor(self,s,tau_Y,G,K,alpha,beta,h):
238 d=self.domain.getDim()
239 k3=kronecker(Function(self.domain))
240 p=-1./d*trace(s)
241 s_dev=s+p*k3
242 tau=sqrt(1./2*inner(s_dev,s_dev))
243 chi=whereNonNegative(tau-alpha*p-tau_Y)
244 sXk3=outer(s,k3)
245 k3Xk3=outer(k3,k3)
246 tmp=G*s_dev/(tau+tau_Y*1.e-15*whereZero(tau,1.e-15))
247 S=G*(swap_axes(k3Xk3,1,2)+swap_axes(k3Xk3,1,3)) \
248 + (K-2./3*G)*k3Xk3 \
249 + sXk3-swap_axes(sXk3,1,3) \
250 + 1./2*(swap_axes(sXk3,0,3)-swap_axes(sXk3,1,2) \
251 -swap_axes(sXk3,1,3)+swap_axes(sXk3,0,2))
252 - chi/(h+G+alpha*beta*K)*outer(tmp+beta*K*k3,tmp+alpha*K*k3)\
253 # print S
254 return S

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