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

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Revision 821 - (show annotations)
Mon Aug 28 08:36:30 2006 UTC (13 years, 9 months ago) by gross
File MIME type: text/x-python
File size: 9710 byte(s)
and some more work 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.dthermal_stress=self.bulk_modulus*self.self.expansion_coefficient*(self.temperature-self.__temperature_old)
100 else:
101 self.dthermal_stress=0.
102 # set PDE coefficients:
103 self.__pde.setValue(A=self.S)
104 self.__pde.setValue(X=self.stress_old-self.dthermal_stress*k3)
105 if self.internal_force: self.__pde.setValue(Y=self.internal_force)
106 if self.external_force: self.__pde.setValue(y=self.external_force)
107 self.__pde.setValue(r=self.prescribed_velocity, \
108 q=self.location_prescribed_velocity)
109 # solve the PDE:
110 self.__pde.setTolerance(self.rel_tol/100.)
111 self.velocity=self.__pde.getSolution(verbose=True)
112 # calculate convergence indicators:
113 self.__diff,diff_old=Lsup(self.velocity-self.__velocity_last),self.__diff
114 self.__velocity_last=self.velocity
115 self.displacement=self.__displacement_old+dt*self.velocity
116 self.__iter+=1
117 if self.debug:
118 for i in range(self.domain.getDim()):
119 self.trace("velocity %d range %e:%e"%(i,inf(self.velocity[i]),sup(self.velocity[i])))
120 self.trace("velocity increment %s"%self.__diff)
121 if self.__iter>2 and diff_old<self.__diff:
122 raise IterationDivergenceError,"no improvement in stress iteration"
123 if self.__iter>self.max_iter:
124 raise IterationDivergenceError,"Maximum number of iterations steps reached"
125
126 def terminateIteration(self):
127 """iteration is terminateIterationd if relative pressure change is less then rel_tol"""
128 return self.__diff<=self.rel_tol*Lsup(self.velocity)+self.abs_tol
129
130 def doStepPostprocessing(self,dt):
131 """
132 accept all the values:
133 """
134 self.displacement=self.__displacement_old
135 self.stress=self.stress_old
136 self.velocity=self.__velocity_old
137 self.temperature=self.__temperature_old
138
139 def getSafeTimeStepSize(self,dt):
140 """
141 returns new step size
142 """
143 d=Lsup(self.velocity-self.__velocity_old)/dt
144 if d>0:
145 return Lsup(self.displacement)/d
146 else:
147 return self.UNDEF_DT
148
149
150
151 class DruckerPrager(Mechanics):
152 """
153
154 """
155
156 def __init__(self,debug=False):
157 """
158 set up model
159 """
160 super(DruckerPrager, self).__init__(debug=debug)
161 self.declareParameter(plastic_stress=0.,
162 friction_parameter=0.,
163 dilatancy_parameter=0.,
164 shear_length=1.e15)
165
166 def doInitialization(self):
167 """
168 initialize model
169 """
170 super(DruckerPrager, self).doInitialization()
171 self.__plastic_stress_old=self.plastic_stress
172 self.__tau_y_old=self.shear_length
173
174 def doStepPreprocessing(self,dt):
175 """
176 step up pressure iteration
177
178 if run within a time dependend problem extrapolation of pressure from previous time steps is used to
179 get an initial guess (that needs some work!!!!!!!)
180 """
181 super(DruckerPrager, self).doStepPreprocessing(dt)
182 self.plastic_stress=self.__plastic_stress_old
183
184 def doStep(self,dt):
185 G=self.shear_modulus
186 K=self.bulk_modulus
187 alpha=self.friction_parameter
188 beta=self.dilatancy_parameter
189 tau_Y=self.shear_length
190 if self.__plastic_stress_old:
191 dps=self.plastic_stress-self.__plastic_stress_old
192 h=(tau_Y-self.__tau_y_old)/(dps+self.abs_tol*whereZero(dps))
193 else:
194 h=0
195 # set new tangential operator:
196 self.S=self.getTangentialTensor(self.stress,
197 tau_Y,G,K,alpha,beta,h)
198 # do the update step:
199 super(DruckerPrager, self).doStep(dt)
200
201 # update stresses:
202 self.stress,self.plastic_stress=self.getNewStress(self.stress_old,self.__plastic_stress_old,
203 self.velocity*dt,
204 self.dthermal_stress,tau_Y,G,K,alpha,beta,h)
205
206 def doStepPostprocessing(self,dt):
207 super(DruckerPrager, self).doStepPostprocessing(dt)
208 self.plastic_stress=self.__plastic_stress_old=self.plastic_stress
209
210 def getNewStress(self,s,gamma_p,du,ds_therm,tau_Y,G,K,alpha,beta,h):
211 k3=kronecker(self.domain)
212 dt=1.
213 g=grad(du)
214 D=symmetric(g)
215 W=nonsymmetric(g)
216 s_e=s+ds_therm+dt*(2*G*D+(K-2./3*G)*trace(D)*k3 \
217 +2*nonsymmetric(matrix_mult(W,s)))
218 p_e=-1./3*trace(s_e)
219 s_e_dev=s_e+p_e*k3
220 tau_e=sqrt(1./2*inner(s_e_dev,s_e_dev))
221 F=tau_e-alpha*p_e-tau_Y
222 chi=whereNonNegative(F)
223 l=chi*F/(h+G+beta*K)
224 s=(1.-l*G/tau_e)*s_e_dev+(p_e+l*beta*K)*k3
225 gamma_p=gamma_p+l
226 return s, gamma_p
227
228
229 def getTangentialTensor(self,s,tau_Y,G,K,alpha,beta,h):
230 d=self.domain.getDim()
231 k3=kronecker(Function(self.domain))
232 p=-1./d*trace(s)
233 s_dev=s+p*k3
234 tau=sqrt(1./2*inner(s_dev,s_dev))
235 chi=whereNonNegative(tau-alpha*p-tau_Y)
236 sXk3=outer(s,k3)
237 k3Xk3=outer(k3,k3)
238 tmp=G*s_dev/tau
239 S=G*(swap_axes(k3Xk3,1,2)+swap_axes(k3Xk3,1,3)) \
240 + (K-2./3*G)*k3Xk3 \
241 + sXk3-swap_axes(sXk3,1,3) \
242 + 1./2*(swap_axes(sXk3,0,3)-swap_axes(sXk3,1,2) \
243 -swap_axes(sXk3,1,3)+swap_axes(sXk3,0,2))
244 # - chi/(h+G+alpha*beta*K)*outer(tmp+beta*K*k3,tmp+alpha*K*k3)\
245 return S

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