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

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Revision 816 - (show annotations)
Thu Aug 24 00:03:01 2006 UTC (12 years, 9 months ago) by gross
File MIME type: text/x-python
File size: 9085 byte(s)
drucker prager in modellib (it does not work yet)
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 displacement: current displacements
19
20 """
21 def __init__(self,debug=False):
22 """
23 set up the model
24
25 @param debug: debug flag
26 @type debug: C{bool}
27 """
28 super(Mechanics, self).__init__(self,debug=debug)
29 self.declareParameter(domain=None, \
30 displacement=None, \
31 stress=None, \
32 velocity=None, \
33 internal_force=Data(), \
34 external_force=Data(), \
35 prescribed_velocity=Data(), \
36 location_prescribed_velocity=Data(), \
37 temperature = None, \
38 expansion_coefficient = 0., \
39 bulk_modulus=1., \
40 shear_modulus=1., \
41 rel_tol=1.e-3,abs_tol=1.e-15,max_iter=10)
42 self.__iter=0
43
44 def doInitialization(self):
45 """
46 initialize model
47 """
48 if not self.displacement: self.displacement=Vector(0.,ContinuousFunction(self.domain))
49 if not self.velocity: self.velocity=Vector(0.,ContinuousFunction(self.domain))
50 if not self.stress: self.stress=Tensor(0.,ContinuousFunction(self.domain))
51 self.__pde=LinearPDE(self.domain)
52 self.__displacement_old=self.displacement
53 self.stress_old=self.stress
54 self.__velocity_old=self.velocity
55 self.__temperature_old=self.temperature
56
57 def doStepPreprocessing(self,dt):
58 """
59 step up pressure iteration
60
61 if run within a time dependend problem extrapolation of pressure from previous time steps is used to
62 get an initial guess (that needs some work!!!!!!!)
63 """
64 self.__iter=0
65 self.__diff=self.UNDEF_DT
66 # set new values:
67 self.displacement=self.__displacement_old
68 self.stress=self.stress_old
69 self.velocity=self.__velocity_old
70 self.temperature=self.__temperature_old
71 self.__velocity_last=self.velocity
72
73 def doStep(self,dt):
74 """
75
76 performs an iteration step of the penalty method.
77 IterationDivergenceError is raised if pressure error cannot be reduced or max_iter is reached.
78
79 requires self.S to be set
80 updates the thermal stress increment
81
82 """
83 k3=kronecker(self.domain)
84 # set new thermal stress increment
85 if self.temperature:
86 self.dthermal_stress=self.bulk_modulus*self.self.expansion_coefficient*(self.temperature-self.__temperature_old)
87 else:
88 self.dthermal_stress=0.
89 # set PDE coefficients:
90 self.__pde.setValue(A=self.S)
91 self.__pde.setValue(X=self.stress_old-self.dthermal_stress*k3)
92 if self.internal_force: self.__pde.setValue(Y=self.internal_force)
93 if self.external_force: self.__pde.setValue(y=self.external_force)
94 self.__pde.setValue(r=self.prescribed_velocity, \
95 q=self.location_prescribed_velocity)
96 # solve the PDE:
97 self.__pde.setTolerance(self.rel_tol/100.)
98 self.velocity=self.__pde.getSolution()
99 # calculate convergence indicators:
100 self.__diff,diff_old=Lsup(self.velocity-self.__velocity_last),self.__diff
101 self.__velocity_last=self.velocity
102 self.displacement=self.__displacement_old+dt*self.velocity
103 self.__iter+=1
104 self.trace("velocity range %e:%e"%(inf(self.velocity),sup(self.velocity)))
105 if self.__iter>2 and diff_old<self.__diff:
106 raise IterationDivergenceError,"no improvement in stress iteration"
107 if self.__iter>self.max_iter:
108 raise IterationDivergenceError,"Maximum number of iterations steps reached"
109
110 def terminateIteration(self):
111 """iteration is terminateIterationd if relative pressure change is less then rel_tol"""
112 return self.__diff<=self.rel_tol*Lsup(self.velocity)+self.abs_tol
113
114 def doStepPostprocessing(self,dt):
115 """
116 accept all the values:
117 """
118 self.displacement=self.__displacement_old
119 self.stress=self.stress_old
120 self.velocity=self.__velocity_old
121 self.temperature=self.__temperature_old
122
123 def getSafeTimeStepSize(self,dt):
124 """
125 returns new step size
126 """
127 d=Lsup(self.velocity-self.__velocity_old)/dt
128 if d>0:
129 return Lsup(self.displacement)/d
130 else:
131 return self.UNDEF_DT
132
133
134
135 class DruckerPrager(Mechanics):
136 """
137
138 """
139
140 def __init__(self,debug=False):
141 """
142 set up model
143 """
144 super(DruckerPrager, self).__init__(debug=debug)
145 self.declareParameter(plastic_stress=0.,
146 friction_parameter=0.,
147 dilatancy_parameter=0.,
148 shear_length=0.)
149
150 def doInitialization(self):
151 """
152 initialize model
153 """
154 super(DruckerPrager, self).doInitialization()
155 self.__plastic_stress_old=self.plastic_stress
156 self.__tau_y_old=self.shear_length
157
158 def doStepPreprocessing(self,dt):
159 """
160 step up pressure iteration
161
162 if run within a time dependend problem extrapolation of pressure from previous time steps is used to
163 get an initial guess (that needs some work!!!!!!!)
164 """
165 super(DruckerPrager, self).doStepPreprocessing(dt)
166 self.plastic_stress=self.__plastic_stress_old
167
168 def doStep(self,dt):
169 G=self.shear_modulus
170 K=self.bulk_modulus
171 alpha=self.friction_parameter
172 beta=self.dilatancy_parameter
173 tau_Y=self.shear_length
174 if self.__plastic_stress_old:
175 dps=self.plastic_stress-self.__plastic_stress_old
176 h=(tau_Y-self.__tau_y_old)/(dps+self.abs_tol*whereZero(dps))
177 else:
178 h=0
179 # set new tangential operator:
180 self.S=self.getTangentialTensor(self.stress,
181 tau_Y,G,K,alpha,beta,h)
182 # do the update step:
183 super(DruckerPrager, self).doStep(dt)
184
185 # update stresses:
186 self.stress,self.plastic_stress=self.getNewStress(self.stress_old,self.__plastic_stress_old,
187 self.velocity*dt,
188 self.dthermal_stress,tau_Y,G,K,alpha,beta,h)
189
190 def doStepPostprocessing(self,dt):
191 super(DruckerPrager, self).doStepPostprocessing(dt)
192 self.plastic_stress=self.__plastic_stress_old=self.plastic_stress
193
194 def getNewStress(self,s,gamma_p,du,ds_therm,tau_Y,G,K,alpha,beta,h):
195 k3=kronecker(self.domain)
196 dt=1.
197 g=grad(du)
198 D=symmetric(g)
199 W=nonsymmetric(g)
200 s_e=s+ds_therm+dt*(2*G*D+(K-2./3*G)*trace(D)*k3 \
201 +2*nonsymmetric(matrix_mult(W,s)))
202 p_e=-1./3*trace(s_e)
203 s_e_dev=s_e+p_e*k3
204 tau_e=sqrt(1./2*inner(s_e_dev,s_e_dev))
205 F=tau_e-alpha*p_e-tau_Y
206 chi=whereNonNegative(F)
207 l=chi*F/(h+G+beta*K)
208 s=(1.-l*G/tau_e)*s_e_dev+(p_e+l*beta*K)*k3
209 gamma_p=gamma_p+l
210 return s, gamma_p
211
212
213 def getTangentialTensor(self,s,tau_Y,G,K,alpha,beta,h):
214 d=self.domain.getDim()
215 k3=kronecker(Function(self.domain))
216 p=-1./d*trace(s)
217 s_dev=s+p*k3
218 tau=sqrt(1./2*inner(s_dev,s_dev))
219 chi=whereNonNegative(tau-alpha*p-tau_Y)
220 sXk3=outer(s,k3)
221 k3Xk3=outer(k3,k3)
222 tmp=G*s_dev/tau
223 S=G*(swap_axes(k3Xk3,1,2)+swap_axes(k3Xk3,1,3)) \
224 + (K-2./3*G)*k3Xk3 \
225 + sXk3-swap_axes(sXk3,1,3) \
226 + 1./2*(swap_axes(sXk3,0,3)+swap_axes(sXk3,1,2) \
227 -swap_axes(sXk3,1,3)-swap_axes(sXk3,0,2))
228 # - chi/(h+G+alpha*beta*K)*outer(tmp+beta*K*k3,tmp+alpha*K*k3)\
229 return S

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