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

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Revision 829 - (show annotations)
Thu Aug 31 01:31:15 2006 UTC (12 years, 9 months ago) by gross
File MIME type: text/x-python
File size: 9956 byte(s)
some changes on the drucker-prager (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 internal_force: =Data()
19 @ivar external_force: =Data()
20 @ivar prescribed_velocity: =Data()
21 @ivar location_fixed_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 location_fixed_velocity=Data(), \
48 temperature = None, \
49 expansion_coefficient = 0., \
50 bulk_modulus=2., \
51 shear_modulus=1., \
52 rel_tol=1.e-3,abs_tol=1.e-15,max_iter=10)
53 self.__iter=0
54
55 def doInitialization(self):
56 """
57 initialize model
58 """
59 if not self.displacement: self.displacement=Vector(0.,ContinuousFunction(self.domain))
60 if not self.velocity: self.velocity=Vector(0.,ContinuousFunction(self.domain))
61 if not self.stress: self.stress=Tensor(0.,ContinuousFunction(self.domain))
62 # open PDE:
63 self.stress_old=self.stress
64 self.__velocity_old=self.velocity
65 self.__temperature_old=self.temperature
66 self.__displacement_old=self.displacement
67 # get node cooridnates:
68 self.__x=self.domain.getX()
69 self.domain.setX(self.__x+self.displacement)
70 # open PDE:
71 self.__pde=LinearPDE(self.domain)
72 self.__pde.setSymmetryOn()
73 def doStepPreprocessing(self,dt):
74 """
75 step up pressure iteration
76
77 if run within a time dependend problem extrapolation of pressure from previous time steps is used to
78 get an initial guess (that needs some work!!!!!!!)
79 """
80 self.__iter=0
81 self.__diff=self.UNDEF_DT
82 # set initial values for the iteration:
83 self.velocity=self.__velocity_old
84 self.temperature=self.__temperature_old
85 self.displacement=self.__displacement_old+self.velocity*dt
86
87 # set temperature strain:
88 if self.temperature:
89 self.deps_therm=self.self.expansion_coefficient*(self.temperature-self.__temperature_old)
90 else:
91 self.deps_therm=0.
92
93 # update geometry
94 self.domain.setX(self.__x+self.displacement)
95 self.stress=self.stress_old
96
97 def doStep(self,dt):
98 """
99
100 performs an iteration step of the penalty method.
101 IterationDivergenceError is raised if pressure error cannot be reduced or max_iter is reached.
102
103 requires self.S to be set
104 updates the thermal stress increment
105
106 """
107 k3=kronecker(self.domain)
108 # set new thermal stress increment
109 if self.temperature:
110 self.deps_therm=self.self.expansion_coefficient*(self.temperature-self.__temperature_old)
111 else:
112 self.deps_therm=0.
113 # set PDE coefficients:
114 self.__pde.setValue(A=self.S)
115 self.__pde.checkSymmetry()
116 self.__pde.setValue(X=-self.stress+self.stress_old-self.bulk_modulus*self.deps_therm*k3)
117 if self.internal_force: self.__pde.setValue(Y=self.internal_force)
118 if self.external_force: self.__pde.setValue(y=self.external_force)
119 self.__pde.setValue(q=self.location_fixed_velocity)
120 # solve the PDE:
121 self.__pde.setTolerance(self.rel_tol**2)
122 du=self.__pde.getSolution(verbose=True)
123 self.velocity+=du/dt
124 # update geometry
125 self.displacement=self.__displacement_old+dt*self.velocity
126 self.domain.setX(self.__x+self.displacement)
127
128 self.__iter+=1
129 if self.debug:
130 for i in range(self.domain.getDim()):
131 self.trace("velocity %d range %e:%e"%(i,inf(self.velocity[i]),sup(self.velocity[i])))
132 for i in range(self.domain.getDim()):
133 self.trace("displacement %d range %e:%e"%(i,inf(self.displacement[i]),sup(self.displacement[i])))
134
135 def terminateIteration(self):
136 """iteration is terminateIterationd if relative pressure change is less then rel_tol"""
137 if self.__iter>2 and self.diff_last<self.diff:
138 raise IterationDivergenceError,"no improvement in stress iteration"
139 if self.__iter>self.max_iter:
140 raise IterationDivergenceError,"Maximum number of iterations steps reached"
141 return self.diff<=self.rel_tol*1.e-2*Lsup(self.stress)+self.abs_tol
142
143 def doStepPostprocessing(self,dt):
144 """
145 accept all the values:
146 """
147 self.__displacement_old=self.displacement
148 self.__velocity_old,self.__velocity_old=self.velocity,self.__velocity_old
149 self.__temperature_old=self.temperature
150 self.stress_old=self.stress
151
152 def getSafeTimeStepSize(self,dt):
153 """
154 returns new step size
155 """
156 d=Lsup(self.velocity-self.__velocity_old)*Lsup(self.displacement)
157 if d>0:
158 return dt/d*self.rel_tol
159 else:
160 return self.UNDEF_DT
161
162
163
164 class DruckerPrager(Mechanics):
165 """
166
167 """
168
169 def __init__(self,debug=False):
170 """
171 set up model
172 """
173 super(DruckerPrager, self).__init__(debug=debug)
174 self.declareParameter(plastic_stress=0.,
175 friction_parameter=0.,
176 dilatancy_parameter=0.,
177 shear_length=1.e15)
178 def doInitialization(self):
179 """
180 """
181 super(DruckerPrager, self).doInitialization()
182
183 def doStepPreprocessing(self):
184 """
185 """
186 super(DruckerPrager, self).doStepPreprocessing(dt)
187 # set initial guess for iteration:
188 self.shear_length=self.__shear_length_old
189 self.plastic_stress=self.__plastic_stress_old
190 # set initial stress:
191 self.updateStress()
192
193
194
195 #================================
196
197 # set new tangential operator:
198 self.S=self.getTangentialTensor()
199 # do the update step:
200
201 super(DruckerPrager, self).doStep(dt)
202 # update stresses:
203 self.updateStress()
204
205 def doStepPostprocessing(self,dt):
206 super(DruckerPrager, self).doStepPostprocessing(dt)
207 self.__plastic_stress_old=self.plastic_stress
208 self.__shear_length_old=self.shear_length
209
210 def setStress(self):
211 G=self.shear_modulus
212 K=self.bulk_modulus
213 alpha=self.friction_parameter
214 beta=self.dilatancy_parameter
215 h=self.hardening
216 k3=kronecker(self.domain)
217 # elastic trial stress:
218 g=grad(self.velocity)
219 D=symmetric(g)
220 W=nonsymmetric(g)
221 s_e=self.stress_old+K*self.deps_therm*k3+ \
222 dt*(2*G*D+(K-2./3*G)*trace(D)*k3 \
223 +2*symmetric(matrix_mult(W,self.stress_old)))
224 p_e=-1./3*trace(s_e)
225 s_e_dev=s_e+p_e*k3
226 tau_e=sqrt(1./2*inner(s_e_dev,s_e_dev))
227 # yield conditon for elastic trial stress:
228 F=tau_e-alpha*p_e-self.shear_length
229 self.__chi=whereNonNegative(F)
230 # plastic stress increment:
231 l=self.__chi*F/(h+G+beta*K)
232 self.__tau=tau_e-G*l
233 self.stress=self.__tau/(tau_e+self.abs_tol*whereZero(tau_e,self.abs_tol))*s_e_dev+(p_e+l*beta*K)*k3
234 self.plastic_stress=self.plastic_stress_old+l
235 # update hardening
236 self.hardening=(self.shear_length-self.__shear_length_old)/(l+self.abs_tol*whereZero(l))
237
238 def setTangentialTensor(self):
239 G=self.shear_modulus
240 K=self.bulk_modulus
241 alpha=self.friction_parameter
242 beta=self.dilatancy_parameter
243 tau_Y=self.shear_length
244 chi=self.__chi
245 h=self.hardening
246 tmp=G*s_dev/(tau+self.abs_tol*whereZero(tau,self.abs_tol))
247
248 k3=kronecker(Function(self.domain))
249 s_dev=self.stress+trace(self.stress)*(k3/d)
250 sXk3=outer(self.stress_old,k3)
251 k3Xk3=outer(k3,k3)
252 S=G*(swap_axes(k3Xk3,1,2)+swap_axes(k3Xk3,1,3)) \
253 + (K-2./3*G)*k3Xk3 \
254 + (sXk3-swap_axes(sXk3,1,3)) \
255 + 1./2*(swap_axes(sXk3,0,3)-swap_axes(sXk3,1,2) \
256 -swap_axes(sXk3,1,3)+swap_axes(sXk3,0,2)) \
257 - outer(chi/(h+G+alpha*beta*K)*(tmp+beta*K*k3),tmp+alpha*K*k3)
258 return S

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