modellib/py_src/mechanics.py

# $Id:$

__copyright__="""  Copyright (c) 2006 by ACcESS MNRF
                    http://www.access.edu.au
                Primary Business: Queensland, Australia"""
__license__="""Licensed under the Open Software License version 3.0
             http://www.opensource.org/licenses/osl-3.0.php"""

from esys.escript import *
from esys.escript.modelframe import Model,IterationDivergenceError
from esys.escript.linearPDEs import LinearPDE

class Mechanics(Model):
      """
      base class for mechanics models in updated lagrangean framework

      @ivar domain: domain (in)
      @ivar displacement: current displacements

      """
      def __init__(self,debug=False):
         """
         set up the model
         
         @param debug: debug flag
         @type debug: C{bool}
         """
         super(Mechanics, self).__init__(self,debug=debug)
         self.declareParameter(domain=None, \
                               displacement=None, \
                               stress=None, \
                               velocity=None, \
                               internal_force=Data(), \
                               external_force=Data(), \
                               prescribed_velocity=Data(), \
                               location_prescribed_velocity=Data(), \
                               temperature = None, \
                               expansion_coefficient = 0., \
                               bulk_modulus=1., \
                               shear_modulus=1., \
                               rel_tol=1.e-3,abs_tol=1.e-15,max_iter=10)
         self.__iter=0

      def doInitialization(self):
           """
           initialize model
           """
           if not self.displacement: self.displacement=Vector(0.,ContinuousFunction(self.domain))
           if not self.velocity: self.velocity=Vector(0.,ContinuousFunction(self.domain))
           if not self.stress: self.stress=Tensor(0.,ContinuousFunction(self.domain))
           self.__pde=LinearPDE(self.domain)
           self.__displacement_old=self.displacement
           self.stress_old=self.stress
           self.__velocity_old=self.velocity
           self.__temperature_old=self.temperature
           
      def doStepPreprocessing(self,dt):
            """
            step up pressure iteration

            if run within a time dependend problem extrapolation of pressure from previous time steps is used to
            get an initial guess (that needs some work!!!!!!!)
            """
            self.__iter=0
            self.__diff=self.UNDEF_DT
            # set new values:
            self.displacement=self.__displacement_old
            self.stress=self.stress_old
            self.velocity=self.__velocity_old
            self.temperature=self.__temperature_old
            self.__velocity_last=self.velocity

      def doStep(self,dt):
          """

          performs an iteration step of the penalty method.
          IterationDivergenceError is raised if pressure error cannot be reduced or max_iter is reached.
     
          requires self.S to be set 
          updates the thermal stress increment

          """
          k3=kronecker(self.domain)
          # set new thermal stress increment
          if self.temperature:
             self.dthermal_stress=self.bulk_modulus*self.self.expansion_coefficient*(self.temperature-self.__temperature_old)
          else:
             self.dthermal_stress=0.
          # set PDE coefficients:
          self.__pde.setValue(A=self.S)
          self.__pde.setValue(X=self.stress_old-self.dthermal_stress*k3)
          if self.internal_force: self.__pde.setValue(Y=self.internal_force)
          if self.external_force: self.__pde.setValue(y=self.external_force)
          self.__pde.setValue(r=self.prescribed_velocity, \
                              q=self.location_prescribed_velocity)
          # solve the PDE:
          self.__pde.setTolerance(self.rel_tol/100.)
          self.velocity=self.__pde.getSolution()
          # calculate convergence indicators:
          self.__diff,diff_old=Lsup(self.velocity-self.__velocity_last),self.__diff
          self.__velocity_last=self.velocity
          self.displacement=self.__displacement_old+dt*self.velocity
          self.__iter+=1
          self.trace("velocity range %e:%e"%(inf(self.velocity),sup(self.velocity)))
          if self.__iter>2 and diff_old<self.__diff:
              raise IterationDivergenceError,"no improvement in stress iteration"
          if self.__iter>self.max_iter:
              raise IterationDivergenceError,"Maximum number of iterations steps reached"

      def terminateIteration(self):
          """iteration is terminateIterationd if relative pressure change is less then rel_tol"""
          return self.__diff<=self.rel_tol*Lsup(self.velocity)+self.abs_tol

      def doStepPostprocessing(self,dt):
           """
           accept all the values:
           """
           self.displacement=self.__displacement_old
           self.stress=self.stress_old
           self.velocity=self.__velocity_old
           self.temperature=self.__temperature_old

      def getSafeTimeStepSize(self,dt):
           """
           returns new step size
           """
           d=Lsup(self.velocity-self.__velocity_old)/dt
           if d>0:
               return Lsup(self.displacement)/d
           else:
               return self.UNDEF_DT


class DruckerPrager(Mechanics):
      """

      """

      def __init__(self,debug=False):
           """
           set up model
           """
           super(DruckerPrager, self).__init__(debug=debug)
           self.declareParameter(plastic_stress=0.,
                                 friction_parameter=0.,
                                 dilatancy_parameter=0.,
                                 shear_length=0.)

      def doInitialization(self):
           """
           initialize model
           """
           super(DruckerPrager, self).doInitialization()
           self.__plastic_stress_old=self.plastic_stress
           self.__tau_y_old=tau_y=self.shear_length

      def doStepPreprocessing(self,dt):
            """
            step up pressure iteration

            if run within a time dependend problem extrapolation of pressure from previous time steps is used to
            get an initial guess (that needs some work!!!!!!!)
            """
            super(DruckerPrager, self).doStepPreprocessing(dt)
            self.plastic_stress=self.__plastic_stress_old
            self.tau_y=self.__tau_y_old

      def doStep(self,dt):
           G=self.shear_modulus
           K=self.bulk_modulus
           alpha=self.friction_parameter
           beta=self.dilatancy_parameter
           tau_Y=self.shear_length
           if self.__plastic_stress_old:
              dps=self.plastic_stress-self.__plastic_stress_old
              h=(tau_Y-self.tau_Y_last)/(dps+self.abs_tol*whereZero(dps))
           else:
              h=0
           # set new tangential operator:
           self.S=self.getTangentialTensor(self.stress,
                                           tau_Y,G,K,alpha,beta,h)
           # do the update step:
           super(DruckerPrager, self).doStep(dt)

           # update stresses:
           self.stress,self.plastic_stress=self.getNewStress(self.stress_old,self.__plastic_stress_old,
                                                        self.velocity*dt,
                                                        self.dthermal_stress,tau_Y,G,K,alpha,beta,h)

      def doStepPostprocessing(self,dt):
          super(DruckerPrager, self).doStepPostprocessing(dt)
          self.plastic_stress=self.__plastic_stress_old=self.plastic_stress
          self.shear_length=self.__tau_y_old

      def getNewStress(self,s,gamma_p,du,ds_therm,tau_Y,G,K,alpha,beta,h):
            k3=kronecker(self.domain)
            dt=1.
            g=grad(du)
            D=symmetric(g)
            W=nonsymmetric(g)
            s_e=s+ds_therm+dt*(2*G*D+(K-2./3*G)*trace(D)*k3 \
                               +2*nonsymmetric(matrix_mult(W,s)))
            p_e=-1./3*trace(s_e)
            s_e_dev=s_e+p_e*k3
            tau_e=sqrt(1./2*inner(s_e_dev,s_e_dev))
            F=tau_e-alpha*p_e-tau_Y
            chi=whereNonNegative(F)
            l=chi*F/(h+G+beta*K)
            s=(1.-l*G/tau_e)*s_e_dev+(p_e+l*beta*K)*k3
            gamma_p=gamma_p+l
            return s, gamma_p
            

      def getTangentialTensor(self,s,tau_Y,G,K,alpha,beta,h):
           d=self.domain.getDim()
           k3=kronecker(Function(self.domain))
           p=-1./d*trace(s)
           s_dev=s+p*k3 
           tau=sqrt(1./2*inner(s_dev,s_dev))
           chi=whereNonNegative(tau-alpha*p-tau_Y)
           sXk3=outer(s,k3)
           k3Xk3=outer(k3,k3)
           tmp=G*s_dev/tau
           S=G*(swap_axes(k3Xk3,1,2)+swap_axes(k3Xk3,1,3)) \
               + (K-2./3*G)*k3Xk3 \
               + sXk3-swap_axes(sXk3,1,3) \
               + 1./2*(swap_axes(sXk3,0,3)+swap_axes(sXk3,1,2) \
                      -swap_axes(sXk3,1,3)-swap_axes(sXk3,0,2))
               # - chi/(h+G+alpha*beta*K)*outer(tmp+beta*K*k3,tmp+alpha*K*k3)\
           return S
1	gross	814	# $Id:$
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_modulusself.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=tau_y=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			self.tau_y=self.__tau_y_old
168
169			def doStep(self,dt):
170			G=self.shear_modulus
171			K=self.bulk_modulus
172			alpha=self.friction_parameter
173			beta=self.dilatancy_parameter
174			tau_Y=self.shear_length
175			if self.__plastic_stress_old:
176			dps=self.plastic_stress-self.__plastic_stress_old
177			h=(tau_Y-self.tau_Y_last)/(dps+self.abs_tol*whereZero(dps))
178			else:
179			h=0
180			# set new tangential operator:
181			self.S=self.getTangentialTensor(self.stress,
182			tau_Y,G,K,alpha,beta,h)
183			# do the update step:
184			super(DruckerPrager, self).doStep(dt)
185
186			# update stresses:
187			self.stress,self.plastic_stress=self.getNewStress(self.stress_old,self.__plastic_stress_old,
188			self.velocity*dt,
189			self.dthermal_stress,tau_Y,G,K,alpha,beta,h)
190
191			def doStepPostprocessing(self,dt):
192			super(DruckerPrager, self).doStepPostprocessing(dt)
193			self.plastic_stress=self.__plastic_stress_old=self.plastic_stress
194			self.shear_length=self.__tau_y_old
195
196			def getNewStress(self,s,gamma_p,du,ds_therm,tau_Y,G,K,alpha,beta,h):
197			k3=kronecker(self.domain)
198			dt=1.
199			g=grad(du)
200			D=symmetric(g)
201			W=nonsymmetric(g)
202			s_e=s+ds_therm+dt(2GD+(K-2./3G)trace(D)k3 \
203			+2*nonsymmetric(matrix_mult(W,s)))
204			p_e=-1./3*trace(s_e)
205			s_e_dev=s_e+p_e*k3
206			tau_e=sqrt(1./2*inner(s_e_dev,s_e_dev))
207			F=tau_e-alpha*p_e-tau_Y
208			chi=whereNonNegative(F)
209			l=chiF/(h+G+betaK)
210			s=(1.-lG/tau_e)s_e_dev+(p_e+lbetaK)*k3
211			gamma_p=gamma_p+l
212			return s, gamma_p
213
214
215			def getTangentialTensor(self,s,tau_Y,G,K,alpha,beta,h):
216			d=self.domain.getDim()
217			k3=kronecker(Function(self.domain))
218			p=-1./d*trace(s)
219			s_dev=s+p*k3
220			tau=sqrt(1./2*inner(s_dev,s_dev))
221			chi=whereNonNegative(tau-alpha*p-tau_Y)
222			sXk3=outer(s,k3)
223			k3Xk3=outer(k3,k3)
224			tmp=G*s_dev/tau
225			S=G*(swap_axes(k3Xk3,1,2)+swap_axes(k3Xk3,1,3)) \
226			+ (K-2./3G)k3Xk3 \
227			+ sXk3-swap_axes(sXk3,1,3) \
228			+ 1./2*(swap_axes(sXk3,0,3)+swap_axes(sXk3,1,2) \
229			-swap_axes(sXk3,1,3)-swap_axes(sXk3,0,2))
230			# - chi/(h+G+alphabetaK)outer(tmp+betaKk3,tmp+alphaK*k3)\
231			return S