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)
          print self.prescribed_velocity
          print self.location_prescribed_velocity
          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=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

      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_old)/(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

      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	# $Id:$
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	print self.prescribed_velocity
95	print self.location_prescribed_velocity
96	self.__pde.setValue(r=self.prescribed_velocity, \
97	q=self.location_prescribed_velocity)
98	# solve the PDE:
99	self.__pde.setTolerance(self.rel_tol/100.)
100	self.velocity=self.__pde.getSolution()
101	# calculate convergence indicators:
102	self.__diff,diff_old=Lsup(self.velocity-self.__velocity_last),self.__diff
103	self.__velocity_last=self.velocity
104	self.displacement=self.__displacement_old+dt*self.velocity
105	self.__iter+=1
106	self.trace("velocity range %e:%e"%(inf(self.velocity),sup(self.velocity)))
107	if self.__iter>2 and diff_old<self.__diff:
108	raise IterationDivergenceError,"no improvement in stress iteration"
109	if self.__iter>self.max_iter:
110	raise IterationDivergenceError,"Maximum number of iterations steps reached"
111
112	def terminateIteration(self):
113	"""iteration is terminateIterationd if relative pressure change is less then rel_tol"""
114	return self.__diff<=self.rel_tol*Lsup(self.velocity)+self.abs_tol
115
116	def doStepPostprocessing(self,dt):
117	"""
118	accept all the values:
119	"""
120	self.displacement=self.__displacement_old
121	self.stress=self.stress_old
122	self.velocity=self.__velocity_old
123	self.temperature=self.__temperature_old
124
125	def getSafeTimeStepSize(self,dt):
126	"""
127	returns new step size
128	"""
129	d=Lsup(self.velocity-self.__velocity_old)/dt
130	if d>0:
131	return Lsup(self.displacement)/d
132	else:
133	return self.UNDEF_DT
134
135
136
137	class DruckerPrager(Mechanics):
138	"""
139
140	"""
141
142	def __init__(self,debug=False):
143	"""
144	set up model
145	"""
146	super(DruckerPrager, self).__init__(debug=debug)
147	self.declareParameter(plastic_stress=0.,
148	friction_parameter=0.,
149	dilatancy_parameter=0.,
150	shear_length=0.)
151
152	def doInitialization(self):
153	"""
154	initialize model
155	"""
156	super(DruckerPrager, self).doInitialization()
157	self.__plastic_stress_old=self.plastic_stress
158	self.__tau_y_old=self.shear_length
159
160	def doStepPreprocessing(self,dt):
161	"""
162	step up pressure iteration
163
164	if run within a time dependend problem extrapolation of pressure from previous time steps is used to
165	get an initial guess (that needs some work!!!!!!!)
166	"""
167	super(DruckerPrager, self).doStepPreprocessing(dt)
168	self.plastic_stress=self.__plastic_stress_old
169
170	def doStep(self,dt):
171	G=self.shear_modulus
172	K=self.bulk_modulus
173	alpha=self.friction_parameter
174	beta=self.dilatancy_parameter
175	tau_Y=self.shear_length
176	if self.__plastic_stress_old:
177	dps=self.plastic_stress-self.__plastic_stress_old
178	h=(tau_Y-self.__tau_y_old)/(dps+self.abs_tol*whereZero(dps))
179	else:
180	h=0
181	# set new tangential operator:
182	self.S=self.getTangentialTensor(self.stress,
183	tau_Y,G,K,alpha,beta,h)
184	# do the update step:
185	super(DruckerPrager, self).doStep(dt)
186
187	# update stresses:
188	self.stress,self.plastic_stress=self.getNewStress(self.stress_old,self.__plastic_stress_old,
189	self.velocity*dt,
190	self.dthermal_stress,tau_Y,G,K,alpha,beta,h)
191
192	def doStepPostprocessing(self,dt):
193	super(DruckerPrager, self).doStepPostprocessing(dt)
194	self.plastic_stress=self.__plastic_stress_old=self.plastic_stress
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