def __init__(self,idx,nodelist=[]):
self.index = idx
self.nodes = nodelist[:]
self.sfns = [qsf0,qsf1,qsf2,qsf3]
self.dsfns = [[dqsf0d1,dqsf0d2],[dqsf1d1,dqsf1d2],
[dqsf2d1,dqsf2d2],[dqsf3d1,dqsf3d2]]
for n in self.nodes:
n.add_element(self)
# Gauss-point-specific data. Initialize plastic strain field
# to be zero.
self.gpdata = {}
for p in self.gausspts():
# Data are the local gamma, the six components of plastic
# strain, and the six components of the yield surface
# center.
self.gpdata[p]=[0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ]
# Use shape-functions directly to represent the stress. The
# shape functions are capable of representing lower-order
# objects, so in principle this should not create any
# difficulties, and is convenient. They are only used on a
# per-element basis, of course.
mmtx = smallmatrix.SmallMatrix(4,4)
rmtx = smallmatrix.SmallMatrix(4,4)
mmtx.clear()
rmtx.clear()
for i in range(4):
rmtx[i,i]=1.0 # Identity matrix.
for j in range(4):
res = 0.0
for p in self.gausspts():
res += self.shapefn(i,p.xi,p.zeta)* \
self.shapefn(j,p.xi,p.zeta)* \
p.weight*self.jacobian(p.xi,p.zeta)
mmtx[i,j]=res
r = mmtx.solve(rmtx)
if r!=0:
print >> sys.stderr, \
"Element mass matrix is singular, run for the hills!"
else:
self.s_mtx = rmtx
def ycheck(cijkl,yld,stress):
eps = 1.0e-10
# Local return-mapping problem -- DOFs are, in order,
# lambda, ep00,ep11,ep22,ep12,ep02,ep01 (voigt order).
mtx = smallmatrix.SmallMatrix(7,7)
rhs = smallmatrix.SmallMatrix(7,1)
#
ep = [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
lmbda = 0.0
#
icount = 0
while icount < 10:
icount += 1
lstress = [ [ stress[i][j]-sum([ sum([ cijkl[i][j][k][l]*ep[voigt[k][l]] for l in range(3) ]) for k in range(3) ]) for j in range(3) ] for i in range(3) ]
mtx.clear()
rhs.clear()
# Build right-hand-side, check for zeroness.
rhs[0,0] = -yld.yeeld(lstress)
dy = yld.dyeeld(lstress)
d2y = yld.d2yeeld(lstress)
for i in range(3):
for j in range(i+1):
rhs[voigt[i][j]+1,0] = -lmbda*dy[i][j]+ep[voigt[i][j]]
# print "\nRHS: ", [ rhs[i,0] for i in range(rhs.rows()) ]
mag = sum( [ rhs[i,0]**2 for i in range(rhs.rows()) ] )
if mag<eps:
break # out of while loop.
# Build matrix.
# First row, consistency equation.
for k in range(3):
for l in range(3):
col = voigt[k][l]+1
mtx[0,col] += sum([ sum([ -dy[i][j]*cijkl[i][j][k][l]
for j in range(3) ])
for i in range(3) ])
# Subsequent rows:
for i in range(3):
for j in range(i+1):
row = voigt[i][j]+1
# Column zero, easy.
mtx[row,0]=dy[i][j]
for m in range(3):
for n in range(3):
col = voigt[m][n]+1
diag = 0.0
if i==m and j==n:
diag = 1.0
mtx[row,col] += sum([ sum([ -lmbda*d2y[i][j][k][l]*cijkl[k][l][m][n] for l in range(3) ]) for k in range(3) ])-diag
# Solve the resulting linearized system.
# for mtxi in range(7):
# print [ mtx[mtxi,j] for j in range(7) ]
rr = mtx.solve(rhs)
if rr==0:
# print "Increments: ", [ rhs[i,0] for i in range(7) ]
lmbda += rhs[0,0]
for i in range(6):
ep[i] += rhs[i+1,0]
# print "Soln: ", [lmbda] + [ep[i] for i in range(6)]
else:
print >> sys.stderr, "Error in solving in ycheck, rr=", rr
# Broke out of loop.
return ep
def ycheck(cijkl,yld,stress,center,gamma):
eps = 1.0e-10
# Local return-mapping problem -- DOFs are, in order,
# lambda, ep00,ep11,ep22,ep12,ep02,ep01 (voigt order).
mtx = smallmatrix.SmallMatrix(14,14)
rhs = smallmatrix.SmallMatrix(14,1)
#
# The variables occur in this order.
lmbda = 0.0
dgamma = 0.0
ep = [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
dcenter = [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
#
icount = 0
while icount < 100:
icount += 1
lstress = [ [ stress[i][j]-sum([ sum([ cijkl[i][j][k][l]*ep[voigt[k][l]] for l in range(3) ]) for k in range(3) ]) for j in range(3) ] for i in range(3) ]
mtx.clear()
rhs.clear()
# Short for "current center"...
ccenter = [ [ center[i][j]+dcenter[voigt[i][j]]
for j in range(3) ] for i in range(3) ]
eptensor = [ [ ep[voigt[i][j]] for j in range(3) ]
for i in range(3) ]
dy = yld.dyeeld(lstress,ccenter)
flow = yld.flow(lstress,ccenter)
dflow = yld.dflow(lstress,ccenter)
ihard = yld.isohard(eptensor)
dihard = yld.disohard(eptensor)
khard = yld.khard(eptensor)
dkhard = yld.dkhard(eptensor)
# Build right-hand-side, check for zeroness.
rhs[0,0] = -yld.yeeld(lstress,ccenter,gamma+dgamma)
rhs[1,0] = -dgamma + ihard
# rhs[1,0] = -dgamma + yld.iso_c*sq_epmag
for i in range(3):
for j in range(i+1):
rhs[voigt[i][j]+2,0] = -lmbda*flow[i][j]+ep[voigt[i][j]]
for i in range(3):
for j in range(i+1):
rhs[voigt[i][j]+8,0] = -dcenter[voigt[i][j]] + khard[i][j]
# print "\nRHS: ", [ rhs[i,0] for i in range(rhs.rows()) ]
mag = sum( [ rhs[i,0]**2 for i in range(rhs.rows()) ] )
if mag<eps:
break # out of while loop.
# Build matrix.
# First row, consistency equation.
mtx[0,1] = -1.0 # Derivative of yield function wrt delta-gamma.
for k in range(3):
for l in range(3):
col = voigt[k][l]+2
mtx[0,col] += sum([ sum([ -dy[i][j]*cijkl[i][j][k][l]
for j in range(3) ])
for i in range(3) ])
col = voigt[k][l]+8
# Derivative of yield function wrt delta-c components.
mtx[0,col] -= dy[k][l]
# Second row, isotropic hardening. No dependence on ccenter.
mtx[1,1]=1.0
for k in range(3):
for l in range(3):
col = voigt[k][l]+2
mtx[1,col] += -dihard[k][l]
# Third through eights rows, flow rule.
for i in range(3):
for j in range(i+1):
row = voigt[i][j]+2
# Column zero, easy.
mtx[row,0]=dy[i][j]
for m in range(3):
for n in range(3):
col = voigt[m][n]+2
diag = 0.0
if i==m and j==n:
diag = 1.0
mtx[row,col] += sum([ sum([ -lmbda*dflow[i][j][k][l]*cijkl[k][l][m][n] for l in range(3) ]) for k in range(3) ])-diag
col = voigt[m][n]+8
mtx[row,col] += -lmbda*dflow[i][j][m][n]
# Ninth through fourteenth rows, kinematic hardening.
for i in range(3):
for j in range(i+1):
row = voigt[i][j]+8
mtx[row,row]=1.0 # Diagonal part, deriv wrt c's.
# Component-wise match-up.
for k in range(3):
for l in range(3):
col = voigt[k][l]+2
mtx[row,col] = -dkhard[i][j][k][l]
# Solve the resulting linearized system.
# for mtxi in range(8):
# print [ mtx[mtxi,j] for j in range(8) ]
rr = mtx.solve(rhs)
if rr==0:
# print "Increments: ", [ rhs[i,0] for i in range(8) ]
lmbda += rhs[0,0]
dgamma += rhs[1,0]
for i in range(6):
ep[i] += rhs[i+2,0]
dcenter[i] += rhs[i+8,0]
# print "Soln: ", [lmbda, dgamma] + [ep[i] for i in range(6)]
else:
print >> sys.stderr, "Error in solving in ycheck, rr=", rr
else:
print >> sys.stderr, "Error, ycheck loop did not converge."
# Broke out of loop.
return [dgamma]+ep+dcenter
def __init__(self,idx,nodelist=[]):
self.index = idx
self.nodes = nodelist[:]
self.sfns = [qsf0,qsf1,qsf2,qsf3]
self.dsfns = [[dqsf0d1,dqsf0d2],[dqsf1d1,dqsf1d2],
[dqsf2d1,dqsf2d2],[dqsf3d1,dqsf3d2]]
for n in self.nodes:
n.add_element(self)
# Gauss-point-specific data. Initialize plastic strain field
# to be zero.
self.gpdata = {}
for p in self.gausspts():
self.gpdata[p]=[0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
# Use shape-functions directly to represent the stress. The
# shape functions are capable of representing lower-order
# objects, so in principle this should not create any
# difficulties, and is convenient. They are only used on a
# per-element basis, of course.
mmtx = smallmatrix.SmallMatrix(4,4)
rmtx = smallmatrix.SmallMatrix(4,4)
mmtx.clear()
rmtx.clear()
for i in range(4):
rmtx[i,i]=1.0 # Identity matrix.
for j in range(4):
res = 0.0
for p in self.gausspts():
res += self.shapefn(i,p.xi,p.zeta)* \
self.shapefn(j,p.xi,p.zeta)* \
p.weight*self.jacobian(p.xi,p.zeta)
mmtx[i,j]=res
r = mmtx.solve(rmtx)
if r!=0:
print >> sys.stderr, \
"Element mass matrix is singular, run for the hills!"
else:
self.s_mtx = rmtx
# G-matrix is indexed by triples, i,j,k, where i is the index
# of the shape function, j is the index of the shape function
# derivative, and k is the component of the derivative, for
# which the entry is the integral over the element.
self.g_mtx = [[[0.0, 0.0], [0.0, 0.0], [0.0, 0.0], [0.0, 0.0]],
[[0.0, 0.0], [0.0, 0.0], [0.0, 0.0], [0.0, 0.0]],
[[0.0, 0.0], [0.0, 0.0], [0.0, 0.0], [0.0, 0.0]],
[[0.0, 0.0], [0.0, 0.0], [0.0, 0.0], [0.0, 0.0]]]
for i in range(4):
for j in range(4):
for k in range(2):
res = 0.0
for p in self.gausspts():
res += self.shapefn(i,p.xi,p.zeta)* \
self.dshapefn(j,k,p.xi,p.zeta)* \
p.weight* \
self.jacobian(p.xi,p.zeta)
self.g_mtx[i][j][k] = res
# Premultiply.
self.sg_mtx = [[[0.0, 0.0], [0.0, 0.0], [0.0, 0.0], [0.0, 0.0]],
[[0.0, 0.0], [0.0, 0.0], [0.0, 0.0], [0.0, 0.0]],
[[0.0, 0.0], [0.0, 0.0], [0.0, 0.0], [0.0, 0.0]],
[[0.0, 0.0], [0.0, 0.0], [0.0, 0.0], [0.0, 0.0]]]
for s in range(4):
for j in range(4):
for k in range(2):
for t in range(4):
self.sg_mtx[s][j][k] += self.s_mtx[s,t]*self.g_mtx[t][j][k]
self.make_fmtx()
