Rocstar  1.0
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MP/Source/v3d10_nl_arruda_boyce.f90
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53 SUBROUTINE v3d10_nl_arruda_boyce(coor,matcstet,lmcstet,R_in,d, &
54  s11,s22,s33,s12,s23,s13, &
55  numnp,nstart,nend,numcstet,numat_vol, &
56  mu,kappa)
57 
58 !________________________________________________________________________
59 !
60 ! V3D4 - Performs displacement based computations for Volumetric 3D,
61 ! 10-node Quadratic Linear Elastic Tetrahedron with quadratic
62 ! interpolation functions. (linear strain tetrahedra).
63 ! Large Deformation. Returns the internal force vector R_in.
64 !
65 ! DATE: 10.2001 AUTHOR: SCOT BREITENFELD
66 !________________________________________________________________________
67 
68  IMPLICIT NONE
69 !-----Global variables
70  INTEGER :: numnp ! number of nodes
71  INTEGER :: numat_vol ! number of volumetric materials
72  INTEGER :: numcstet ! number of LSTets
73 !-- coordinate array
74  REAL*8, DIMENSION(1:3,1:numnp) :: coor
75 !-- internal force
76  REAL*8, DIMENSION(1:3*numnp) :: r_in
77 !-- displacement vector
78  REAL*8, DIMENSION(1:3*numnp) :: d
79 !-- CSTet stress
80  REAL*8, DIMENSION(1:4,1:numcstet) :: s11, s22, s33, s12, s23, s13
81 !-- connectivity table for CSTet
82  INTEGER, DIMENSION(1:10,1:numcstet) :: lmcstet
83 !-- mat number for CSTet element
84  INTEGER, DIMENSION(1:numcstet) :: matcstet
85 !---- Local variables
86 !-- node numbers
87  INTEGER :: n1,n2,n3,n4,n5,n6,n7,n8,n9,n10
88 !-- x, y, and z displacements of nodes
89  REAL*8 :: u1,u2,u3,u4,u5,u6,u7,u8,u9,u10
90  REAL*8 :: v1,v2,v3,v4,v5,v6,v7,v8,v9,v10
91  REAL*8 :: w1,w2,w3,w4,w5,w6,w7,w8,w9,w10
92 !-- 6*volume and the volume
93  REAL*8 :: vx6,vx6inv
94 !-- spacial derivatives
95  REAL*8 :: b1,b2,b3,b4,b5,b6,b7,b8,b9,b10
96  REAL*8 :: b11,b12,b13,b14,b15,b16,b17,b18,b19,b20
97  REAL*8 :: b21,b22,b23,b24,b25,b26,b27,b28,b29,b30
98 !-- partial derivatives of the displacement
99  REAL*8 :: dudx,dvdy,dwdz,dudy,dvdx,dvdz,dwdy,dudz,dwdx
100 !-- strains
101  REAL*8 :: e11,e22,e33,e12,e23,e13
102 !-- coordinate holding variable
103  REAL*8 :: x1,x2,x3,x4,x5,x6,x7,x8,x9,x10
104  REAL*8 :: y1,y2,y3,y4,y5,y6,y7,y8,y9,y10
105  REAL*8 :: z1,z2,z3,z4,z5,z6,z7,z8,z9,z10
106 !-- dummy and counters
107  INTEGER :: i,j,nstart,nend
108  REAL*8 :: aux1,aux2,aux3,aux4,aux5,aux6,aux7,aux8,aux9,aux10,aux11,aux12
109 !-- partial internal force
110  REAL*8 :: r1,r2,r3,r4,r5,r6,r7,r8,r9,r10,r11,r12,r13,r14,r15,r16,r17,r18
111  REAL*8 :: r19,r20,r21,r22,r23,r24,r25,r26,r27,r28,r29,r30
112  REAL*8 :: g1, g2, g3, g4
113  REAL*8 :: xn1, xn2, xn3, xn4
114 
115  INTEGER :: k1n1,k1n2,k1n3,k1n4,k1n5,k1n6,k1n7,k1n8,k1n9,k1n10
116  INTEGER :: k2n1,k2n2,k2n3,k2n4,k2n5,k2n6,k2n7,k2n8,k2n9,k2n10
117  INTEGER :: k3n1,k3n2,k3n3,k3n4,k3n5,k3n6,k3n7,k3n8,k3n9,k3n10
118 ! --
119  REAL*8 :: f11, f12, f13, f21, f22, f23, f31, f32, f33
120 
121 !-- Coordinate subtractions
122  REAL*8 :: x14, x24, x34, y14, y24, y34, z14, z24, z34
123 !-- Coordinate subtractions: These are to speed up B calculation
124  REAL*8 :: x12, x13, y12, y13, z12, z13
125  REAL*8 :: val11, val21, val31
126  REAL*8, DIMENSION(1:numat_vol) :: mu, kappa
127 
128  REAL*8,DIMENSION(1:4,1:4) :: gaussintpt = reshape( &
129  (/0.58541020d0,0.13819660d0,0.13819660d0,0.13819660d0, &
130  0.13819660d0,0.58541020d0,0.13819660d0,0.13819660d0, &
131  0.13819660d0,0.13819660d0,0.58541020d0,0.13819660d0, &
132  0.13819660d0,0.13819660d0,0.13819660d0,0.58541020d0/),(/4,4/) )
133 
134  INTEGER :: igpt
135 
136  REAL*8, DIMENSION(1:3,1:3) :: fij, cij
137  INTEGER :: kk,ll,mm
138 
139  DO i = nstart, nend
140 
141  j = matcstet(i)
142 
143  n1 = lmcstet(1,i)
144  n2 = lmcstet(2,i)
145  n3 = lmcstet(3,i)
146  n4 = lmcstet(4,i)
147  n5 = lmcstet(5,i)
148  n6 = lmcstet(6,i)
149  n7 = lmcstet(7,i)
150  n8 = lmcstet(8,i)
151  n9 = lmcstet(9,i)
152  n10 = lmcstet(10,i)
153 
154  k3n1 = 3*n1
155  k3n2 = 3*n2
156  k3n3 = 3*n3
157  k3n4 = 3*n4
158  k3n5 = 3*n5
159  k3n6 = 3*n6
160  k3n7 = 3*n7
161  k3n8 = 3*n8
162  k3n9 = 3*n9
163  k3n10 = 3*n10
164 
165  k2n1 = k3n1 - 1
166  k2n2 = k3n2 - 1
167  k2n3 = k3n3 - 1
168  k2n4 = k3n4 - 1
169  k2n5 = k3n5 - 1
170  k2n6 = k3n6 - 1
171  k2n7 = k3n7 - 1
172  k2n8 = k3n8 - 1
173  k2n9 = k3n9 - 1
174  k2n10 = k3n10 - 1
175 
176  k1n1 = k3n1 - 2
177  k1n2 = k3n2 - 2
178  k1n3 = k3n3 - 2
179  k1n4 = k3n4 - 2
180  k1n5 = k3n5 - 2
181  k1n6 = k3n6 - 2
182  k1n7 = k3n7 - 2
183  k1n8 = k3n8 - 2
184  k1n9 = k3n9 - 2
185  k1n10 = k3n10 - 2
186  ! k#n# dummy variables replaces:
187  u1 = d(k1n1) ! (3*n1 -2)
188  u2 = d(k1n2) ! (3*n2 -2)
189  u3 = d(k1n3) ! (3*n3 -2)
190  u4 = d(k1n4) ! (3*n4 -2)
191  u5 = d(k1n5) ! (3*n5 -2)
192  u6 = d(k1n6) ! (3*n6 -2)
193  u7 = d(k1n7) ! (3*n7 -2)
194  u8 = d(k1n8) ! (3*n8 -2)
195  u9 = d(k1n9) ! (3*n9 -2)
196  u10 = d(k1n10) ! (3*n10-2)
197  v1 = d(k2n1) ! (3*n1 -1)
198  v2 = d(k2n2) ! (3*n2 -1)
199  v3 = d(k2n3) ! (3*n3 -1)
200  v4 = d(k2n4) ! (3*n4 -1)
201  v5 = d(k2n5) ! (3*n5 -1)
202  v6 = d(k2n6) ! (3*n6 -1)
203  v7 = d(k2n7) ! (3*n7 -1)
204  v8 = d(k2n8) ! (3*n8 -1)
205  v9 = d(k2n9) ! (3*n9 -1)
206  v10 = d(k2n10) ! (3*n10-1)
207  w1 = d(k3n1) ! (3*n1)
208  w2 = d(k3n2) ! (3*n2)
209  w3 = d(k3n3) ! (3*n3)
210  w4 = d(k3n4) ! (3*n4)
211  w5 = d(k3n5) ! (3*n5)
212  w6 = d(k3n6) ! (3*n6)
213  w7 = d(k3n7) ! (3*n7)
214  w8 = d(k3n8) ! (3*n8)
215  w9 = d(k3n9) ! (3*n9)
216  w10 = d(k3n10) ! (3*n10)
217 
218  x1 = coor(1,n1)
219  x2 = coor(1,n2)
220  x3 = coor(1,n3)
221  x4 = coor(1,n4)
222  y1 = coor(2,n1)
223  y2 = coor(2,n2)
224  y3 = coor(2,n3)
225  y4 = coor(2,n4)
226  z1 = coor(3,n1)
227  z2 = coor(3,n2)
228  z3 = coor(3,n3)
229  z4 = coor(3,n4)
230 
231  x12 = x1 - x2 ! not used in vol. calc
232  x13 = x1 - x3 ! not used in vol. calc
233  x14 = x1 - x4
234  x24 = x2 - x4
235  x34 = x3 - x4
236  y12 = y1 - y2 ! not used in vol. calc
237  y13 = y1 - y3 ! not used in vol. calc
238  y14 = y1 - y4
239  y24 = y2 - y4
240  y34 = y3 - y4
241  z12 = z1 - z2 ! not used in vol. calc
242  z13 = z1 - z3 ! not used in vol. calc
243  z14 = z1 - z4
244  z24 = z2 - z4
245  z34 = z3 - z4
246 
247  val11 = y24*z34 - z24*y34
248  val21 = -( x24*z34 - z24*x34 )
249  val31 = x24*y34 - y24*x34
250 
251  vx6 = -( x14*val11 + y14*val21 + z14*val31 )
252 
253  vx6inv = 1.d0 / vx6
254 
255  aux1 = -(y3*z4 - y4*z3 - y2*z4 + y2*z3 + z2*y4 - z2*y3)
256  aux2 = (x3*z4 - x4*z3 - x2*z4 + x2*z3 + z2*x4 - z2*x3)
257  aux3 = -(x3*y4 - x4*y3 - x2*y4 + x2*y3 + y2*x4 - y2*x3)
258  aux4 = (y3*z4 - y4*z3 - y1*z4 + y1*z3 + z1*y4 - z1*y3)
259  aux5 = -(x3*z4 - x4*z3 - x1*z4 + x1*z3 + z1*x4 - z1*x3)
260  aux6 = (x3*y4 - x4*y3 - x1*y4 + x1*y3 + y1*x4 - y1*x3)
261  aux7 = -(y2*z4 - z2*y4 - y1*z4 + y1*z2 + z1*y4 - z1*y2)
262  aux8 = (x2*z4 - z2*x4 - x1*z4 + x1*z2 + z1*x4 - z1*x2)
263  aux9 = -(x2*y4 - y2*x4 - x1*y4 + x1*y2 + y1*x4 - y1*x2)
264  aux10 = (y2*z3 - z2*y3 - y1*z3 + y1*z2 + z1*y3 - z1*y2)
265  aux11 =-(x2*z3 - z2*x3 - x1*z3 + x1*z2 + z1*x3 - z1*x2)
266  aux12 = (x2*y3 - y2*x3 - x1*y3 + x1*y2 + y1*x3 - y1*x2)
267 
268  r1 = 0.d0
269  r2 = 0.d0
270  r3 = 0.d0
271  r4 = 0.d0
272  r5 = 0.d0
273  r6 = 0.d0
274  r7 = 0.d0
275  r8 = 0.d0
276  r9 = 0.d0
277  r10 = 0.d0
278  r11 = 0.d0
279  r12 = 0.d0
280  r13 = 0.d0
281  r14 = 0.d0
282  r15 = 0.d0
283  r16 = 0.d0
284  r17 = 0.d0
285  r18 = 0.d0
286  r19 = 0.d0
287  r20 = 0.d0
288  r21 = 0.d0
289  r22 = 0.d0
290  r23 = 0.d0
291  r24 = 0.d0
292  r25 = 0.d0
293  r26 = 0.d0
294  r27 = 0.d0
295  r28 = 0.d0
296  r29 = 0.d0
297  r30 = 0.d0
298 
299  DO igpt = 1, 4
300 
301  g1 = gaussintpt(igpt,1)
302  g2 = gaussintpt(igpt,2)
303  g3 = gaussintpt(igpt,3)
304  g4 = gaussintpt(igpt,4)
305 
306 
307  xn1 = (4.d0*g1-1.d0) ! derivative of shape function
308  xn2 = (4.d0*g2-1.d0) ! dN_i/dzeta_i
309  xn3 = (4.d0*g3-1.d0)
310  xn4 = (4.d0*g4-1.d0)
311 ! xN5 = 4.d0*g1*g2
312 ! xN6 = 4.d0*g2*g3
313 ! xN7 = 4.d0*g3*g1
314 ! xN8 = 4.d0*g1*g4
315 ! xN9 = 4.d0*g2*g4
316 ! xN10= 4.d0*g3*g4
317 
318  b1 = aux1*xn1
319  b2 = aux2*xn1
320  b3 = aux3*xn1
321  b4 = aux4*xn2
322  b5 = aux5*xn2
323  b6 = aux6*xn2
324  b7 = aux7*xn3
325  b8 = aux8*xn3
326  b9 = aux9*xn3
327  b10 = aux10*xn4
328  b11 = aux11*xn4
329  b12 = aux12*xn4
330 
331  b13 = 4.d0*(g2*aux1 + g1*aux4)
332  b14 = 4.d0*(g2*aux2 + g1*aux5)
333  b15 = 4.d0*(g2*aux3 + g1*aux6)
334 
335  b16 = 4.d0*(g3*aux4 + g2*aux7)
336  b17 = 4.d0*(g3*aux5 + g2*aux8)
337  b18 = 4.d0*(g3*aux6 + g2*aux9)
338 
339  b19 = 4.d0*(g1*aux7 + g3*aux1)
340  b20 = 4.d0*(g1*aux8 + g3*aux2)
341  b21 = 4.d0*(g1*aux9 + g3*aux3)
342 
343  b22 = 4.d0*(g4*aux1 + g1*aux10)
344  b23 = 4.d0*(g4*aux2 + g1*aux11)
345  b24 = 4.d0*(g4*aux3 + g1*aux12)
346 
347  b25 = 4.d0*(g4*aux4 + g2*aux10)
348  b26 = 4.d0*(g4*aux5 + g2*aux11)
349  b27 = 4.d0*(g4*aux6 + g2*aux12)
350 
351  b28 = 4.d0*(g4*aux7 + g3*aux10)
352  b29 = 4.d0*(g4*aux8 + g3*aux11)
353  b30 = 4.d0*(g4*aux9 + g3*aux12)
354 
355 
356 !-----Calculate displacement gradient (H)
357  dudx = (b1*u1 + b4*u2 + b7*u3 + b10*u4 + b13*u5 + b16*u6 + b19*u7 + b22*u8 + b25*u9 + b28*u10)*vx6inv
358  dvdy = (b2*v1 + b5*v2 + b8*v3 + b11*v4 + b14*v5 + b17*v6 + b20*v7 + b23*v8 + b26*v9 + b29*v10)*vx6inv
359  dwdz = (b3*w1 + b6*w2 + b9*w3 + b12*w4 + b15*w5 + b18*w6 + b21*w7 + b24*w8 + b27*w9 + b30*w10)*vx6inv
360  dudy = (b2*u1 + b5*u2 + b8*u3 + b11*u4 + b14*u5 + b17*u6 + b20*u7 + b23*u8 + b26*u9 + b29*u10)*vx6inv
361  dvdx = (b1*v1 + b4*v2 + b7*v3 + b10*v4 + b13*v5 + b16*v6 + b19*v7 + b22*v8 + b25*v9 + b28*v10)*vx6inv
362  dvdz = (b3*v1 + b6*v2 + b9*v3 + b12*v4 + b15*v5 + b18*v6 + b21*v7 + b24*v8 + b27*v9 + b30*v10)*vx6inv
363  dwdy = (b2*w1 + b5*w2 + b8*w3 + b11*w4 + b14*w5 + b17*w6 + b20*w7 + b23*w8 + b26*w9 + b29*w10)*vx6inv
364  dudz = (b3*u1 + b6*u2 + b9*u3 + b12*u4 + b15*u5 + b18*u6 + b21*u7 + b24*u8 + b27*u9 + b30*u10)*vx6inv
365  dwdx = (b1*w1 + b4*w2 + b7*w3 + b10*w4 + b13*w5 + b16*w6 + b19*w7 + b22*w8 + b25*w9 + b28*w10)*vx6inv
366 
367 !
368 ! deformation gradients F
369 !
370  f11 = 1.d0 + ( dudx )
371  f22 = 1.d0 + ( dvdy )
372  f33 = 1.d0 + ( dwdz )
373  f12 = dudy
374  f21 = dvdx
375  f23 = dvdz
376  f32 = dwdy
377  f13 = dudz
378  f31 = dwdx
379 
380 !-- (1) Deformation Gradient Fij
381 
382  fij(1,1) = f11
383  fij(1,2) = f12
384  fij(1,3) = f13
385  fij(2,1) = f21
386  fij(2,2) = f22
387  fij(2,3) = f23
388  fij(3,1) = f31
389  fij(3,2) = f32
390  fij(3,3) = f33
391 
392 !-- (2) right Cauchy-Green deformation Tensor Cij = Fmi Fmj
393 ! T
394 ! C = F F
395 
396  DO kk=1,3
397  DO ll=1,3
398  cij(kk,ll) = 0.d0
399  DO mm=1,3
400  cij(kk,ll)=cij(kk,ll)+fij(mm,kk)*fij(mm,ll)
401  ENDDO
402  ENDDO
403  ENDDO
404 
405 !
406 ! Arruda-Boyce Nonlinear Elasticity Model
407 !
408 ! -- NOTE: ci(7,j) : shear modulus
409 
410  CALL arruda_boyce(cij, &
411  s11(igpt,i),s22(igpt,i),s33(igpt,i),s12(igpt,i),s23(igpt,i),s13(igpt,i),i, &
412  mu(j),kappa(j))
413 
414  r1 = r1 + &
415  ( s11(igpt,i)*b1*(1.d0+dudx) + s22(igpt,i)*b2*dudy + s33(igpt,i)*b3*dudz &
416  + s12(igpt,i)*( b2*(1.d0+dudx) + b1*dudy ) &
417  + s23(igpt,i)*( b3*dudy + b2*dudz ) &
418  + s13(igpt,i)*( b3*(1.d0+dudx) + b1*dudz ) )
419  r2 = r2 +&
420  ( s11(igpt,i)*b1*dvdx + s22(igpt,i)*b2*(1.d0+dvdy) + s33(igpt,i)*b3*dvdz &
421  + s12(igpt,i)*( b1*(1.d0+dvdy) + b2*dvdx ) &
422  + s23(igpt,i)*( b3*(1.d0+dvdy) + b2*dvdz ) &
423  + s13(igpt,i)*( b3*dvdx + b1*dvdz ) )
424  r3 = r3 + &
425  ( s11(igpt,i)*b1*dwdx + s22(igpt,i)*b2*dwdy + s33(igpt,i)*b3*(1.d0+dwdz) &
426  + s12(igpt,i)*( b2*dwdx + b1*dwdy ) &
427  + s23(igpt,i)*( b3*dwdy + b2*(1.d0 + dwdz) ) &
428  + s13(igpt,i)*( b3*dwdx + b1*(1.d0 + dwdz) ) )
429 
430  r4 = r4 + &
431  ( s11(igpt,i)*b4*(1.d0+dudx) + s22(igpt,i)*b5*dudy + s33(igpt,i)*b6*dudz &
432  + s12(igpt,i)*( b5*(1.d0+dudx) + b4*dudy ) &
433  + s23(igpt,i)*( b6*dudy + b5*dudz ) &
434  + s13(igpt,i)*( b6*(1.d0+dudx) + b4*dudz ) )
435  r5 = r5 + &
436  ( s11(igpt,i)*b4*dvdx + s22(igpt,i)*b5*(1.d0+dvdy) + s33(igpt,i)*b6*dvdz &
437  + s12(igpt,i)*( b4*(1.d0+dvdy) + b5*dvdx ) &
438  + s23(igpt,i)*( b6*(1.d0+dvdy) + b5*dvdz ) &
439  + s13(igpt,i)*( b6*dvdx + b4*dvdz ) )
440  r6 = r6 + &
441  ( s11(igpt,i)*b4*dwdx + s22(igpt,i)*b5*dwdy + s33(igpt,i)*b6*(1.d0+dwdz) &
442  + s12(igpt,i)*( b5*dwdx + b4*dwdy ) &
443  + s23(igpt,i)*( b6*dwdy + b5*(1.d0 + dwdz) ) &
444  + s13(igpt,i)*( b6*dwdx + b4*(1.d0 + dwdz) ) )
445 
446  r7 = r7 + &
447  ( s11(igpt,i)*b7*(1.d0+dudx) + s22(igpt,i)*b8*dudy + s33(igpt,i)*b9*dudz &
448  + s12(igpt,i)*( b8*(1.d0+dudx) + b7*dudy ) &
449  + s23(igpt,i)*( b9*dudy + b8*dudz ) &
450  + s13(igpt,i)*( b9*(1.d0+dudx) + b7*dudz ) )
451  r8 = r8 + &
452  ( s11(igpt,i)*b7*dvdx + s22(igpt,i)*b8*(1.d0+dvdy) + s33(igpt,i)*b9*dvdz &
453  + s12(igpt,i)*( b7*(1.d0+dvdy) + b8*dvdx ) &
454  + s23(igpt,i)*( b9*(1.d0+dvdy) + b8*dvdz ) &
455  + s13(igpt,i)*( b9*dvdx + b7*dvdz ) )
456  r9 = r9 + &
457  ( s11(igpt,i)*b7*dwdx + s22(igpt,i)*b8*dwdy + s33(igpt,i)*b9*(1.d0+dwdz) &
458  + s12(igpt,i)*( b8*dwdx + b7*dwdy ) &
459  + s23(igpt,i)*( b9*dwdy + b8*(1.d0 + dwdz) ) &
460  + s13(igpt,i)*( b9*dwdx + b7*(1.d0 + dwdz) ) )
461 
462  r10 = r10 + &
463  ( s11(igpt,i)*b10*(1.d0+dudx) + s22(igpt,i)*b11*dudy+s33(igpt,i)*b12*dudz &
464  + s12(igpt,i)*( b11*(1.d0+dudx) + b10*dudy ) &
465  + s23(igpt,i)*( b12*dudy + b11*dudz ) &
466  + s13(igpt,i)*( b12*(1.d0+dudx) + b10*dudz ) )
467  r11 = r11 + &
468  ( s11(igpt,i)*b10*dvdx + s22(igpt,i)*b11*(1.d0+dvdy)+s33(igpt,i)*b12*dvdz &
469  + s12(igpt,i)*( b10*(1.d0+dvdy) + b11*dvdx ) &
470  + s23(igpt,i)*( b12*(1.d0+dvdy) + b11*dvdz ) &
471  + s13(igpt,i)*( b12*dvdx + b10*dvdz ) )
472  r12 = r12 + &
473  ( s11(igpt,i)*b10*dwdx + s22(igpt,i)*b11*dwdy+s33(igpt,i)*b12*(1.d0+dwdz) &
474  + s12(igpt,i)*( b11*dwdx + b10*dwdy ) &
475  + s23(igpt,i)*( b12*dwdy + b11*(1.d0 + dwdz) ) &
476  + s13(igpt,i)*( b12*dwdx + b10*(1.d0 + dwdz) ) )
477 
478  r13 = r13 + &
479  ( s11(igpt,i)*b13*(1.d0+dudx) + s22(igpt,i)*b14*dudy + s33(igpt,i)*b15*dudz &
480  + s12(igpt,i)*( b14*(1.d0+dudx) + b13*dudy ) &
481  + s23(igpt,i)*( b15*dudy + b14*dudz ) &
482  + s13(igpt,i)*( b15*(1.d0+dudx) + b13*dudz ) )
483  r14 = r14 + &
484  ( s11(igpt,i)*b13*dvdx + s22(igpt,i)*b14*(1.d0+dvdy) + s33(igpt,i)*b15*dvdz &
485  + s12(igpt,i)*( b13*(1.d0+dvdy) + b14*dvdx ) &
486  + s23(igpt,i)*( b15*(1.d0+dvdy) + b14*dvdz ) &
487  + s13(igpt,i)*( b15*dvdx + b13*dvdz ) )
488  r15 = r15 + &
489  ( s11(igpt,i)*b13*dwdx + s22(igpt,i)*b14*dwdy + s33(igpt,i)*b15*(1.d0+dwdz) &
490  + s12(igpt,i)*( b14*dwdx + b13*dwdy ) &
491  + s23(igpt,i)*( b15*dwdy + b14*(1.d0 + dwdz) ) &
492  + s13(igpt,i)*( b15*dwdx + b13*(1.d0 + dwdz) ) )
493 
494  r16 = r16 + &
495  ( s11(igpt,i)*b16*(1.d0+dudx) + s22(igpt,i)*b17*dudy + s33(igpt,i)*b18*dudz &
496  + s12(igpt,i)*( b17*(1.d0+dudx) + b16*dudy ) &
497  + s23(igpt,i)*( b18*dudy + b17*dudz ) &
498  + s13(igpt,i)*( b18*(1.d0+dudx) + b16*dudz ) )
499  r17 = r17 + &
500  ( s11(igpt,i)*b16*dvdx + s22(igpt,i)*b17*(1.d0+dvdy) + s33(igpt,i)*b18*dvdz &
501  + s12(igpt,i)*( b16*(1.d0+dvdy) + b17*dvdx ) &
502  + s23(igpt,i)*( b18*(1.d0+dvdy) + b17*dvdz ) &
503  + s13(igpt,i)*( b18*dvdx + b16*dvdz ) )
504  r18 = r18 + &
505  ( s11(igpt,i)*b16*dwdx + s22(igpt,i)*b17*dwdy + s33(igpt,i)*b18*(1.d0+dwdz) &
506  + s12(igpt,i)*( b17*dwdx + b16*dwdy ) &
507  + s23(igpt,i)*( b18*dwdy + b17*(1.d0 + dwdz) ) &
508  + s13(igpt,i)*( b18*dwdx + b16*(1.d0 + dwdz) ) )
509 
510  r19 = r19 + &
511  ( s11(igpt,i)*b19*(1.d0+dudx) + s22(igpt,i)*b20*dudy + s33(igpt,i)*b21*dudz &
512  + s12(igpt,i)*( b20*(1.d0+dudx) + b19*dudy ) &
513  + s23(igpt,i)*( b21*dudy + b20*dudz ) &
514  + s13(igpt,i)*( b21*(1.d0+dudx) + b19*dudz ) )
515  r20 = r20 + &
516  ( s11(igpt,i)*b19*dvdx + s22(igpt,i)*b20*(1.d0+dvdy) + s33(igpt,i)*b21*dvdz &
517  + s12(igpt,i)*( b19*(1.d0+dvdy) + b20*dvdx ) &
518  + s23(igpt,i)*( b21*(1.d0+dvdy) + b20*dvdz ) &
519  + s13(igpt,i)*( b21*dvdx + b19*dvdz ) )
520  r21 = r21 + &
521  ( s11(igpt,i)*b19*dwdx + s22(igpt,i)*b20*dwdy + s33(igpt,i)*b21*(1.d0+dwdz) &
522  + s12(igpt,i)*( b20*dwdx + b19*dwdy ) &
523  + s23(igpt,i)*( b21*dwdy + b20*(1.d0 + dwdz) ) &
524  + s13(igpt,i)*( b21*dwdx + b19*(1.d0 + dwdz) ) )
525 
526  r22 = r22 + &
527  ( s11(igpt,i)*b22*(1.d0+dudx) + s22(igpt,i)*b23*dudy+s33(igpt,i)*b24*dudz &
528  + s12(igpt,i)*( b23*(1.d0+dudx) + b22*dudy ) &
529  + s23(igpt,i)*( b24*dudy + b23*dudz ) &
530  + s13(igpt,i)*( b24*(1.d0+dudx) + b22*dudz ) )
531  r23 = r23 + &
532  ( s11(igpt,i)*b22*dvdx + s22(igpt,i)*b23*(1.d0+dvdy)+s33(igpt,i)*b24*dvdz &
533  + s12(igpt,i)*( b22*(1.d0+dvdy) + b23*dvdx ) &
534  + s23(igpt,i)*( b24*(1.d0+dvdy) + b23*dvdz ) &
535  + s13(igpt,i)*( b24*dvdx + b22*dvdz ) )
536  r24 = r24 + &
537  ( s11(igpt,i)*b22*dwdx + s22(igpt,i)*b23*dwdy+s33(igpt,i)*b24*(1.d0+dwdz) &
538  + s12(igpt,i)*( b23*dwdx + b22*dwdy ) &
539  + s23(igpt,i)*( b24*dwdy + b23*(1.d0 + dwdz) ) &
540  + s13(igpt,i)*( b24*dwdx + b22*(1.d0 + dwdz) ) )
541 
542  r25 = r25 + &
543  ( s11(igpt,i)*b25*(1.d0+dudx) + s22(igpt,i)*b26*dudy+s33(igpt,i)*b27*dudz &
544  + s12(igpt,i)*( b26*(1.d0+dudx) + b25*dudy ) &
545  + s23(igpt,i)*( b27*dudy + b26*dudz ) &
546  + s13(igpt,i)*( b27*(1.d0+dudx) + b25*dudz ) )
547  r26 = r26 + &
548  ( s11(igpt,i)*b25*dvdx + s22(igpt,i)*b26*(1.d0+dvdy)+s33(igpt,i)*b27*dvdz &
549  + s12(igpt,i)*( b25*(1.d0+dvdy) + b26*dvdx ) &
550  + s23(igpt,i)*( b27*(1.d0+dvdy) + b26*dvdz ) &
551  + s13(igpt,i)*( b27*dvdx + b25*dvdz ) )
552  r27 = r27 + &
553  ( s11(igpt,i)*b25*dwdx + s22(igpt,i)*b26*dwdy+s33(igpt,i)*b27*(1.d0+dwdz) &
554  + s12(igpt,i)*( b26*dwdx + b25*dwdy ) &
555  + s23(igpt,i)*( b27*dwdy + b26*(1.d0 + dwdz) ) &
556  + s13(igpt,i)*( b27*dwdx + b25*(1.d0 + dwdz) ) )
557 
558  r28 = r28 + &
559  ( s11(igpt,i)*b28*(1.d0+dudx) + s22(igpt,i)*b29*dudy+s33(igpt,i)*b30*dudz &
560  + s12(igpt,i)*( b29*(1.d0+dudx) + b28*dudy ) &
561  + s23(igpt,i)*( b30*dudy + b29*dudz ) &
562  + s13(igpt,i)*( b30*(1.d0+dudx) + b28*dudz ) )
563  r29 = r29 + &
564  ( s11(igpt,i)*b28*dvdx + s22(igpt,i)*b29*(1.d0+dvdy)+s33(igpt,i)*b30*dvdz &
565  + s12(igpt,i)*( b28*(1.d0+dvdy) + b29*dvdx ) &
566  + s23(igpt,i)*( b30*(1.d0+dvdy) + b29*dvdz ) &
567  + s13(igpt,i)*( b30*dvdx + b28*dvdz ) )
568  r30 = r30 + &
569  ( s11(igpt,i)*b28*dwdx + s22(igpt,i)*b29*dwdy+s33(igpt,i)*b30*(1.d0+dwdz) &
570  + s12(igpt,i)*( b29*dwdx + b28*dwdy ) &
571  + s23(igpt,i)*( b30*dwdy + b29*(1.d0 + dwdz) ) &
572  + s13(igpt,i)*( b30*dwdx + b28*(1.d0 + dwdz) ) )
573 
574  ENDDO
575 
576 !Wi (i.e. weight) for 4 guass point integration is 1/4
577 
578 ! Wi * 1/6 because the volume of a reference tetrahedra in
579 ! volume coordinates is 1/6
580 
581 ! ASSEMBLE THE INTERNAL FORCE VECTOR
582 !
583 ! local node 1
584  r_in(k1n1) = r_in(k1n1) - r1*0.04166666666666667d0
585  r_in(k2n1) = r_in(k2n1) - r2*0.04166666666666667d0
586  r_in(k3n1) = r_in(k3n1) - r3*0.04166666666666667d0
587 ! local node 2
588  r_in(k1n2) = r_in(k1n2) - r4*0.04166666666666667d0
589  r_in(k2n2) = r_in(k2n2) - r5*0.04166666666666667d0
590  r_in(k3n2) = r_in(k3n2) - r6*0.04166666666666667d0
591 ! local node 3
592  r_in(k1n3) = r_in(k1n3) - r7*0.04166666666666667d0
593  r_in(k2n3) = r_in(k2n3) - r8*0.04166666666666667d0
594  r_in(k3n3) = r_in(k3n3) - r9*0.04166666666666667d0
595 ! local node 4
596  r_in(k1n4) = r_in(k1n4) - r10*0.04166666666666667d0
597  r_in(k2n4) = r_in(k2n4) - r11*0.04166666666666667d0
598  r_in(k3n4) = r_in(k3n4) - r12*0.04166666666666667d0
599 ! local node 5
600  r_in(k1n5) = r_in(k1n5) - r13*0.04166666666666667d0
601  r_in(k2n5) = r_in(k2n5) - r14*0.04166666666666667d0
602  r_in(k3n5) = r_in(k3n5) - r15*0.04166666666666667d0
603 ! local node 6
604  r_in(k1n6) = r_in(k1n6) - r16*0.04166666666666667d0
605  r_in(k2n6) = r_in(k2n6) - r17*0.04166666666666667d0
606  r_in(k3n6) = r_in(k3n6) - r18*0.04166666666666667d0
607 ! local node 7
608  r_in(k1n7) = r_in(k1n7) - r19*0.04166666666666667d0
609  r_in(k2n7) = r_in(k2n7) - r20*0.04166666666666667d0
610  r_in(k3n7) = r_in(k3n7) - r21*0.04166666666666667d0
611 ! local node 8
612  r_in(k1n8) = r_in(k1n8) - r22*0.04166666666666667d0
613  r_in(k2n8) = r_in(k2n8) - r23*0.04166666666666667d0
614  r_in(k3n8) = r_in(k3n8) - r24*0.04166666666666667d0
615 ! local node 9
616  r_in(k1n9) = r_in(k1n9) - r25*0.04166666666666667d0
617  r_in(k2n9) = r_in(k2n9) - r26*0.04166666666666667d0
618  r_in(k3n9) = r_in(k3n9) - r27*0.04166666666666667d0
619 ! local node 10
620  r_in(k1n10) = r_in(k1n10) - r28*0.04166666666666667d0
621  r_in(k2n10) = r_in(k2n10) - r29*0.04166666666666667d0
622  r_in(k3n10) = r_in(k3n10) - r30*0.04166666666666667d0
623 
624  ENDDO
625  RETURN
626 END SUBROUTINE v3d10_nl_arruda_boyce
627 
v3d10_nl_arruda_boyce
subroutine v3d10_nl_arruda_boyce(coor, matcstet, lmcstet, R_in, d, S11, S22, S33, S12, S23, S13, numnp, nstart, nend, numcstet, numat_vol, mu, kappa)
Definition: v3d10_nl_arruda_boyce.f90:53
d
const NT & d
Definition: rational_rotation.h:73
i
blockLoc i
Definition: read.cpp:79
j
j indices j
Definition: Indexing.h:6
arruda_boyce
subroutine arruda_boyce(Cij, S11, S22, S33, S12, S23, S13, ielem, mu, kappa)
Definition: arruda_boyce.f90:53