Rocstar  1.0
Rocstar multiphysics simulation application
 All Classes Namespaces Files Functions Variables Typedefs Enumerations Enumerator Friends Macros Groups Pages
v3d10_nl_arruda_boyce.f90
Go to the documentation of this file.
1 !*********************************************************************
2 !* Illinois Open Source License *
3 !* *
4 !* University of Illinois/NCSA *
5 !* Open Source License *
6 !* *
7 !* Copyright@2008, University of Illinois. All rights reserved. *
8 !* *
9 !* Developed by: *
10 !* *
11 !* Center for Simulation of Advanced Rockets *
12 !* *
13 !* University of Illinois *
14 !* *
15 !* www.csar.uiuc.edu *
16 !* *
17 !* Permission is hereby granted, free of charge, to any person *
18 !* obtaining a copy of this software and associated documentation *
19 !* files (the "Software"), to deal with the Software without *
20 !* restriction, including without limitation the rights to use, *
21 !* copy, modify, merge, publish, distribute, sublicense, and/or *
22 !* sell copies of the Software, and to permit persons to whom the *
23 !* Software is furnished to do so, subject to the following *
24 !* conditions: *
25 !* *
26 !* *
27 !* @ Redistributions of source code must retain the above copyright *
28 !* notice, this list of conditions and the following disclaimers. *
29 !* *
30 !* @ Redistributions in binary form must reproduce the above *
31 !* copyright notice, this list of conditions and the following *
32 !* disclaimers in the documentation and/or other materials *
33 !* provided with the distribution. *
34 !* *
35 !* @ Neither the names of the Center for Simulation of Advanced *
36 !* Rockets, the University of Illinois, nor the names of its *
37 !* contributors may be used to endorse or promote products derived *
38 !* from this Software without specific prior written permission. *
39 !* *
40 !* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, *
41 !* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES *
42 !* OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND *
43 !* NONINFRINGEMENT. IN NO EVENT SHALL THE CONTRIBUTORS OR *
44 !* COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER *
45 !* LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, *
46 !* ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE *
47 !* USE OR OTHER DEALINGS WITH THE SOFTWARE. *
48 !*********************************************************************
49 !* Please acknowledge The University of Illinois Center for *
50 !* Simulation of Advanced Rockets in works and publications *
51 !* resulting from this software or its derivatives. *
52 !*********************************************************************
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 !!****f* Rocfrac/Rocfrac/Source/v3d10_NL_ARRUDA_BOYCE.f90
59 !!
60 !! NAME
61 !! v3d10_NL_ARRUDA_BOYCE
62 !!
63 !! FUNCTION
64 !!
65 !! Computes the internal force for a large deformation,
66 !! hyperelastic arruda-boyce 10-node tetrahedral.
67 !!
68 !! INPUTS
69 !!
70 !! NumNP -- Number of nodes
71 !! numcstet -- Number of elements
72 !! Coor -- number of coordinates
73 !! Matcstet -- Material id
74 !! d -- nodal displacement
75 !! mu -- shear modulus
76 !! kappa -- bulk modulus
77 !!
78 !! lmcstet -- Nodal connectivity
79 !! nstart, nend -- element beginning and end loop counter
80 !! numat_vol -- number of materials
81 !!
82 !! OUTPUT
83 !!
84 !! Rin -- internal force vector
85 !! S11,S22,S33,S12,S23,S13 -- Stresses at gauss points
86 !!
87 !!****
88 
89  IMPLICIT NONE
90 !-----Global variables
91  INTEGER :: numnp ! number of nodes
92  INTEGER :: numat_vol ! number of volumetric materials
93  INTEGER :: numcstet ! number of LSTets
94 !-- coordinate array
95  REAL*8, DIMENSION(1:3,1:numnp) :: coor
96 !-- internal force
97  REAL*8, DIMENSION(1:3*numnp) :: r_in
98 !-- displacement vector
99  REAL*8, DIMENSION(1:3*numnp) :: d
100 !-- CSTet stress
101  REAL*8, DIMENSION(1:4,1:numcstet) :: s11, s22, s33, s12, s23, s13
102 !-- connectivity table for CSTet
103  INTEGER, DIMENSION(1:10,1:numcstet) :: lmcstet
104 !-- mat number for CSTet element
105  INTEGER, DIMENSION(1:numcstet) :: matcstet
106 !---- Local variables
107 !-- node numbers
108  INTEGER :: n1,n2,n3,n4,n5,n6,n7,n8,n9,n10
109 !-- x, y, and z displacements of nodes
110  REAL*8 :: u1,u2,u3,u4,u5,u6,u7,u8,u9,u10
111  REAL*8 :: v1,v2,v3,v4,v5,v6,v7,v8,v9,v10
112  REAL*8 :: w1,w2,w3,w4,w5,w6,w7,w8,w9,w10
113 !-- 6*volume and the volume
114  REAL*8 :: vx6,vx6inv
115 !-- spacial derivatives
116  REAL*8 :: b1,b2,b3,b4,b5,b6,b7,b8,b9,b10
117  REAL*8 :: b11,b12,b13,b14,b15,b16,b17,b18,b19,b20
118  REAL*8 :: b21,b22,b23,b24,b25,b26,b27,b28,b29,b30
119 !-- partial derivatives of the displacement
120  REAL*8 :: dudx,dvdy,dwdz,dudy,dvdx,dvdz,dwdy,dudz,dwdx
121 !-- strains
122  REAL*8 :: e11,e22,e33,e12,e23,e13
123 !-- coordinate holding variable
124  REAL*8 :: x1,x2,x3,x4,x5,x6,x7,x8,x9,x10
125  REAL*8 :: y1,y2,y3,y4,y5,y6,y7,y8,y9,y10
126  REAL*8 :: z1,z2,z3,z4,z5,z6,z7,z8,z9,z10
127 !-- dummy and counters
128  INTEGER :: i,j,nstart,nend
129  REAL*8 :: aux1,aux2,aux3,aux4,aux5,aux6,aux7,aux8,aux9,aux10,aux11,aux12
130 !-- partial internal force
131  REAL*8 :: r1,r2,r3,r4,r5,r6,r7,r8,r9,r10,r11,r12,r13,r14,r15,r16,r17,r18
132  REAL*8 :: r19,r20,r21,r22,r23,r24,r25,r26,r27,r28,r29,r30
133  REAL*8 :: g1, g2, g3, g4
134  REAL*8 :: xn1, xn2, xn3, xn4
135 
136  INTEGER :: k1n1,k1n2,k1n3,k1n4,k1n5,k1n6,k1n7,k1n8,k1n9,k1n10
137  INTEGER :: k2n1,k2n2,k2n3,k2n4,k2n5,k2n6,k2n7,k2n8,k2n9,k2n10
138  INTEGER :: k3n1,k3n2,k3n3,k3n4,k3n5,k3n6,k3n7,k3n8,k3n9,k3n10
139 ! --
140  REAL*8 :: f11, f12, f13, f21, f22, f23, f31, f32, f33
141 
142 !-- Coordinate subtractions
143  REAL*8 :: x14, x24, x34, y14, y24, y34, z14, z24, z34
144 !-- Coordinate subtractions: These are to speed up B calculation
145  REAL*8 :: x12, x13, y12, y13, z12, z13
146  REAL*8 :: val11, val21, val31
147  REAL*8, DIMENSION(1:numat_vol) :: mu, kappa
148 
149  REAL*8,DIMENSION(1:4,1:4) :: gaussintpt = reshape( &
150  (/0.58541020d0,0.13819660d0,0.13819660d0,0.13819660d0, &
151  0.13819660d0,0.58541020d0,0.13819660d0,0.13819660d0, &
152  0.13819660d0,0.13819660d0,0.58541020d0,0.13819660d0, &
153  0.13819660d0,0.13819660d0,0.13819660d0,0.58541020d0/),(/4,4/) )
154 
155  INTEGER :: igpt
156 
157  REAL*8, DIMENSION(1:3,1:3) :: fij, cij
158  INTEGER :: kk,ll,mm
159 
160  DO i = nstart, nend
161 
162  j = matcstet(i)
163 
164  n1 = lmcstet(1,i)
165  n2 = lmcstet(2,i)
166  n3 = lmcstet(3,i)
167  n4 = lmcstet(4,i)
168  n5 = lmcstet(5,i)
169  n6 = lmcstet(6,i)
170  n7 = lmcstet(7,i)
171  n8 = lmcstet(8,i)
172  n9 = lmcstet(9,i)
173  n10 = lmcstet(10,i)
174 
175  k3n1 = 3*n1
176  k3n2 = 3*n2
177  k3n3 = 3*n3
178  k3n4 = 3*n4
179  k3n5 = 3*n5
180  k3n6 = 3*n6
181  k3n7 = 3*n7
182  k3n8 = 3*n8
183  k3n9 = 3*n9
184  k3n10 = 3*n10
185 
186  k2n1 = k3n1 - 1
187  k2n2 = k3n2 - 1
188  k2n3 = k3n3 - 1
189  k2n4 = k3n4 - 1
190  k2n5 = k3n5 - 1
191  k2n6 = k3n6 - 1
192  k2n7 = k3n7 - 1
193  k2n8 = k3n8 - 1
194  k2n9 = k3n9 - 1
195  k2n10 = k3n10 - 1
196 
197  k1n1 = k3n1 - 2
198  k1n2 = k3n2 - 2
199  k1n3 = k3n3 - 2
200  k1n4 = k3n4 - 2
201  k1n5 = k3n5 - 2
202  k1n6 = k3n6 - 2
203  k1n7 = k3n7 - 2
204  k1n8 = k3n8 - 2
205  k1n9 = k3n9 - 2
206  k1n10 = k3n10 - 2
207  ! k#n# dummy variables replaces:
208  u1 = d(k1n1) ! (3*n1 -2)
209  u2 = d(k1n2) ! (3*n2 -2)
210  u3 = d(k1n3) ! (3*n3 -2)
211  u4 = d(k1n4) ! (3*n4 -2)
212  u5 = d(k1n5) ! (3*n5 -2)
213  u6 = d(k1n6) ! (3*n6 -2)
214  u7 = d(k1n7) ! (3*n7 -2)
215  u8 = d(k1n8) ! (3*n8 -2)
216  u9 = d(k1n9) ! (3*n9 -2)
217  u10 = d(k1n10) ! (3*n10-2)
218  v1 = d(k2n1) ! (3*n1 -1)
219  v2 = d(k2n2) ! (3*n2 -1)
220  v3 = d(k2n3) ! (3*n3 -1)
221  v4 = d(k2n4) ! (3*n4 -1)
222  v5 = d(k2n5) ! (3*n5 -1)
223  v6 = d(k2n6) ! (3*n6 -1)
224  v7 = d(k2n7) ! (3*n7 -1)
225  v8 = d(k2n8) ! (3*n8 -1)
226  v9 = d(k2n9) ! (3*n9 -1)
227  v10 = d(k2n10) ! (3*n10-1)
228  w1 = d(k3n1) ! (3*n1)
229  w2 = d(k3n2) ! (3*n2)
230  w3 = d(k3n3) ! (3*n3)
231  w4 = d(k3n4) ! (3*n4)
232  w5 = d(k3n5) ! (3*n5)
233  w6 = d(k3n6) ! (3*n6)
234  w7 = d(k3n7) ! (3*n7)
235  w8 = d(k3n8) ! (3*n8)
236  w9 = d(k3n9) ! (3*n9)
237  w10 = d(k3n10) ! (3*n10)
238 
239  x1 = coor(1,n1)
240  x2 = coor(1,n2)
241  x3 = coor(1,n3)
242  x4 = coor(1,n4)
243  y1 = coor(2,n1)
244  y2 = coor(2,n2)
245  y3 = coor(2,n3)
246  y4 = coor(2,n4)
247  z1 = coor(3,n1)
248  z2 = coor(3,n2)
249  z3 = coor(3,n3)
250  z4 = coor(3,n4)
251 
252  x12 = x1 - x2 ! not used in vol. calc
253  x13 = x1 - x3 ! not used in vol. calc
254  x14 = x1 - x4
255  x24 = x2 - x4
256  x34 = x3 - x4
257  y12 = y1 - y2 ! not used in vol. calc
258  y13 = y1 - y3 ! not used in vol. calc
259  y14 = y1 - y4
260  y24 = y2 - y4
261  y34 = y3 - y4
262  z12 = z1 - z2 ! not used in vol. calc
263  z13 = z1 - z3 ! not used in vol. calc
264  z14 = z1 - z4
265  z24 = z2 - z4
266  z34 = z3 - z4
267 
268  val11 = y24*z34 - z24*y34
269  val21 = -( x24*z34 - z24*x34 )
270  val31 = x24*y34 - y24*x34
271 
272  vx6 = -( x14*val11 + y14*val21 + z14*val31 )
273 
274  vx6inv = 1.d0 / vx6
275 
276  aux1 = -(y3*z4 - y4*z3 - y2*z4 + y2*z3 + z2*y4 - z2*y3)
277  aux2 = (x3*z4 - x4*z3 - x2*z4 + x2*z3 + z2*x4 - z2*x3)
278  aux3 = -(x3*y4 - x4*y3 - x2*y4 + x2*y3 + y2*x4 - y2*x3)
279  aux4 = (y3*z4 - y4*z3 - y1*z4 + y1*z3 + z1*y4 - z1*y3)
280  aux5 = -(x3*z4 - x4*z3 - x1*z4 + x1*z3 + z1*x4 - z1*x3)
281  aux6 = (x3*y4 - x4*y3 - x1*y4 + x1*y3 + y1*x4 - y1*x3)
282  aux7 = -(y2*z4 - z2*y4 - y1*z4 + y1*z2 + z1*y4 - z1*y2)
283  aux8 = (x2*z4 - z2*x4 - x1*z4 + x1*z2 + z1*x4 - z1*x2)
284  aux9 = -(x2*y4 - y2*x4 - x1*y4 + x1*y2 + y1*x4 - y1*x2)
285  aux10 = (y2*z3 - z2*y3 - y1*z3 + y1*z2 + z1*y3 - z1*y2)
286  aux11 =-(x2*z3 - z2*x3 - x1*z3 + x1*z2 + z1*x3 - z1*x2)
287  aux12 = (x2*y3 - y2*x3 - x1*y3 + x1*y2 + y1*x3 - y1*x2)
288 
289  r1 = 0.d0
290  r2 = 0.d0
291  r3 = 0.d0
292  r4 = 0.d0
293  r5 = 0.d0
294  r6 = 0.d0
295  r7 = 0.d0
296  r8 = 0.d0
297  r9 = 0.d0
298  r10 = 0.d0
299  r11 = 0.d0
300  r12 = 0.d0
301  r13 = 0.d0
302  r14 = 0.d0
303  r15 = 0.d0
304  r16 = 0.d0
305  r17 = 0.d0
306  r18 = 0.d0
307  r19 = 0.d0
308  r20 = 0.d0
309  r21 = 0.d0
310  r22 = 0.d0
311  r23 = 0.d0
312  r24 = 0.d0
313  r25 = 0.d0
314  r26 = 0.d0
315  r27 = 0.d0
316  r28 = 0.d0
317  r29 = 0.d0
318  r30 = 0.d0
319 
320  DO igpt = 1, 4
321 
322  g1 = gaussintpt(igpt,1)
323  g2 = gaussintpt(igpt,2)
324  g3 = gaussintpt(igpt,3)
325  g4 = gaussintpt(igpt,4)
326 
327 
328  xn1 = (4.d0*g1-1.d0) ! derivative of shape function
329  xn2 = (4.d0*g2-1.d0) ! dN_i/dzeta_i
330  xn3 = (4.d0*g3-1.d0)
331  xn4 = (4.d0*g4-1.d0)
332 ! xN5 = 4.d0*g1*g2
333 ! xN6 = 4.d0*g2*g3
334 ! xN7 = 4.d0*g3*g1
335 ! xN8 = 4.d0*g1*g4
336 ! xN9 = 4.d0*g2*g4
337 ! xN10= 4.d0*g3*g4
338 
339  b1 = aux1*xn1
340  b2 = aux2*xn1
341  b3 = aux3*xn1
342  b4 = aux4*xn2
343  b5 = aux5*xn2
344  b6 = aux6*xn2
345  b7 = aux7*xn3
346  b8 = aux8*xn3
347  b9 = aux9*xn3
348  b10 = aux10*xn4
349  b11 = aux11*xn4
350  b12 = aux12*xn4
351 
352  b13 = 4.d0*(g2*aux1 + g1*aux4)
353  b14 = 4.d0*(g2*aux2 + g1*aux5)
354  b15 = 4.d0*(g2*aux3 + g1*aux6)
355 
356  b16 = 4.d0*(g3*aux4 + g2*aux7)
357  b17 = 4.d0*(g3*aux5 + g2*aux8)
358  b18 = 4.d0*(g3*aux6 + g2*aux9)
359 
360  b19 = 4.d0*(g1*aux7 + g3*aux1)
361  b20 = 4.d0*(g1*aux8 + g3*aux2)
362  b21 = 4.d0*(g1*aux9 + g3*aux3)
363 
364  b22 = 4.d0*(g4*aux1 + g1*aux10)
365  b23 = 4.d0*(g4*aux2 + g1*aux11)
366  b24 = 4.d0*(g4*aux3 + g1*aux12)
367 
368  b25 = 4.d0*(g4*aux4 + g2*aux10)
369  b26 = 4.d0*(g4*aux5 + g2*aux11)
370  b27 = 4.d0*(g4*aux6 + g2*aux12)
371 
372  b28 = 4.d0*(g4*aux7 + g3*aux10)
373  b29 = 4.d0*(g4*aux8 + g3*aux11)
374  b30 = 4.d0*(g4*aux9 + g3*aux12)
375 
376 
377 !-----Calculate displacement gradient (H)
378  dudx = (b1*u1 + b4*u2 + b7*u3 + b10*u4 + b13*u5 + b16*u6 + b19*u7 + b22*u8 + b25*u9 + b28*u10)*vx6inv
379  dvdy = (b2*v1 + b5*v2 + b8*v3 + b11*v4 + b14*v5 + b17*v6 + b20*v7 + b23*v8 + b26*v9 + b29*v10)*vx6inv
380  dwdz = (b3*w1 + b6*w2 + b9*w3 + b12*w4 + b15*w5 + b18*w6 + b21*w7 + b24*w8 + b27*w9 + b30*w10)*vx6inv
381  dudy = (b2*u1 + b5*u2 + b8*u3 + b11*u4 + b14*u5 + b17*u6 + b20*u7 + b23*u8 + b26*u9 + b29*u10)*vx6inv
382  dvdx = (b1*v1 + b4*v2 + b7*v3 + b10*v4 + b13*v5 + b16*v6 + b19*v7 + b22*v8 + b25*v9 + b28*v10)*vx6inv
383  dvdz = (b3*v1 + b6*v2 + b9*v3 + b12*v4 + b15*v5 + b18*v6 + b21*v7 + b24*v8 + b27*v9 + b30*v10)*vx6inv
384  dwdy = (b2*w1 + b5*w2 + b8*w3 + b11*w4 + b14*w5 + b17*w6 + b20*w7 + b23*w8 + b26*w9 + b29*w10)*vx6inv
385  dudz = (b3*u1 + b6*u2 + b9*u3 + b12*u4 + b15*u5 + b18*u6 + b21*u7 + b24*u8 + b27*u9 + b30*u10)*vx6inv
386  dwdx = (b1*w1 + b4*w2 + b7*w3 + b10*w4 + b13*w5 + b16*w6 + b19*w7 + b22*w8 + b25*w9 + b28*w10)*vx6inv
387 
388 !
389 ! deformation gradients F
390 !
391  f11 = 1.d0 + ( dudx )
392  f22 = 1.d0 + ( dvdy )
393  f33 = 1.d0 + ( dwdz )
394  f12 = dudy
395  f21 = dvdx
396  f23 = dvdz
397  f32 = dwdy
398  f13 = dudz
399  f31 = dwdx
400 
401 !-- (1) Deformation Gradient Fij
402 
403  fij(1,1) = f11
404  fij(1,2) = f12
405  fij(1,3) = f13
406  fij(2,1) = f21
407  fij(2,2) = f22
408  fij(2,3) = f23
409  fij(3,1) = f31
410  fij(3,2) = f32
411  fij(3,3) = f33
412 
413 !-- (2) right Cauchy-Green deformation Tensor Cij = Fmi Fmj
414 ! T
415 ! C = F F
416 
417  DO kk=1,3
418  DO ll=1,3
419  cij(kk,ll) = 0.d0
420  DO mm=1,3
421  cij(kk,ll)=cij(kk,ll)+fij(mm,kk)*fij(mm,ll)
422  ENDDO
423  ENDDO
424  ENDDO
425 
426 !
427 ! Arruda-Boyce Nonlinear Elasticity Model
428 !
429 ! -- NOTE: ci(7,j) : shear modulus
430 
431  CALL arruda_boyce(cij, &
432  s11(igpt,i),s22(igpt,i),s33(igpt,i),s12(igpt,i),s23(igpt,i),s13(igpt,i),i, &
433  mu(j),kappa(j))
434 
435  r1 = r1 + &
436  ( s11(igpt,i)*b1*(1.d0+dudx) + s22(igpt,i)*b2*dudy + s33(igpt,i)*b3*dudz &
437  + s12(igpt,i)*( b2*(1.d0+dudx) + b1*dudy ) &
438  + s23(igpt,i)*( b3*dudy + b2*dudz ) &
439  + s13(igpt,i)*( b3*(1.d0+dudx) + b1*dudz ) )
440  r2 = r2 +&
441  ( s11(igpt,i)*b1*dvdx + s22(igpt,i)*b2*(1.d0+dvdy) + s33(igpt,i)*b3*dvdz &
442  + s12(igpt,i)*( b1*(1.d0+dvdy) + b2*dvdx ) &
443  + s23(igpt,i)*( b3*(1.d0+dvdy) + b2*dvdz ) &
444  + s13(igpt,i)*( b3*dvdx + b1*dvdz ) )
445  r3 = r3 + &
446  ( s11(igpt,i)*b1*dwdx + s22(igpt,i)*b2*dwdy + s33(igpt,i)*b3*(1.d0+dwdz) &
447  + s12(igpt,i)*( b2*dwdx + b1*dwdy ) &
448  + s23(igpt,i)*( b3*dwdy + b2*(1.d0 + dwdz) ) &
449  + s13(igpt,i)*( b3*dwdx + b1*(1.d0 + dwdz) ) )
450 
451  r4 = r4 + &
452  ( s11(igpt,i)*b4*(1.d0+dudx) + s22(igpt,i)*b5*dudy + s33(igpt,i)*b6*dudz &
453  + s12(igpt,i)*( b5*(1.d0+dudx) + b4*dudy ) &
454  + s23(igpt,i)*( b6*dudy + b5*dudz ) &
455  + s13(igpt,i)*( b6*(1.d0+dudx) + b4*dudz ) )
456  r5 = r5 + &
457  ( s11(igpt,i)*b4*dvdx + s22(igpt,i)*b5*(1.d0+dvdy) + s33(igpt,i)*b6*dvdz &
458  + s12(igpt,i)*( b4*(1.d0+dvdy) + b5*dvdx ) &
459  + s23(igpt,i)*( b6*(1.d0+dvdy) + b5*dvdz ) &
460  + s13(igpt,i)*( b6*dvdx + b4*dvdz ) )
461  r6 = r6 + &
462  ( s11(igpt,i)*b4*dwdx + s22(igpt,i)*b5*dwdy + s33(igpt,i)*b6*(1.d0+dwdz) &
463  + s12(igpt,i)*( b5*dwdx + b4*dwdy ) &
464  + s23(igpt,i)*( b6*dwdy + b5*(1.d0 + dwdz) ) &
465  + s13(igpt,i)*( b6*dwdx + b4*(1.d0 + dwdz) ) )
466 
467  r7 = r7 + &
468  ( s11(igpt,i)*b7*(1.d0+dudx) + s22(igpt,i)*b8*dudy + s33(igpt,i)*b9*dudz &
469  + s12(igpt,i)*( b8*(1.d0+dudx) + b7*dudy ) &
470  + s23(igpt,i)*( b9*dudy + b8*dudz ) &
471  + s13(igpt,i)*( b9*(1.d0+dudx) + b7*dudz ) )
472  r8 = r8 + &
473  ( s11(igpt,i)*b7*dvdx + s22(igpt,i)*b8*(1.d0+dvdy) + s33(igpt,i)*b9*dvdz &
474  + s12(igpt,i)*( b7*(1.d0+dvdy) + b8*dvdx ) &
475  + s23(igpt,i)*( b9*(1.d0+dvdy) + b8*dvdz ) &
476  + s13(igpt,i)*( b9*dvdx + b7*dvdz ) )
477  r9 = r9 + &
478  ( s11(igpt,i)*b7*dwdx + s22(igpt,i)*b8*dwdy + s33(igpt,i)*b9*(1.d0+dwdz) &
479  + s12(igpt,i)*( b8*dwdx + b7*dwdy ) &
480  + s23(igpt,i)*( b9*dwdy + b8*(1.d0 + dwdz) ) &
481  + s13(igpt,i)*( b9*dwdx + b7*(1.d0 + dwdz) ) )
482 
483  r10 = r10 + &
484  ( s11(igpt,i)*b10*(1.d0+dudx) + s22(igpt,i)*b11*dudy+s33(igpt,i)*b12*dudz &
485  + s12(igpt,i)*( b11*(1.d0+dudx) + b10*dudy ) &
486  + s23(igpt,i)*( b12*dudy + b11*dudz ) &
487  + s13(igpt,i)*( b12*(1.d0+dudx) + b10*dudz ) )
488  r11 = r11 + &
489  ( s11(igpt,i)*b10*dvdx + s22(igpt,i)*b11*(1.d0+dvdy)+s33(igpt,i)*b12*dvdz &
490  + s12(igpt,i)*( b10*(1.d0+dvdy) + b11*dvdx ) &
491  + s23(igpt,i)*( b12*(1.d0+dvdy) + b11*dvdz ) &
492  + s13(igpt,i)*( b12*dvdx + b10*dvdz ) )
493  r12 = r12 + &
494  ( s11(igpt,i)*b10*dwdx + s22(igpt,i)*b11*dwdy+s33(igpt,i)*b12*(1.d0+dwdz) &
495  + s12(igpt,i)*( b11*dwdx + b10*dwdy ) &
496  + s23(igpt,i)*( b12*dwdy + b11*(1.d0 + dwdz) ) &
497  + s13(igpt,i)*( b12*dwdx + b10*(1.d0 + dwdz) ) )
498 
499  r13 = r13 + &
500  ( s11(igpt,i)*b13*(1.d0+dudx) + s22(igpt,i)*b14*dudy + s33(igpt,i)*b15*dudz &
501  + s12(igpt,i)*( b14*(1.d0+dudx) + b13*dudy ) &
502  + s23(igpt,i)*( b15*dudy + b14*dudz ) &
503  + s13(igpt,i)*( b15*(1.d0+dudx) + b13*dudz ) )
504  r14 = r14 + &
505  ( s11(igpt,i)*b13*dvdx + s22(igpt,i)*b14*(1.d0+dvdy) + s33(igpt,i)*b15*dvdz &
506  + s12(igpt,i)*( b13*(1.d0+dvdy) + b14*dvdx ) &
507  + s23(igpt,i)*( b15*(1.d0+dvdy) + b14*dvdz ) &
508  + s13(igpt,i)*( b15*dvdx + b13*dvdz ) )
509  r15 = r15 + &
510  ( s11(igpt,i)*b13*dwdx + s22(igpt,i)*b14*dwdy + s33(igpt,i)*b15*(1.d0+dwdz) &
511  + s12(igpt,i)*( b14*dwdx + b13*dwdy ) &
512  + s23(igpt,i)*( b15*dwdy + b14*(1.d0 + dwdz) ) &
513  + s13(igpt,i)*( b15*dwdx + b13*(1.d0 + dwdz) ) )
514 
515  r16 = r16 + &
516  ( s11(igpt,i)*b16*(1.d0+dudx) + s22(igpt,i)*b17*dudy + s33(igpt,i)*b18*dudz &
517  + s12(igpt,i)*( b17*(1.d0+dudx) + b16*dudy ) &
518  + s23(igpt,i)*( b18*dudy + b17*dudz ) &
519  + s13(igpt,i)*( b18*(1.d0+dudx) + b16*dudz ) )
520  r17 = r17 + &
521  ( s11(igpt,i)*b16*dvdx + s22(igpt,i)*b17*(1.d0+dvdy) + s33(igpt,i)*b18*dvdz &
522  + s12(igpt,i)*( b16*(1.d0+dvdy) + b17*dvdx ) &
523  + s23(igpt,i)*( b18*(1.d0+dvdy) + b17*dvdz ) &
524  + s13(igpt,i)*( b18*dvdx + b16*dvdz ) )
525  r18 = r18 + &
526  ( s11(igpt,i)*b16*dwdx + s22(igpt,i)*b17*dwdy + s33(igpt,i)*b18*(1.d0+dwdz) &
527  + s12(igpt,i)*( b17*dwdx + b16*dwdy ) &
528  + s23(igpt,i)*( b18*dwdy + b17*(1.d0 + dwdz) ) &
529  + s13(igpt,i)*( b18*dwdx + b16*(1.d0 + dwdz) ) )
530 
531  r19 = r19 + &
532  ( s11(igpt,i)*b19*(1.d0+dudx) + s22(igpt,i)*b20*dudy + s33(igpt,i)*b21*dudz &
533  + s12(igpt,i)*( b20*(1.d0+dudx) + b19*dudy ) &
534  + s23(igpt,i)*( b21*dudy + b20*dudz ) &
535  + s13(igpt,i)*( b21*(1.d0+dudx) + b19*dudz ) )
536  r20 = r20 + &
537  ( s11(igpt,i)*b19*dvdx + s22(igpt,i)*b20*(1.d0+dvdy) + s33(igpt,i)*b21*dvdz &
538  + s12(igpt,i)*( b19*(1.d0+dvdy) + b20*dvdx ) &
539  + s23(igpt,i)*( b21*(1.d0+dvdy) + b20*dvdz ) &
540  + s13(igpt,i)*( b21*dvdx + b19*dvdz ) )
541  r21 = r21 + &
542  ( s11(igpt,i)*b19*dwdx + s22(igpt,i)*b20*dwdy + s33(igpt,i)*b21*(1.d0+dwdz) &
543  + s12(igpt,i)*( b20*dwdx + b19*dwdy ) &
544  + s23(igpt,i)*( b21*dwdy + b20*(1.d0 + dwdz) ) &
545  + s13(igpt,i)*( b21*dwdx + b19*(1.d0 + dwdz) ) )
546 
547  r22 = r22 + &
548  ( s11(igpt,i)*b22*(1.d0+dudx) + s22(igpt,i)*b23*dudy+s33(igpt,i)*b24*dudz &
549  + s12(igpt,i)*( b23*(1.d0+dudx) + b22*dudy ) &
550  + s23(igpt,i)*( b24*dudy + b23*dudz ) &
551  + s13(igpt,i)*( b24*(1.d0+dudx) + b22*dudz ) )
552  r23 = r23 + &
553  ( s11(igpt,i)*b22*dvdx + s22(igpt,i)*b23*(1.d0+dvdy)+s33(igpt,i)*b24*dvdz &
554  + s12(igpt,i)*( b22*(1.d0+dvdy) + b23*dvdx ) &
555  + s23(igpt,i)*( b24*(1.d0+dvdy) + b23*dvdz ) &
556  + s13(igpt,i)*( b24*dvdx + b22*dvdz ) )
557  r24 = r24 + &
558  ( s11(igpt,i)*b22*dwdx + s22(igpt,i)*b23*dwdy+s33(igpt,i)*b24*(1.d0+dwdz) &
559  + s12(igpt,i)*( b23*dwdx + b22*dwdy ) &
560  + s23(igpt,i)*( b24*dwdy + b23*(1.d0 + dwdz) ) &
561  + s13(igpt,i)*( b24*dwdx + b22*(1.d0 + dwdz) ) )
562 
563  r25 = r25 + &
564  ( s11(igpt,i)*b25*(1.d0+dudx) + s22(igpt,i)*b26*dudy+s33(igpt,i)*b27*dudz &
565  + s12(igpt,i)*( b26*(1.d0+dudx) + b25*dudy ) &
566  + s23(igpt,i)*( b27*dudy + b26*dudz ) &
567  + s13(igpt,i)*( b27*(1.d0+dudx) + b25*dudz ) )
568  r26 = r26 + &
569  ( s11(igpt,i)*b25*dvdx + s22(igpt,i)*b26*(1.d0+dvdy)+s33(igpt,i)*b27*dvdz &
570  + s12(igpt,i)*( b25*(1.d0+dvdy) + b26*dvdx ) &
571  + s23(igpt,i)*( b27*(1.d0+dvdy) + b26*dvdz ) &
572  + s13(igpt,i)*( b27*dvdx + b25*dvdz ) )
573  r27 = r27 + &
574  ( s11(igpt,i)*b25*dwdx + s22(igpt,i)*b26*dwdy+s33(igpt,i)*b27*(1.d0+dwdz) &
575  + s12(igpt,i)*( b26*dwdx + b25*dwdy ) &
576  + s23(igpt,i)*( b27*dwdy + b26*(1.d0 + dwdz) ) &
577  + s13(igpt,i)*( b27*dwdx + b25*(1.d0 + dwdz) ) )
578 
579  r28 = r28 + &
580  ( s11(igpt,i)*b28*(1.d0+dudx) + s22(igpt,i)*b29*dudy+s33(igpt,i)*b30*dudz &
581  + s12(igpt,i)*( b29*(1.d0+dudx) + b28*dudy ) &
582  + s23(igpt,i)*( b30*dudy + b29*dudz ) &
583  + s13(igpt,i)*( b30*(1.d0+dudx) + b28*dudz ) )
584  r29 = r29 + &
585  ( s11(igpt,i)*b28*dvdx + s22(igpt,i)*b29*(1.d0+dvdy)+s33(igpt,i)*b30*dvdz &
586  + s12(igpt,i)*( b28*(1.d0+dvdy) + b29*dvdx ) &
587  + s23(igpt,i)*( b30*(1.d0+dvdy) + b29*dvdz ) &
588  + s13(igpt,i)*( b30*dvdx + b28*dvdz ) )
589  r30 = r30 + &
590  ( s11(igpt,i)*b28*dwdx + s22(igpt,i)*b29*dwdy+s33(igpt,i)*b30*(1.d0+dwdz) &
591  + s12(igpt,i)*( b29*dwdx + b28*dwdy ) &
592  + s23(igpt,i)*( b30*dwdy + b29*(1.d0 + dwdz) ) &
593  + s13(igpt,i)*( b30*dwdx + b28*(1.d0 + dwdz) ) )
594 
595  ENDDO
596 
597 !Wi (i.e. weight) for 4 guass point integration is 1/4
598 
599 ! Wi * 1/6 because the volume of a reference tetrahedra in
600 ! volume coordinates is 1/6
601 
602 ! ASSEMBLE THE INTERNAL FORCE VECTOR
603 !
604 ! local node 1
605  r_in(k1n1) = r_in(k1n1) - r1*0.04166666666666667d0
606  r_in(k2n1) = r_in(k2n1) - r2*0.04166666666666667d0
607  r_in(k3n1) = r_in(k3n1) - r3*0.04166666666666667d0
608 ! local node 2
609  r_in(k1n2) = r_in(k1n2) - r4*0.04166666666666667d0
610  r_in(k2n2) = r_in(k2n2) - r5*0.04166666666666667d0
611  r_in(k3n2) = r_in(k3n2) - r6*0.04166666666666667d0
612 ! local node 3
613  r_in(k1n3) = r_in(k1n3) - r7*0.04166666666666667d0
614  r_in(k2n3) = r_in(k2n3) - r8*0.04166666666666667d0
615  r_in(k3n3) = r_in(k3n3) - r9*0.04166666666666667d0
616 ! local node 4
617  r_in(k1n4) = r_in(k1n4) - r10*0.04166666666666667d0
618  r_in(k2n4) = r_in(k2n4) - r11*0.04166666666666667d0
619  r_in(k3n4) = r_in(k3n4) - r12*0.04166666666666667d0
620 ! local node 5
621  r_in(k1n5) = r_in(k1n5) - r13*0.04166666666666667d0
622  r_in(k2n5) = r_in(k2n5) - r14*0.04166666666666667d0
623  r_in(k3n5) = r_in(k3n5) - r15*0.04166666666666667d0
624 ! local node 6
625  r_in(k1n6) = r_in(k1n6) - r16*0.04166666666666667d0
626  r_in(k2n6) = r_in(k2n6) - r17*0.04166666666666667d0
627  r_in(k3n6) = r_in(k3n6) - r18*0.04166666666666667d0
628 ! local node 7
629  r_in(k1n7) = r_in(k1n7) - r19*0.04166666666666667d0
630  r_in(k2n7) = r_in(k2n7) - r20*0.04166666666666667d0
631  r_in(k3n7) = r_in(k3n7) - r21*0.04166666666666667d0
632 ! local node 8
633  r_in(k1n8) = r_in(k1n8) - r22*0.04166666666666667d0
634  r_in(k2n8) = r_in(k2n8) - r23*0.04166666666666667d0
635  r_in(k3n8) = r_in(k3n8) - r24*0.04166666666666667d0
636 ! local node 9
637  r_in(k1n9) = r_in(k1n9) - r25*0.04166666666666667d0
638  r_in(k2n9) = r_in(k2n9) - r26*0.04166666666666667d0
639  r_in(k3n9) = r_in(k3n9) - r27*0.04166666666666667d0
640 ! local node 10
641  r_in(k1n10) = r_in(k1n10) - r28*0.04166666666666667d0
642  r_in(k2n10) = r_in(k2n10) - r29*0.04166666666666667d0
643  r_in(k3n10) = r_in(k3n10) - r30*0.04166666666666667d0
644 
645  ENDDO
646  RETURN
647 END SUBROUTINE v3d10_nl_arruda_boyce
648 
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