37
38
39
40#include "implicit_f.inc"
41
42
43
44
45
46
47 INTEGER NEL,NUPARAM,NUVAR,JTHE,INLOC
48 INTEGER ,DIMENSION(NEL), INTENT(IN) :: NGL
50 . time,timestep
51 my_real,
DIMENSION(NUPARAM),
INTENT(IN) ::
52 . uparam
53 my_real,
DIMENSION(NEL),
INTENT(IN) ::
54 . rho,tempel,dplanl,
55 . depsxx,depsyy,depsxy,depsyz,depszx,
56 . sigoxx,sigoyy,sigoxy,sigoyz,sigozx,
57 . gs , thkly
58
59 my_real ,
DIMENSION(NEL),
INTENT(OUT) ::
60 . soundsp,sigy,et,
61 . signxx,signyy,signxy,signyz,signzx
62
63 my_real ,
DIMENSION(NEL),
INTENT(INOUT) ::
64 . pla,dpla,epsd,off,thk,temp,seq
65 my_real ,
DIMENSION(NEL,NUVAR),
INTENT(INOUT) ::
66 . uvar
67
68
69
70
71 INTEGER I,II,NINDX,INDEX(NEL),NICE
72
74 . young,bulk,lam,g,g2,nu,cdr,kdr,hard,yld0,qvoce,bvoce,jcc,
75 . epsp0,mtemp,tini,tref,eta,cp,dpis,dpad,asrate,afiltr,a11,a12,
76 . nnu, normsig
78 . sigdr2,yld2i,
79 . dtemp,dpdt,dlam,ddep
81 . dpxx,dpyy,dpxy,dpzz,dsdrdj2,dsdrdj3,
82 . dj3dsxx,dj3dsyy,dj3dsxy,dj3dszz,
83 .
84 .
85 . normxx,normyy,normxy,normzz,
86 . denom,dphi,sig_dfdsig,dfdsig2,
87 . dphi_dsig,dphi_dyld,dphi_dfdr,dpdt_nl,
88 . dyld_dpla,dyld_dtemp,dtemp_dlam,dlam_nl
89
91 . dsigxx,dsigyy,dsigxy,trsig,
92 . sxx,syy,sxy,szz,sigm,j2,j3,sigdr,yld,weitemp,
93 . hardp,fhard,frate,ftherm,fdr,phi0,phi,dpla_dlam,
94 . dezz
95
96
97
98
99
100
101
102
103
104
105
106
107 young = uparam(1)
108 bulk = uparam(2)
109 g = uparam(3)
110 g2 = uparam(4)
111 lam = uparam(5)
112 nu = uparam(6)
113 nnu = uparam(7)
114 a11 = uparam(9)
115 a12 = uparam(10)
116
117 nice = nint(uparam(11))
118 cdr = uparam(12)
119 kdr = uparam(13)
120 tini = uparam(14)
121 hard = uparam(15)
122 yld0 = uparam(16)
123 qvoce = uparam(17)
124 bvoce = uparam(18)
125
126 jcc = uparam(20)
127 epsp0 = uparam(21)
128
129 mtemp = uparam(22)
130 tref = uparam(23)
131 eta = uparam(24)
132 cp = uparam(25)
133 dpis = uparam(26)
134 dpad = uparam(27)
135
136 asrate = uparam(28)
137 afiltr = asrate*timestep/(asrate*timestep + one)
138
139
140 DO i=1,nel
141 IF (off(i) < em01) off(i) = zero
142 IF (off(i) < one) off(i) = off(i)*four_over_5
143
144 phi0(i) = uvar(i,1)
145
146 dpla(i) = zero
147 et(i) = one
148 hardp(i) = zero
149 ENDDO
150
151 epsd(1:nel) = uvar(1:nel,2)
152
153
154 IF (time == zero) THEN
155 temp(1:nel) = tini
156 ENDIF
157 IF (cp > zero) THEN
158 IF (jthe == 0) THEN
159 IF (inloc == 0) THEN
160 DO i=1,nel
161
162 IF (epsd(i) < dpis) THEN
163 weitemp(i) = zero
164 ELSEIF (epsd(i) > dpad) THEN
165 weitemp(i) = one
166 ELSE
167 weitemp(i) = ((epsd(i)-dpis)**2 )
168 . * (three*dpad - two*epsd(i) - dpis)
169 . / ((dpad-dpis)**3)
170 ENDIF
171 ENDDO
172 ENDIF
173 ELSE
174 temp(1:nel) = tempel(1:nel)
175 ENDIF
176 ENDIF
177
178
179 DO i = 1,nel
180
181 fhard(i) = yld0 + hard*pla(i) + qvoce*(one-exp(-bvoce*pla(i)))
182
183 frate(i) = one
184 IF (epsd(i) > epsp0) frate(i) = frate(i) + jcc*log(epsd(i)/epsp0)
185
186 ftherm(i) = one
187 IF (cp > zero) ftherm(i) = one - mtemp * (temp(i) - tref)
188
189 yld(i) = fhard(i)*frate(i)*ftherm(i)
190
191 yld(i) =
max(em10, yld(i))
192 ENDDO
193
194
195
196
197 DO i=1,nel
198
199
200 signxx(i) = sigoxx(i) + a11*depsxx(i) + a12*depsyy(i)
201 signyy(i) = sigoyy(i) + a11*depsyy(i) + a12*depsxx(i)
202 signxy(i) = sigoxy(i) + depsxy(i)*g
203 signyz(i) = sigoyz(i) + depsyz(i)*gs(i)
204 signzx(i) = sigozx(i) + depszx(i)*gs(i)
205
206 trsig(i) = signxx(i) + signyy(i)
207 sigm(i) = -trsig(i) * third
208
209 sxx(i) = signxx(i) + sigm(i)
210 syy(i) = signyy(i) + sigm(i)
211 szz(i) = sigm(i)
212 sxy(i) = signxy(i)
213 dezz(i) = -nnu*depsxx(i) - nnu*depsyy(i)
214
215 j2(i) = half*(sxx(i)**2 + syy(i)**2 + szz(i)**2 ) + sxy(i)**2
216
217 j3(i) = sxx(i)*syy(i)*szz(i) - szz(i)*sxy(i)**2
218
219 fdr(i) = j2(i)**3 - cdr*(j3(i)**2)
220
221 IF (fdr(i) > zero) THEN
222 sigdr(i) = kdr * exp((one/six)*log(fdr(i)))
223 ELSE
224 sigdr(i) = zero
225 ENDIF
226 ENDDO
227
228
229
230
231 phi(1:nel) = (sigdr(1:nel) / yld(1:nel))**2 - one
232
233
234 nindx = 0
235 DO i=1,nel
236 IF (phi(i) >= zero .AND. off(i) == one) THEN
237 nindx=nindx+1
238 index(nindx)=i
239 ENDIF
240 ENDDO
241
242
243
244
245#include "vectorize.inc"
246 DO ii=1,nindx
247
248
249 i = index(ii)
250
251
252 dsigxx(i) = a11*depsxx(i) + a12*depsyy(i)
253 dsigyy(i) = a11*depsyy(i) + a12*depsxx(i)
254 dsigxy(i) = depsxy(i)*g
255 dlam = zero
256
257
258 trsig(i) = sigoxx(i) + sigoyy(i)
259 sigm(i) = -trsig(i) * third
260 sxx(i) = sigoxx(i) + sigm(i)
261 syy(i) = sigoyy(i) + sigm(i)
262 szz(i) = sigm(i)
263 sxy(i) = sigoxy(i)
264 j2(i) = half*(sxx(i)**2 + syy(i)**2 + szz(i)**2) + sxy(i)**2
265 j3(i) = sxx(i)*syy(i)*szz(i) - szz(i)*sxy(i)**2
266 fdr(i) = j2(i)**3 - cdr*(j3(i)**2)
267 sigdr(i) = kdr * exp((one/six)*log(fdr(i)))
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283 yld2i = one/(yld(i)**2)
284 dphi_dsig = two*sigdr(i)*yld2i
285
286
287 normsig = sqrt(sigoxx(i)*sigoxx(i)
288 . + sigoyy(i)*sigoyy(i)
289 . + two*sigoxy(i)*sigoxy(i))
290 normsig =
max(normsig,one)
291
292
293 fdr(i) = (j2(i)/(normsig**2))**3 - cdr*((j3(i)/(normsig**3))**2)
294 dphi_dfdr = dphi_dsig*kdr*(one/six)*exp(-(five/six)*log(fdr(i)))
295 dsdrdj2 = dphi_dfdr*three*(j2(i)/(normsig**2))**2
296 dsdrdj3 = -dphi_dfdr*two*cdr*(j3(i)/(normsig**3))
297
298 dj3dsxx = two_third*(syy(i)*szz(i))/(normsig**2)
299 . - third*(sxx(i)*szz(i))/(normsig**2)
300 . - third*(sxx(i)*syy(i)-sxy(i)**2)/(normsig**2)
301 dj3dsyy = - third*(syy(i)*szz(i))/(normsig**2)
302 . + two_third*(sxx(i)*szz(i))/(normsig**2)
303 . - third*(sxx(i)*syy(i)-sxy(i)**2)/(normsig**2)
304 dj3dszz = - third*(syy(i)*szz(i))/(normsig**2)
305 . - third*(sxx(i)*szz(i))/(normsig**2)
306 . + two_third*(sxx(i)*syy(i)-sxy(i)**2)/(normsig**2)
307 dj3dsxy = two*(sxx(i)*sxy(i) + sxy(i)*syy(i))/(normsig**2)
308
309 normxx = dsdrdj2*sxx(i)/normsig + dsdrdj3*dj3dsxx
310 normyy = dsdrdj2*syy(i)/normsig + dsdrdj3*dj3dsyy
311 normzz = dsdrdj2*szz(i)/normsig + dsdrdj3*dj3dszz
312 normxy = two*dsdrdj2*sxy(i)/normsig + dsdrdj3*dj3dsxy
313
314
315 phi(i) = phi0(i)
316
317
318 dphi = normxx * dsigxx(i)
319 . + normyy * dsigyy(i)
320 . + normxy * dsigxy(i)
321
322
323
324
325
326
327 dfdsig2 = normxx * (a11*normxx + a12*normyy)
328 . + normyy * (a11*normyy + a12*normxx)
329 . + normxy * normxy * g
330
331
332
333
334
335
336 hardp(i) = hard + qvoce*bvoce*exp(-bvoce*pla(i))
337 dyld_dpla = hardp(i)*frate(i)*ftherm(i)
338
339
340
341 sig_dfdsig = sigoxx(i) * normxx
342 . + sigoyy(i) * normyy
343 . + sigoxy(i) * normxy
344 dpla_dlam(i) = sig_dfdsig / yld(i)
345
346
347
348 IF (jthe == 0 .AND. cp > zero .AND. inloc == 0) THEN
349
350
351 dyld_dtemp = -fhard(i)*frate(i)*mtemp
352
353
354 dtemp_dlam = weitemp(i)*(eta/(rho(i)*cp))*sig_dfdsig
355 ELSE
356 dyld_dtemp = zero
357 dtemp_dlam = zero
358 ENDIF
359
360
361
362 sigdr2 = sigdr(i)**2
363 dphi_dyld = -two*sigdr2/(yld(i)**3)
364
365
366 denom = dfdsig2 - (dphi_dyld * dyld_dpla * dpla_dlam(i))
367 IF (jthe == 0 .AND. cp > zero .AND. inloc == 0) THEN
368 denom = denom - (dphi_dyld * dyld_dtemp * dtemp_dlam)
369 ENDIF
370 denom = sign(
max(abs(denom),em20) ,denom)
371
372
373
374
375
376 dlam = (dphi + phi(i)) / denom
377 dlam =
max(dlam, zero)
378
379
380 dpxx = dlam * normxx
381 dpyy = dlam * normyy
382 dpzz = dlam * normzz
383 dpxy = dlam * normxy
384
385
386 signxx(i) = sigoxx(i) + dsigxx(i) - (a11*dpxx + a12*dpyy)
387 signyy(i) = sigoyy(i) + dsigyy(i) - (a11*dpyy + a12*dpxx)
388 signxy(i) = sigoxy(i) + dsigxy(i) - dpxy*g
389 trsig(i) = signxx(i) + signyy(i)
390 sigm(i) = -trsig(i) * third
391 sxx(i) = signxx(i) + sigm(i)
392 syy(i) = signyy(i) + sigm(i)
393 szz(i) = sigm(i)
394 sxy(i) = signxy(i)
395
396
397 ddep = (dlam/yld(i))*sig_dfdsig
398 dpla(i) = dpla(i) + ddep
399 pla(i) = pla(i) + ddep
400
401
402 j2(i) = half*(sxx(i)**2 + syy(i)**2 + szz(i)**2 ) + sxy(i)**2
403 j3(i) = sxx(i) * syy(i) * szz(i) - szz(i) * sxy(i)**2
404 fdr(i) = j2(i)**3 - cdr*(j3(i)**2)
405 sigdr(i) = kdr * exp((one/six)*log(fdr(i)))
406
407
408 IF (jthe == 0 .AND. cp > zero .AND. inloc == 0) THEN
409 dtemp = weitemp(i)*yld(i)*ddep*eta/(rho(i)*cp)
410 temp(i) = temp(i) + dtemp
411 ftherm(i) = one - mtemp* (temp(i) - tref)
412 ENDIF
413
414
415 fhard(i) = yld0 + hard * pla(i) + qvoce*(one-exp(-bvoce*pla(i)))
416
417
418 yld(i) = fhard(i) * frate(i) * ftherm(i)
419 yld(i) =
max(yld(i), em10)
420
421
422 sigdr2 = sigdr(i)**2
423 yld2i = one / yld(i)**2
424 phi(i) = sigdr2 * yld2i - one
425
426
427 IF (inloc == 0) THEN
428 dezz(i) = dezz(i) + nnu*dpxx + nnu*dpyy + dpzz
429 ENDIF
430 ENDDO
431
432
433
434
435
436 DO i=1,nel
437
438 IF (dpla(i) > zero) THEN
439 uvar(i,1) = phi(i)
440 et(i) = hardp(i)*frate(i) / (hardp(i)*frate(i) + young)
441 ELSE
442 uvar(i,1) = zero
443 et(i) = one
444 ENDIF
445 seq(i) = sigdr(i)
446
447 dpdt = dpla(i) /
max(em20,timestep)
448 epsd(i) = afiltr * dpdt + (one - afiltr) * epsd(i)
449 uvar(i,2) = epsd(i)
450
451 soundsp(i) = sqrt(a11/rho(i))
452
453 sigy(i) = yld(i)
454
455 IF ((inloc > 0).AND.(off(i) == one).AND.(dplanl(i)>zero)) THEN
456 yld2i = one/(yld(i)**2)
457 dphi_dsig = two*sigdr(i)*yld2i
458 normsig = sqrt(signxx(i)*signxx(i)
459 . + signyy(i)*signyy(i)
460 . + two*signxy(i)*signxy(i))
461 normsig =
max(normsig,one)
462 fdr(i) = (j2(i)/(normsig**2))**3 - cdr*((j3(i)/(normsig**3))**2)
463 IF (fdr(i) > zero) THEN
464 dphi_dfdr = dphi_dsig*kdr*(one/six)*exp(-(five/six)*log(fdr(i)))
465 ELSE
466 dphi_dfdr = zero
467 ENDIF
468 dsdrdj2 = dphi_dfdr*three*(j2(i)/(normsig**2))**2
469 dsdrdj3 = -dphi_dfdr*two*cdr*(j3(i)/(normsig**3))
470 dj3dsxx = two_third*(syy(i)*szz(i))/(normsig**2)
471 . - third*(sxx(i)*szz(i))/(normsig**2)
472 . - third*(sxx(i)*syy(i)-sxy(i)**2)/(normsig**2)
473 dj3dsyy = - third*(syy(i)*szz(i))/(normsig**2)
474 . + two_third*(sxx(i)*szz(i))/(normsig**2)
475 . - third*(sxx(i)*syy(i)-sxy(i)**2)/(normsig**2)
476 dj3dszz = - third*(syy(i)*szz(i))/(normsig**2)
477 . - third*(sxx(i)*szz(i))/(normsig**2)
478 . + two_third*(sxx(i)*syy(i)-sxy(i)**2)/(normsig**2)
479 dj3dsxy = two*(sxx(i)*sxy(i) + sxy(i)*syy(i))/(normsig**2)
480 normxx = dsdrdj2*sxx(i)/normsig + dsdrdj3*dj3dsxx
481 normyy = dsdrdj2*syy(i)/normsig + dsdrdj3*dj3dsyy
482 normzz = dsdrdj2*szz(i)/normsig + dsdrdj3*dj3dszz
483 normxy = two*dsdrdj2*sxy(i)/normsig + dsdrdj3*dj3dsxy
484 sig_dfdsig = signxx(i) * normxx
485 . + signyy(i) * normyy
486 . + signxy(i) * normxy
487 IF (sig_dfdsig > em01) THEN
488 dlam_nl = (yld(i)*dplanl(i))/sig_dfdsig
489 dezz(i) = dezz(i) + nnu*(dlam_nl*normxx)
490 . + nnu*(dlam_nl*normyy)
491 . + dlam_nl*normzz
492 ENDIF
493 IF (cp > zero .AND. jthe == 0) THEN
494
495 dpdt_nl = dplanl(i)/
max(timestep,em20)
496 IF (dpdt_nl < dpis) THEN
497 weitemp(i) = zero
498 ELSEIF (dpdt_nl > dpad) THEN
499 weitemp(i) = one
500 ELSE
501 weitemp(i) = ((dpdt_nl-dpis)**2 )
502 . * (three*dpad - two*dpdt_nl - dpis)
503 . / ((dpad-dpis)**3)
504 ENDIF
505 dtemp = weitemp(i)*dplanl(i)*yld(i)*eta/(rho(i)*cp)
506 temp(i) = temp(i) + dtemp
507 ENDIF
508 ENDIF
509
510 thk(i) = thk(i) + dezz(i)*thkly(i)*off(i)
511 ENDDO
512