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mat104c_nldam_nice.F
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23!||====================================================================
24!|| mat104c_nldam_nice ../engine/source/materials/mat/mat104/mat104c_nldam_nice.F
25!||--- called by ------------------------------------------------------
26!|| sigeps104c ../engine/source/materials/mat/mat104/sigeps104c.F
27!||====================================================================
28 SUBROUTINE mat104c_nldam_nice(
29 1 NEL ,NGL ,NUPARAM ,NUVAR ,
30 2 TIME ,TIMESTEP,UPARAM ,UVAR ,JTHE ,OFF ,
31 3 GS ,RHO ,PLA ,DPLA ,EPSD ,SOUNDSP ,
32 4 DEPSXX ,DEPSYY ,DEPSXY ,DEPSYZ ,DEPSZX ,
33 5 SIGOXX ,SIGOYY ,SIGOXY ,SIGOYZ ,SIGOZX ,
34 6 SIGNXX ,SIGNYY ,SIGNXY ,SIGNYZ ,SIGNZX ,THKLY ,
35 7 THK ,SIGY ,ET ,TEMPEL ,DPLA_NL ,DMG ,
36 8 TEMP ,SEQ ,PLA_NL ,PLAP_NL )
37 !=======================================================================
38 ! Implicit types
39 !=======================================================================
40#include "implicit_f.inc"
41 !=======================================================================
42 ! Common
43 !=======================================================================
44#include "com01_c.inc"
45 !=======================================================================
46 ! Dummy arguments
47 !=======================================================================
48 INTEGER NEL,NUPARAM,NUVAR,JTHE
49 INTEGER ,DIMENSION(NEL), INTENT(IN) :: NGL
50 my_real
51 . TIME,TIMESTEP
52 my_real,DIMENSION(NUPARAM), INTENT(IN) ::
53 . UPARAM
54 my_real,DIMENSION(NEL), INTENT(IN) ::
55 . RHO,TEMPEL,
56 . depsxx,depsyy,depsxy,depsyz,depszx,
57 . sigoxx,sigoyy,sigoxy,sigoyz,sigozx,
58 . gs,thkly,pla_nl,plap_nl,dpla_nl
59c
60 my_real ,DIMENSION(NEL), INTENT(OUT) ::
61 . soundsp,sigy,et,
62 . signxx,signyy,signxy,signyz,signzx
63c
64 my_real ,DIMENSION(NEL), INTENT(INOUT) ::
65 . pla,dpla,epsd,off,thk,temp,seq
66 my_real ,DIMENSION(NEL,6), INTENT(INOUT) ::
67 . dmg
68 my_real ,DIMENSION(NEL,NUVAR), INTENT(INOUT) ::
69 . uvar
70c
71 !=======================================================================
72 ! Local Variables
73 !=======================================================================
74 INTEGER I,K,II,IGURSON,NINDX,INDEX(NEL),NICE
75c
76 my_real ::
77 . young,bulk,lam,g,g2,nu,cdr,kdr,hard,yld0,qvoce,bvoce,jcc,
78 . epsp0,mtemp,tini,tref,eta,cp,dpis,dpad,asrate,afiltr,hkhi,
79 . q1,q2,ed,an,epn,kw,fr,fc,f0,a11,a12,nnu
80 my_real ::
81 . dti,h,ldav,sigvm,sigdr2,yld2i,omega,
82 . dtemp,fcosh,fsinh,dpdt,dlam,ddep
83 my_real ::
84 . dpxx,dpyy,dpxy,dpzz,dsdrdj2,dsdrdj3,
85 . dj3dsxx,dj3dsyy,dj3dsxy,dj3dszz,
86 . dj2dsxx,dj2dsyy,dj2dsxy,
87 . dfdsxx,dfdsyy,dfdsxy,
88 . denom,dphi,sdpla,sdv_dfdsig,dfdsig2,
89 . dphi_dsig,dphi_dyld,dphi_dfdr,dphi_dfs,dfs_dft,
90 . dfn_dlam,dfsh_dlam,dfg_dlam,dft_dlam,dfdpla,normsig,
91 . dfn,dfsh,dfg,dft,dyld_dpla,dyld_dtemp,dtemp_dlam
92c
93 my_real, DIMENSION(NEL) ::
94 . dsigxx,dsigyy,dsigxy,trsig,trdep,
95 . sxx,syy,sxy,szz,sigm,j2,j3,sigdr,yld,weitemp,trdfds,
96 . hardp,fhard,frate,ftherm,fdr,triax,etat,sigdr_old,
97 . fdam,phi0,phi,ft,fs,fg,fn,fsh,dpla_dlam,dezz,dphi_dtrsig,
98 . normxx,normyy,normxy,normzz,sig_dfdsig,dlam_nl
99c
100 !=======================================================================
101 ! drucker - voce - johnson-cook material law with gurson damage
102 ! USING NON LOCAL PEERLINGS METHOD
103 !=======================================================================
104 !UVAR(1) PHI YIELD FUNCTION VALUE
105 !UVAR(2) YLD YIELD STRESS
106 !=======================================================================
107c
108 !=======================================================================
109 ! - INITIALISATION OF COMPUTATION ON TIME STEP
110 !=======================================================================
111 ! Recovering model parameters
112 ! Elastic parameters
113 young = uparam(1) ! Young modulus
114 bulk = uparam(2) ! Bulk modulus
115 g = uparam(3) ! Shear modulus
116 g2 = uparam(4) ! 2*Shear modulus
117 lam = uparam(5) ! Lambda Hooke parameter
118 nu = uparam(6) ! Poisson ration
119 nnu = uparam(7) ! NU/(1-NU)
120 a11 = uparam(9) ! Diagonal term, elastic matrix in plane stress
121 a12 = uparam(10) ! Non-diagonal term, elastic matrix in plane stress
122 ! Plastic criterion and hardening parameters [Drucker, 1948]
123 cdr = uparam(12) ! Drucker coefficient
124 kdr = uparam(13) ! drucker 1/k coefficient
125 tini = uparam(14) ! Initial temperature
126 hard = uparam(15) ! Linear hardening
127 yld0 = uparam(16) ! Initial yield stress
128 qvoce = uparam(17) ! 1st Voce parameter
129 bvoce = uparam(18) ! 2nd Voce parameter
130 ! strain-rate dependence parameters
131 jcc = uparam(20) ! Johnson-Cook strain rate coefficient
132 epsp0 = uparam(21) ! Johnson-Cook reference strain rate
133 ! Thermal softening and self-heating parameters
134 mtemp = uparam(22) ! Thermal softening slope
135 tref = uparam(23) ! Reference temperature
136 eta = uparam(24) ! Taylor-Quinney coefficient
137 cp = uparam(25) ! Thermal mass capacity
138 dpis = uparam(26) ! Isothermal plastic strain rate
139 dpad = uparam(27) ! Adiabatic plastic strain rate
140 ! Plastic strain-rate filtering parameters
141 asrate = uparam(28) ! Plastic strain rate filtering frequency
142 afiltr = asrate*timestep/(asrate*timestep + one)
143 dti = one / max(timestep, em20)
144c
145 ! Gurson damage model parameters parameters
146 igurson = nint(uparam(30)) ! Gurson switch flag:
147 ! = 0 => no damage model
148 ! = 1 => local damage model
149 ! = 2 => non local (Forest - micromorphic) damage model
150 ! = 3 => non local (Peerlings) damage model
151 q1 = uparam(31) ! Gurson yield criterion 1st parameter
152 q2 = uparam(32) ! Gurson yield criterion 2nd parameter
153 ed = uparam(34) ! Plastic strain trigger for nucleation
154 an = uparam(35) ! Nucleation rate
155 kw = uparam(36) ! Shear coefficient (Nahshon & Hutchinson)
156 fr = uparam(37) ! Failure void volume fraction
157 fc = uparam(38) ! Critical void volume fraction
158 f0 = uparam(39) ! Initial void volume fraction
159 hkhi = uparam(40) ! Micromorphic penalty parameter
160c
161 ! Recovering internal variables
162 DO i=1,nel
163 ! If the element is failing
164 IF (off(i) < em03) off(i) = zero
165 IF (off(i) < one) off(i) = off(i)*four_over_5
166 ! User inputs
167 phi0(i) = uvar(i,1) ! Previous yield function value
168 yld(i) = uvar(i,2) ! Previous yield stress
169 ! Damage variables
170 fg(i) = dmg(i,2) ! Growth damage
171 fn(i) = dmg(i,3) ! Nucleation damage
172 fsh(i) = dmg(i,4) ! Shear damage
173 ft(i) = dmg(i,5) ! Total damage
174 fs(i) = dmg(i,6) ! Effective damage
175 ! Standard inputs
176 dpla(i) = zero ! Initialization of the plastic strain increment
177 et(i) = one ! Initialization of hourglass coefficient
178 hardp(i) = zero ! initialization of hardening modulus
179 dezz(i) = zero ! Initialization of the transverse strain increment
180 dlam_nl(i) = zero ! Initialization of the non-local plastic multiplier
181 sig_dfdsig(i) = zero ! Initialization of the stress - normal scalar product
182 normxx(i) = zero ! Initialization of the x component of the normal tensor
183 normyy(i) = zero ! Initialization of the y component of the normal tensor
184 normzz(i) = zero ! Initialization of the z component of the normal tensor
185 ENDDO
186c
187 ! Initialization of damage, temperature and self-heating weight factor
188 IF (time == zero) THEN
189 temp(1:nel) = tini
190 IF (isigi == 0) THEN
191 dmg(1:nel,5) = f0
192 ft(1:nel) = f0
193 dmg(1:nel,1) = f0/fr
194 IF (f0<fc) THEN
195 dmg(1:nel,6) = f0
196 ELSE
197 dmg(1:nel,6) = fc + (one/q1-fc)*(f0-fc)/(fr-fc)
198 ENDIF
199 fs(1:nel) = dmg(1:nel,6)
200 ENDIF
201 ENDIF
202 IF (cp > zero) THEN
203 IF (jthe == 0) THEN
204 DO i=1,nel
205 ! Computation of the weight factor
206 IF (plap_nl(i) < dpis) THEN
207 weitemp(i) = zero
208 ELSEIF (plap_nl(i) > dpad) THEN
209 weitemp(i) = one
210 ELSE
211 weitemp(i) = ((plap_nl(i)-dpis)**2 )
212 . * (three*dpad - two*plap_nl(i) - dpis)
213 . / ((dpad-dpis)**3)
214 ENDIF
215 ENDDO
216 ELSE
217 temp(1:nel) = tempel(1:nel)
218 ENDIF
219 ENDIF
220c
221 !========================================================================
222 ! NON-LOCAL VARIABLES UPDATE
223 !========================================================================
224 DO i=1,nel
225c
226 ! Previous value of Drucker equivalent stress
227 trsig(i) = sigoxx(i) + sigoyy(i)
228 sigm(i) = -trsig(i) * third
229 sxx(i) = sigoxx(i) + sigm(i)
230 syy(i) = sigoyy(i) + sigm(i)
231 szz(i) = sigm(i)
232 sxy(i) = sigoxy(i)
233 j2(i) = half*(sxx(i)**2 + syy(i)**2 + szz(i)**2) + sxy(i)**2
234 j3(i) = sxx(i) * syy(i) * szz(i) - szz(i) * sxy(i)**2
235 fdr(i) = j2(i)**3 - cdr*(j3(i)**2)
236 IF (fdr(i) > zero) THEN
237 sigdr(i) = kdr * exp((one/six)*log(fdr(i)))
238 ELSE
239 sigdr(i) = zero
240 ENDIF
241 sigdr_old(i) = sigdr(i)
242c
243 ! Computation of the stress triaxiality and the etaT factor
244 IF (sigdr(i)>zero) THEN
245 triax(i) = (trsig(i)*third)/sigdr(i)
246 ELSE
247 triax(i) = zero
248 ENDIF
249 IF (trsig(i)<zero) THEN
250 etat(i) = zero
251 ELSE
252 etat(i) = one
253 ENDIF
254c
255 ! Normal to the previous yield surface
256 IF (yld(i)>zero) THEN
257 yld2i = one / yld(i)**2
258 dphi_dsig = two * sigdr(i) * yld2i
259 fsinh = sinh(q2*etat(i)*trsig(i)/(yld(i)*two))
260 dphi_dtrsig(i) = q1*q2*etat(i)*fs(i)*fsinh/yld(i)
261 ELSE
262 yld2i = zero
263 dphi_dsig = zero
264 fsinh = zero
265 dphi_dtrsig(i) = zero
266 ENDIF
267c
268 ! Computation of the Eulerian norm of the stress tensor
269 normsig = sqrt(sigoxx(i)*sigoxx(i)
270 . + sigoyy(i)*sigoyy(i)
271 . + two*sigoxy(i)*sigoxy(i))
272 normsig = max(normsig,one)
273c
274 ! Computation of the normal to the yield surface
275 fdr(i) = (j2(i)/(normsig**2))**3 - cdr*((j3(i)/(normsig**3))**2)
276 IF (fdr(i) > zero) THEN
277 dphi_dfdr = dphi_dsig*kdr*(one/six)*exp(-(five/six)*log(fdr(i)))
278 ELSE
279 dphi_dfdr = zero
280 ENDIF
281 dsdrdj2 = dphi_dfdr*three*(j2(i)/(normsig**2))**2
282 dsdrdj3 = -dphi_dfdr*two*cdr*(j3(i)/(normsig**3))
283 ! dJ3/dS
284 dj3dsxx = two_third*(syy(i)*szz(i))/(normsig**2)
285 . - third*(sxx(i)*szz(i))/(normsig**2)
286 . - third*(sxx(i)*syy(i)-sxy(i)**2)/(normsig**2)
287 dj3dsyy = - third*(syy(i)*szz(i))/(normsig**2)
288 . + two_third*(sxx(i)*szz(i))/(normsig**2)
289 . - third*(sxx(i)*syy(i)-sxy(i)**2)/(normsig**2)
290 dj3dszz = - third*(syy(i)*szz(i))/(normsig**2)
291 . - third*(sxx(i)*szz(i))/(normsig**2)
292 . + two_third*(sxx(i)*syy(i)-sxy(i)**2)/(normsig**2)
293 dj3dsxy = two*(sxx(i)*sxy(i) + sxy(i)*syy(i))/(normsig**2)
294 ! dPhi/dSig
295 normxx(i) = dsdrdj2*sxx(i)/normsig + dsdrdj3*dj3dsxx + dphi_dtrsig(i)
296 normyy(i) = dsdrdj2*syy(i)/normsig + dsdrdj3*dj3dsyy + dphi_dtrsig(i)
297 normzz(i) = dsdrdj2*szz(i)/normsig + dsdrdj3*dj3dszz + dphi_dtrsig(i)
298 normxy(i) = two*dsdrdj2*sxy(i)/normsig + dsdrdj3*dj3dsxy
299 trdfds(i) = normxx(i) + normyy(i) + normzz(i)
300 sig_dfdsig(i) = sigoxx(i)*normxx(i) + sigoyy(i)*normyy(i)
301 . + sigoxy(i)*normxy(i)
302c
303 ! Computation of the non-local plastic multiplier
304 IF (sig_dfdsig(i) > zero) THEN
305 dlam_nl(i) = ((one - ft(i))*yld(i)*dpla_nl(i))/max(sig_dfdsig(i),em20)
306 ELSE
307 dlam_nl(i) = zero
308 ENDIF
309c
310 ! Damage growth update
311 IF ((trdfds(i)>zero).AND.(ft(i)>zero).AND.(ft(i)<fr)) THEN
312 fg(i) = fg(i) + (one-ft(i))*dlam_nl(i)*trdfds(i)
313 ENDIF
314 fg(i) = max(fg(i),zero)
315c
316 ! Nucleation damage update
317 IF ((pla_nl(i) >= ed).AND.(ft(i)<fr)) THEN
318 ! Case for positive stress triaxiality
319 IF (triax(i)>=zero) THEN
320 fn(i) = fn(i) + an*dpla_nl(i)
321 ! Case for negative stress triaxiality
322 ELSEIF ((triax(i)<zero).AND.(triax(i)>=-third)) THEN
323 fn(i) = fn(i) + an*max(one + three*triax(i),zero)*dpla_nl(i)
324 ENDIF
325 ENDIF
326 fn(i) = max(fn(i),zero)
327c
328 ! Shear damage update
329 IF ((sigdr(i) > zero).AND.(ft(i)>zero).AND.(ft(i)<fr)) THEN
330 sigvm = sqrt(max(em20,three*(j2(i)/(normsig**2))))
331 omega = one - ((twenty7 *(j3(i)/(normsig**3)))/(two*(sigvm**3)))**2
332 omega = max(omega,zero)
333 omega = min(omega,one)
334 sdpla = (sxx(i)*normxx(i)+syy(i)*normyy(i)+ szz(i)*normzz(i)
335 . + sxy(i)*normxy(i))*dlam_nl(i)
336 fsh(i) = fsh(i) + kw*omega*ft(i)*(sdpla/sigdr(i))
337 ENDIF
338 fsh(i) = max(fsh(i),zero)
339c
340 ! Total damage update
341 ft(i) = f0 + fg(i) + fn(i) + fsh(i)
342 ft(i) = min(ft(i), fr)
343 IF (ft(i) >= fr) THEN
344 IF (off(i)==one) off(i) = four_over_5
345 ENDIF
346c
347 ! Effective update
348 IF (ft(i) < fc)THEN
349 fs(i) = ft(i)
350 ELSE
351 fs(i) = fc + (one/q1 - fc) * (ft(i)-fc)/(fr-fc)
352 ENDIF
353 fs(i) = min(fs(i),one/q1)
354c
355 ! Temperature update
356 IF (cp > zero) THEN
357 IF (jthe == 0) THEN
358 dtemp = weitemp(i)*(one-ft(i))*yld(i)*dpla_nl(i)*eta/(rho(i)*cp)
359 temp(i) = temp(i) + dtemp
360 ENDIF
361 ENDIF
362 ENDDO
363c
364 ! computation of the initial yield stress
365 DO i=1,nel
366 ! a) - Hardening law
367 fhard(i) = yld0 + hard*pla(i) + qvoce*(one-exp(-bvoce*pla(i)))
368 ! b) - Correction factor for strain-rate dependence (Johnson-Cook)
369 frate(i) = one
370 IF (epsd(i) > epsp0) frate(i) = frate(i) + jcc*log(epsd(i)/epsp0)
371 ! c) - Correction factor for thermal effects
372 ftherm(i) = one
373 IF (cp > zero) ftherm(i) = one - mtemp*(temp(i) - tref)
374 ! d) - Computation of the yield function
375 yld(i) = fhard(i)*frate(i)*ftherm(i)
376 ! e) - Checking values
377 yld(i) = max(em10, yld(i))
378 ENDDO
379c
380 !========================================================================
381 ! - COMPUTATION OF TRIAL VALUES
382 !========================================================================
383 DO i=1,nel
384c
385 ! Computation of the trial stress tensor
386 signxx(i) = sigoxx(i) + (a11*depsxx(i) + a12*depsyy(i))
387 signyy(i) = sigoyy(i) + (a11*depsyy(i) + a12*depsxx(i))
388 signxy(i) = sigoxy(i) + (depsxy(i)*g)
389 signyz(i) = sigoyz(i) + (depsyz(i)*gs(i))
390 signzx(i) = sigozx(i) + (depszx(i)*gs(i))
391 ! Computation of the trace of the trial stress tensor
392 trsig(i) = signxx(i) + signyy(i)
393 sigm(i) = -trsig(i) * third
394 ! Computation of the deviatoric trial stress tensor
395 sxx(i) = signxx(i) + sigm(i)
396 syy(i) = signyy(i) + sigm(i)
397 szz(i) = sigm(i)
398 sxy(i) = signxy(i)
399 ! Second deviatoric invariant
400 j2(i) = half*(sxx(i)**2 + syy(i)**2 + szz(i)**2) + sxy(i)**2
401 ! Third deviatoric invariant
402 j3(i) = sxx(i)*syy(i)*szz(i) - szz(i)*sxy(i)**2
403 ! Drucker equivalent stress
404 fdr(i) = j2(i)**3 - cdr*(j3(i)**2)
405 ! Checking equivalent stress values
406 IF (fdr(i) > zero) THEN
407 sigdr(i) = kdr * exp((one/six)*log(fdr(i))) ! FDR(I)**(1/6)
408 ELSE
409 sigdr(i) = zero
410 ENDIF
411 ! Computation of the stress triaxiality and the etaT factor
412 IF (sigdr(i)>zero) THEN
413 triax(i) = (trsig(i)*third)/sigdr(i)
414 ELSE
415 triax(i) = zero
416 ENDIF
417 IF (trsig(i)<zero) THEN
418 etat(i) = zero
419 ELSE
420 etat(i) = one
421 ENDIF
422c
423 ! Update out of plane strain increment
424 IF (off(i) == one) THEN
425 dezz(i) = -nnu*depsxx(i)-nnu*depsyy(i)
426 IF (sig_dfdsig(i) > em01) THEN
427 dezz(i) = dezz(i) + nnu*(dlam_nl(i)*normxx(i))
428 . + nnu*(dlam_nl(i)*normyy(i))
429 . + dlam_nl(i)*normzz(i)
430 ENDIF
431 ENDIF
432 ENDDO
433c
434 !========================================================================
435 ! - COMPUTATION OF YIELD FONCTION
436 !========================================================================
437 DO i=1,nel
438 fdam(i) = two*q1*fs(i)*cosh(q2*etat(i)*trsig(i)/yld(i)/two) - (q1*fs(i))**2
439 phi(i) = (sigdr(i) / yld(i))**2 - one + fdam(i)
440 ENDDO
441c
442 ! Checking plastic behavior for all elements
443 nindx = 0
444 DO i=1,nel
445 IF ((phi(i) >= zero).AND.(off(i) == one).AND.(ft(i)<fr)) THEN
446 nindx = nindx+1
447 index(nindx)=i
448 ENDIF
449 ENDDO
450c
451 !====================================================================
452 ! - PLASTIC CORRECTION WITH NICE - EXPLICIT METHOD
453 !====================================================================
454#include "vectorize.inc"
455 DO ii=1,nindx
456c
457 ! Number of the element with plastic behaviour
458 i = index(ii)
459c
460 ! Computation of the trial stress increment
461 dsigxx(i) = a11*depsxx(i) + a12*depsyy(i)
462 dsigyy(i) = a11*depsyy(i) + a12*depsxx(i)
463 dsigxy(i) = depsxy(i)*g
464 dlam = zero
465c
466 ! Note : in this part, the purpose is to compute in one iteration
467 ! a plastic multiplier allowing to update internal variables to satisfy
468 ! the consistency condition.
469 ! Its expression is : DLAMBDA = - (PHI_OLD + DPHI) / DPHI_DLAMBDA
470 ! -> PHI_OLD : old value of yield function (known)
471 ! -> DPHI : yield function prediction (to compute)
472 ! -> DPHI_DLAMBDA : derivative of PHI with respect to DLAMBDA by taking
473 ! into account of internal variables kinetic :
474 ! plasticity, temperature and damage (to compute)
475c
476 ! 1 - Computation of DPHI_DSIG the normal to the yield surface
477 !-------------------------------------------------------------
478c
479 ! DPHI_DSIG already computed above
480c
481 ! Restoring previous value of the yield function
482 phi(i) = phi0(i)
483c
484 ! Computation of yield surface trial increment DPHI
485 dphi = normxx(i) * dsigxx(i)
486 . + normyy(i) * dsigyy(i)
487 . + normxy(i) * dsigxy(i)
488c
489 ! 2 - Computation of DPHI_DLAMBDA
490 !---------------------------------------------------------
491c
492 ! a) Derivative with respect stress increments tensor DSIG
493 ! --------------------------------------------------------
494 dfdsig2 = normxx(i) * (a11*normxx(i) + a12*normyy(i))
495 . + normyy(i) * (a11*normyy(i) + a12*normxx(i))
496 . + normxy(i) * normxy(i) * g
497c
498 ! b) Derivatives with respect to plastic strain P
499 ! ------------------------------------------------
500c
501 ! i) Derivative of the yield stress with respect to plastic strain dYLD / dPLA
502 ! ----------------------------------------------------------------------------
503 hardp(i) = hard + qvoce*bvoce*exp(-bvoce*pla(i))
504 dyld_dpla = hardp(i)*frate(i)*ftherm(i)
505c
506 ! ii) Derivative of dPLA with respect to DLAM
507 ! -------------------------------------------
508 dpla_dlam(i) = sig_dfdsig(i) / ((one - ft(i))*yld(i))
509c
510 ! c) Derivative with respect to the yield stress
511 ! ----------------------------------------------
512 sigdr2 = sigdr_old(i)**2
513 trsig(i) = sigoxx(i) + sigoyy(i)
514 dphi_dyld = -two*sigdr2/yld(i)**3-dphi_dtrsig(i)*trsig(i)/yld(i)
515c
516 ! d) Derivative of PHI with respect to DLAM ( = -DENOM)
517 denom = dfdsig2 - (dphi_dyld * dyld_dpla * dpla_dlam(i))
518 denom = sign(max(abs(denom),em20) ,denom)
519c
520 ! 3 - Computation of plastic multiplier and variables update
521 !----------------------------------------------------------
522c
523 ! Computation of the plastic multiplier
524 dlam = (dphi + phi(i)) / denom
525 dlam = max(dlam, zero)
526c
527 ! Plastic strains tensor update
528 dpxx = dlam * normxx(i)
529 dpyy = dlam * normyy(i)
530 dpzz = dlam * normzz(i)
531 dpxy = dlam * normxy(i)
532 trdep(i) = dpxx + dpyy + dpzz
533c
534 ! Elasto-plastic stresses update
535 signxx(i) = sigoxx(i) + dsigxx(i) - (a11*dpxx + a12*dpyy)
536 signyy(i) = sigoyy(i) + dsigyy(i) - (a11*dpyy + a12*dpxx)
537 signxy(i) = sigoxy(i) + dsigxy(i) - dpxy*g
538 trsig(i) = signxx(i) + signyy(i)
539 sigm(i) = -trsig(i) * third
540 sxx(i) = signxx(i) + sigm(i)
541 syy(i) = signyy(i) + sigm(i)
542 szz(i) = sigm(i)
543 sxy(i) = signxy(i)
544c
545 ! Cumulated plastic strain and strain rate update
546 ddep = (dlam/((one - ft(i))*yld(i)))*sig_dfdsig(i)
547 dpla(i) = dpla(i) + ddep
548 pla(i) = pla(i) + ddep
549c
550 ! Drucker equivalent stress update
551 j2(i) = half*(sxx(i)**2 + syy(i)**2 + szz(i)**2) + sxy(i)**2
552 j3(i) = sxx(i) * syy(i) * szz(i) - szz(i) * sxy(i)**2
553 fdr(i) = j2(i)**3 - cdr*(j3(i)**2)
554 sigdr(i) = kdr * exp((one/six)*log(fdr(i)))
555 ! Computation of the stress triaxiality and the etaT factor
556 triax(i) = (trsig(i)*third)/sigdr(i)
557 IF (trsig(i)<zero) THEN
558 etat(i) = zero
559 ELSE
560 etat(i) = one
561 ENDIF
562c
563 ! Hardening law update
564 fhard(i) = yld0 + hard * pla(i) + qvoce*(one-exp(-bvoce*pla(i)))
565c
566 ! Yield stress update
567 yld(i) = fhard(i) * frate(i) * ftherm(i)
568 yld(i) = max(yld(i), em10)
569c
570 ! Yield function value update
571 sigdr2 = sigdr(i)**2
572 yld2i = one / yld(i)**2
573 fcosh = cosh(q2*etat(i)*trsig(i)/(yld(i)*two))
574 fdam(i) = two*q1*fs(i)*fcosh - (q1*fs(i))**2
575 phi(i) = sigdr2 * yld2i - one + fdam(i)
576c
577 ENDDO
578 !===================================================================
579 ! - END OF PLASTIC CORRECTION WITH NICE - EXPLICIT METHOD
580 !===================================================================
581c
582 ! Storing new values
583 DO i=1,nel
584 ! USR Outputs & coefficient for hourglass
585 IF (dpla(i) > zero) THEN
586 uvar(i,1) = phi(i) ! Yield function value
587 et(i) = hardp(i)*frate(i) / (hardp(i)*frate(i) + young)
588 ELSE
589 uvar(i,1) = zero
590 et(i) = one
591 ENDIF
592 uvar(i,2) = yld(i) ! Yield stress
593 ! Standard outputs
594 dmg(i,1) = ft(i)/fr ! Normalized total damage
595 dmg(i,2) = fg(i) ! Growth damage
596 dmg(i,3) = fn(i) ! Nucleation damage
597 dmg(i,4) = fsh(i) ! Shear damage
598 dmg(i,5) = min(ft(i),fr) ! Total damage
599 dmg(i,6) = min(fs(i),one/q1) ! Effective damage
600 seq(i) = sigdr(i) ! Equivalent stress
601 ! If element is broken
602 IF (ft(i) >= fr) THEN
603 dpla(i) = zero
604 signxx(i) = zero
605 signyy(i) = zero
606 signxy(i) = zero
607 signyz(i) = zero
608 signzx(i) = zero
609 seq(i) = zero
610 ENDIF
611 ! Plastic strain-rate (filtered)
612 dpdt = dpla(i) / max(em20,timestep)
613 epsd(i) = afiltr * dpdt + (one - afiltr) * epsd(i)
614 ! Computation of the sound speed
615 soundsp(i) = sqrt((a11)/rho(i))
616 ! Storing the yield stress
617 sigy(i) = yld(i)
618 ! Computation of the thickness variation
619 thk(i) = thk(i) + dezz(i)*thkly(i)*off(i)
620 ENDDO
621c
622 END
the
end diagonal values have been computed in the(sparse) matrix id.SOL
min
#define min(a, b)
Definition macros.h:20
max
#define max(a, b)
Definition macros.h:21
mat104c_nldam_nice
subroutine mat104c_nldam_nice(nel, ngl, nuparam, nuvar, time, timestep, uparam, uvar, jthe, off, gs, rho, pla, dpla, epsd, soundsp, depsxx, depsyy, depsxy, depsyz, depszx, sigoxx, sigoyy, sigoxy, sigoyz, sigozx, signxx, signyy, signxy, signyz, signzx, thkly, thk, sigy, et, tempel, dpla_nl, dmg, temp, seq, pla_nl, plap_nl)
Definition mat104c_nldam_nice.F:37