MATVP

Bulk Data Entry Defines material properties for nonlinear creep materials.

Format A: For Power law-based definition (CTYPE=TIMEC, TIMET, HYPERB)

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
MATVP MID CTYPE A n m B R dH  
  thetaZ                

Format B: For material parameter calibration from test data (CTYPE=TEST)

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
MATVP MID TEST TID SIG ALB AUB nLB nUB
mLB mUB

Format C: For Anand material model (CTYPE=ANAND)

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
MATVP MID ANAND A n m ξ MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqOVdGhaaa@37B6@ R dH
thetaZ a s ^ MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabm4Cayaaja aaaa@36FB@ A0 A1 A2 A3 A4
  S1 S2 S3            

Format D: For Darveaux material model (CTYPE=DARVEAU)

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
MATVP MID DARVEAU C s s MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4qamaaBa aaleaacaWGZbGaam4Caaqabaaaaa@38D7@ n   α MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqySdegaaa@3792@ R dH
thetaZ ε T MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyTdu2aaS baaSqaaiaadsfaaeqaaaaa@389F@ B          

Example A

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
MATVP 101 STRAIN 3.28e-11 3.15 -0.2        

Example B

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
MATVP 102 TEST 1001 39.3

Definitions

Field Contents SI Unit Example
MID Unique material identification number.

No default (Integer > 0)

 
CTYPE Specifies the creep material model type.
STRAIN (Default)
Based on strain hardening form.
TIMEC
Based on time hardening form using creep time.
TIMET
Based on time hardening form using total time.
HYPERB
Based on hyperbolic Sine hardening form.
ANAND
Based on Anand material model
DARVEAU
Based on Darveaux material model
TEST
Based on experimental test data. 9.
 
A Material parameter.

No default (Real > 0.0)

 
C s s MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4qamaaBa aaleaacaWGZbGaam4Caaqabaaaaa@38D7@ Material parameter

No default (Real > 0.0)

 
n Material parameter.

No default (Real > 0.0)

 
m Material parameter.

No default (-1.0 ≤ Real ≤ 0.0) for CTYPE = STRAIN, TIMEC, TIMET

No default (Real) for CTYPE=ANAND

 
B Material parameter. 8

No default (Real > 0.0)

 
α MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqySdegaaa@3792@ Material parameter.

No default (Real > 0.0)

 
ξ MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqOVdGhaaa@37B6@ Material parameter.

No default (Real > 0.0)

 
R Universal gas constant. 8

No default (Real > 0.0)

 
dH Activation energy. 8

No default (Real > 0.0)

 
thetaZ Absolute zero temperature.

Default = 0.0 (Real)

 
ε T MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyTdu2aaS baaSqaaiaadsfaaeqaaaaa@389F@ Material parameter.

No default (Real)

 
a Material parameter.

No default (Real)

 
s ^ MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabm4Cayaaja aaaa@36FB@ Material parameter.

No default (Real > 0.0)

 
A0 Material parameter.

No default (Real)

 
A1 Material parameter.

Default = 0.0 (Real)

 
A2 Material parameter.

Default = 0.0 (Real)

 
A3 Material parameter.

Default = 0.0 (Real)

 
A4 Material parameter.

Default = 0.0 (Real)

 
S1 Material parameter.

No default (Real)

 
S2 Material parameter.

Default = 0.0 (Real)

 
S3 Material parameter.

Default = 0.0 (Real)

 
TID Table identification number of a TABLES1 entry containing experimental test data. 9
In the TABLES1 definition,
  • y-values should be the creep strains
  • x-values should be the time points.

(Integer > 0)

 
SIG von Mises stress of the experimental test data.

No default (Real ≥ 0.0)

 
ALB Lower bound for the material parameter A. 10

No default (Real > 0.0)

 
AUB Upper bound for the material parameter A. 10

No default (Real > 0.0)

 
nLB Lower bound for the material parameter n.

Default = 0.0 (Real ≧ 0.0)

 
nUB Upper bound for the material parameter n.

Default = 6.0 (Real > 0.0)

 
mLB Lower bound for the material parameter m.

Default = -1.0 (-1 ≦ Real < 0.0)

 
mUB Upper bound for the material parameter m.

Default = 0.0 (-1 < Real ≦ 0.0)

 

Comments

  1. Support information for MATVP is:
    • Analysis types: Nonlinear static/transient for both small/large displacement types.
    • Elements: CHEXA, CTETRA, CPENTA, CPYRA.
  2. Specifying a MAT1 and a MATVP Bulk Data Entry with the same MID allows modeling creep material. Specifying a MAT1, a MATS1 and a MATVP Bulk Data Entry with the same MID can model a creep material with plasticity.
  3. You can choose explicit or implicit time integration for creep materials by using the TINT field of the VISCO card.
  4. The formulation for different material models are as follows:
    STRAIN hardening formulation:(1)
    ε ¯ ˙ c = A 1 m + 1 σ ¯ n m + 1 ( ( m + 1 ) ε ¯ c ) m m + 1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGafqyTduMbae HbaiaadaahaaWcbeqaaiaadogaaaGccqGH9aqpcaWGbbWaaWbaaSqa beaadaWcaaqaaiaaigdaaeaacaWGTbGaey4kaSIaaGymaaaaaaGccu aHdpWCgaqeamaaCaaaleqabaWaaSaaaeaacaWGUbaabaGaamyBaiab gUcaRiaaigdaaaaaaOWaaeWaaeaadaqadaqaaiaad2gacqGHRaWkca aIXaaacaGLOaGaayzkaaGafqyTduMbaebadaahaaWcbeqaaiaadoga aaaakiaawIcacaGLPaaadaahaaWcbeqaamaalaaabaGaamyBaaqaai aad2gacqGHRaWkcaaIXaaaaaaaaaa@501B@
    TIME hardening formulation:(2)
    ε ¯ ˙ c = A σ ¯ n t m MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGafqyTduMbae HbaiaadaahaaWcbeqaaiaadogaaaGccqGH9aqpcaWGbbGafq4WdmNb aebadaahaaWcbeqaaiaad6gaaaGccaWG0bWaaWbaaSqabeaacaWGTb aaaaaa@3FC6@
    Where,
    ε ¯ ˙ c = 2 3 ε ˙ c : ε ˙ c MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGafqyTduMbae HbaiaadaahaaWcbeqaaiaadogaaaGccqGH9aqpdaGcaaqaamaalaaa baGaaGOmaaqaaiaaiodaaaGafqyTduMbaiaadaahaaWcbeqaaiaado gaaaGccaGG6aGafqyTduMbaiaadaahaaWcbeqaaiaadogaaaaabeaa aaa@41CE@
    Equivalent creep strain rate
    σ ¯ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGafq4WdmNbae baaaa@37D2@
    Equivalent deviatoric stress
    t MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiDaaaa@36F0@
    Total time
    HYPERB material model formulation:(3)
    ε ¯ ˙ c = Asinh n ( B σ ¯ ) exp ( d H R ( θ θ z ) ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGafqyTduMbae HbaiaadaahaaWcbeqaaiaadogaaaGcqaaaaaaaaaWdbiabg2da9iaa bgeacaqGZbGaaeyAaiaab6gacaqGObWdamaaCaaaleqabaWdbiaad6 gaaaGccaGGOaGaamOqaiqbeo8aZzaaraGaaiykaiaabwgacaqG4bGa aeiCamaabmaabaGaeyOeI0YaaSaaaeaacaWGKbGaamisaaqaaiaadk fadaqadaqaaiabeI7aXjabgkHiTiabeI7aXnaaCaaaleqabaGaamOE aaaaaOGaayjkaiaawMcaaaaaaiaawIcacaGLPaaaaaa@52C9@
    Where,
    θ and θ z MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcqaaaaaaaaaWdbe aacqaH4oqCdaahaaWcbeqaaiaadQhaaaaaaa@38F8@
    The current and absolute zero temperatures, respectively.
    If d H MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcqaaaaaaaaaWdbe aacaWGKbGaamisaaaa@37CC@ is set to zero, the temperature dependence is absent.
    Anand material model formulation:(4)
    ˙ ¯ c = A sinh 1 m ξ σ ¯ s exp d H R θ θ Z MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa0aaaeaacu GHiiIZgaGaaaaadaahaaWcbeqaaiaadogaaaGccqGH9aqpcaWGbbGa ci4CaiaacMgacaGGUbGaaiiAamaaCaaaleqabaWaaSaaaeaacaaIXa aabaGaamyBaaaaaaGcdaqadaqaaiabe67a4naalaaabaWaa0aaaeaa cqaHdpWCaaaabaGaam4CaaaaaiaawIcacaGLPaaaciGGLbGaaiiEai aacchadaqadaqaaiabgkHiTmaalaaabaGaamizaiaadIeaaeaacaWG sbWaaeWaaeaacqaH4oqCcqGHsislcqaH4oqCdaahaaWcbeqaaiaadQ faaaaakiaawIcacaGLPaaaaaaacaGLOaGaayzkaaaaaa@5542@
    (5)
    s ˙ = h o 1 s s * a s i g n 1 s s * ˙ ¯ c MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabm4Cayaaca Gaeyypa0JaamiAamaaBaaaleaacaWGVbaabeaakmaaemaabaGaaGym aiabgkHiTmaalaaabaGaam4CaaqaaiaadohadaahaaWcbeqaaiaacQ caaaaaaaGccaGLhWUaayjcSdWaaWbaaSqabeaacaWGHbaaaOGaam4C aiaadMgacaWGNbGaamOBamaabmaabaGaaGymaiabgkHiTmaalaaaba Gaam4CaaqaaiaadohadaahaaWcbeqaaiaacQcaaaaaaaGccaGLOaGa ayzkaaWaa0aaaeaacuGHiiIZgaGaaaaadaahaaWcbeqaaiaadogaaa aaaa@4F6B@
    (6)
    s * = s ^ 1 A ˙ ¯ c exp d H R θ θ Z n MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4CaiaacQ cacqGH9aqpceWGZbGbaKaadaWadaqaamaalaaabaGaaGymaaqaaiaa dgeaaaWaa0aaaeaacuGHiiIZgaGaaaaadaahaaWcbeqaaiaadogaaa GcciGGLbGaaiiEaiaacchadaqadaqaamaalaaabaGaamizaiaadIea aeaacaWGsbWaaeWaaeaacqaH4oqCcqGHsislcqaH4oqCdaahaaWcbe qaaiaadQfaaaaakiaawIcacaGLPaaaaaaacaGLOaGaayzkaaaacaGL BbGaayzxaaWaaWbaaSqabeaacaWGUbaaaaaa@4F00@
    (7)
    h 0 = A 0 + A 1 θ θ Z + A 2 θ θ Z 2 + A 3 ˙ ¯ c + A 4 ˙ ¯ c 2 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiAamaaBa aaleaacaaIWaaabeaakiabg2da9iaadgeadaWgaaWcbaGaaGimaaqa baGccqGHRaWkcaWGbbWaaSbaaSqaaiaaigdaaeqaaOWaaeWaaeaacq aH4oqCcqGHsislcqaH4oqCdaahaaWcbeqaaiaadQfaaaaakiaawIca caGLPaaacqGHRaWkcaWGbbWaaSbaaSqaaiaaikdaaeqaaOWaaeWaae aacqaH4oqCcqGHsislcqaH4oqCdaahaaWcbeqaaiaadQfaaaaakiaa wIcacaGLPaaadaahaaWcbeqaaiaaikdaaaGccqGHRaWkcaWGbbWaaS baaSqaaiaaiodaaeqaaOWaa0aaaeaacuGHiiIZgaGaaaaadaahaaWc beqaaiaadogaaaGccqGHRaWkcaWGbbWaaSbaaSqaaiaaisdaaeqaaO WaaeWaaeaadaqdaaqaaiqbgIGioBaacaaaamaaCaaaleqabaGaam4y aaaaaOGaayjkaiaawMcaamaaCaaaleqabaGaaGOmaaaaaaa@5BC5@
    (8)
    s 0 = S 1 + S 2 θ θ Z + A 3 θ θ Z 2 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4CamaaBa aaleaacaaIWaaabeaakiabg2da9iaadofadaWgaaWcbaGaaGymaaqa baGccqGHRaWkcaWGtbWaaSbaaSqaaiaaikdaaeqaaOWaaeWaaeaacq aH4oqCcqGHsislcqaH4oqCdaahaaWcbeqaaiaadQfaaaaakiaawIca caGLPaaacqGHRaWkcaWGbbWaaSbaaSqaaiaaiodaaeqaaOWaaeWaae aacqaH4oqCcqGHsislcqaH4oqCdaahaaWcbeqaaiaadQfaaaaakiaa wIcacaGLPaaadaahaaWcbeqaaiaaikdaaaaaaa@4ECA@
    Where,
    s MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4Caaaa@36EB@
    Deformation resistance
    s 0 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4CamaaBa aaleaacaaIWaaabeaaaaa@37D1@
    Initial deformation resistance
    Darveaux material model formulation:(9)
    ˙ ¯ s c = C ss sinh n α σ ¯ exp dH R θ θ Z ˙ ¯ c = ˙ ¯ s c 1+ T Bexp B ˙ ¯ s c t MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaadaqdaa qaaiqbgIGioBaacaaaamaaDaaaleaacaWGZbaabaGaam4yaaaakiab g2da9iaadoeadaWgaaWcbaGaam4CaiaadohaaeqaaOGaci4CaiaacM gacaGGUbGaaiiAamaaCaaaleqabaGaamOBaaaakmaabmaabaGaeqyS de2aa0aaaeaacqaHdpWCaaaacaGLOaGaayzkaaGaciyzaiaacIhaca GGWbWaaeWaaeaacqGHsisldaWcaaqaaiaadsgacaWGibaabaGaamOu amaabmaabaGaeqiUdeNaeyOeI0IaeqiUde3aaWbaaSqabeaacaWGAb aaaaGccaGLOaGaayzkaaaaaaGaayjkaiaawMcaaaqaamaanaaabaGa fyicI4SbaiaaaaWaaWbaaSqabeaacaWGJbaaaOGaeyypa0Zaa0aaae aacuGHiiIZgaGaaaaadaqhaaWcbaGaam4CaaqaaiaadogaaaGcdaqa daqaaiaaigdacqGHRaWkcqGHiiIZdaWgaaWcbaGaamivaaqabaGcca WGcbGaciyzaiaacIhacaGGWbWaaeWaaeaacqGHsislcaWGcbWaa0aa aeaacuGHiiIZgaGaaaaadaqhaaWcbaGaam4CaaqaaiaadogaaaGcca WG0baacaGLOaGaayzkaaaacaGLOaGaayzkaaaaaaa@6F31@
  5. The units of various CTYPE material parameters:
    • STRAIN, TIMEC, TIMET
      Material Parameter
      Units
      A
      F n L 2 n T ( m + 1 ) MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOramaaCa aaleqabaGaeyOeI0IaamOBaaaakiaadYeadaahaaWcbeqaaiaaikda caWGUbaaaOGaamivamaaCaaaleqabaGaeyOeI0Iaaiikaiaad2gacq GHRaWkcaaIXaGaaiykaaaaaaa@4168@
    • HYPERB
      Material Parameter
      Units
      A
      T 1 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamivamaaCa aaleqabaGaeyOeI0IaaGymaaaaaaa@38A2@
      B
      F 1 L 2 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOramaaCa aaleqabaGaeyOeI0IaaGymaaaakiaadYeadaahaaWcbeqaaiaaikda aaaaaa@3A58@
      dH
      J M 1 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOsaiaad2 eadaahaaWcbeqaaiabgkHiTiaaigdaaaaaaa@396A@
      R
      J M 1 θ 1 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOsaiaad2 eadaahaaWcbeqaaiabgkHiTiaaigdaaaGccqaH4oqCdaahaaWcbeqa aiabgkHiTiaaigdaaaaaaa@3CFF@
      thetaZ
      θ MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqiUdehaaa@37AA@
    • ANAND
      Material Parameter
      Units
      A
      T 1 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamivamaaCa aaleqabaGaeyOeI0IaaGymaaaaaaa@38A2@
      B
      F 1 L 2 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOramaaCa aaleqabaGaeyOeI0IaaGymaaaakiaadYeadaahaaWcbeqaaiaaikda aaaaaa@3A58@
      dH
      J M 1 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOsaiaad2 eadaahaaWcbeqaaiabgkHiTiaaigdaaaaaaa@396A@
      R
      J M 1 θ 1 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOsaiaad2 eadaahaaWcbeqaaiabgkHiTiaaigdaaaGccqaH4oqCdaahaaWcbeqa aiabgkHiTiaaigdaaaaaaa@3CFF@
      thetaZ
      θ MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqiUdehaaa@37AA@
      A0
      F L 2 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOraiaadY eadaahaaWcbeqaaiabgkHiTiaaikdaaaaaaa@3966@
      s ^ MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabm4Cayaaja aaaa@36FB@
      F L 2 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOraiaadY eadaahaaWcbeqaaiabgkHiTiaaikdaaaaaaa@3966@
      S1
      F L 2 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOraiaadY eadaahaaWcbeqaaiabgkHiTiaaikdaaaaaaa@3966@
      S2
      F L 2 θ 1 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOraiaadY eadaahaaWcbeqaaiabgkHiTiaaikdaaaGccqaH4oqCdaahaaWcbeqa aiabgkHiTiaaigdaaaaaaa@3CFB@
      S3
      F L 2 θ 2 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOraiaadY eadaahaaWcbeqaaiabgkHiTiaaikdaaaGccqaH4oqCdaahaaWcbeqa aiabgkHiTiaaikdaaaaaaa@3CFC@
      A1
      F L 2 θ 1 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOraiaadY eadaahaaWcbeqaaiabgkHiTiaaikdaaaGccqaH4oqCdaahaaWcbeqa aiabgkHiTiaaigdaaaaaaa@3CFB@
      A2
      F L 2 θ 2 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOraiaadY eadaahaaWcbeqaaiabgkHiTiaaikdaaaGccqaH4oqCdaahaaWcbeqa aiabgkHiTiaaikdaaaaaaa@3CFC@
      A3
      F L 2 T MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOraiaadY eadaahaaWcbeqaaiabgkHiTiaaikdaaaGccaWGubaaaa@3A49@
      A4
      F L 2 T 2 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOraiaadY eadaahaaWcbeqaaiabgkHiTiaaikdaaaGccaWGubWaaWbaaSqabeaa caaIYaaaaaaa@3B32@
    • DARVEAU
      Material Parameter
      Units
      C s s MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4qamaaBa aaleaacaWGZbGaam4Caaqabaaaaa@38D7@
      T 1 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamivamaaCa aaleqabaGaeyOeI0IaaGymaaaaaaa@38A2@
      dH
      J M 1 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOsaiaad2 eadaahaaWcbeqaaiabgkHiTiaaigdaaaaaaa@396A@
      R
      J M 1 θ 1 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOsaiaad2 eadaahaaWcbeqaaiabgkHiTiaaigdaaaGccqaH4oqCdaahaaWcbeqa aiabgkHiTiaaigdaaaaaaa@3CFF@
      α MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqySdegaaa@3792@
      F 1 L 2 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOramaaCa aaleqabaGaeyOeI0IaaGymaaaakiaadYeadaahaaWcbeqaaiaaikda aaaaaa@3A58@
    Where,
    F MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOraaaa@36C2@
    Force
    L MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOraaaa@36C2@
    Length
    T MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOraaaa@36C2@
    Time

    Consider switching to another set of units if the values are too small. All other material parameters not mentioned above are dimensionless.

  6. A VISCO Subcase Entry is mandatory to conduct creep material analysis in a particular subcase.
  7. If CNTNLSUB is used with the time hardening form:
    • TIMEC indicates the accumulative time, only from the subcases with the VISCO entry.
    • TIMET indicates the accumulative time from all the connected subcases.

    For example, if there are 4 subcases – 1, 2, 3 and 5, where only Subcases 1, 3, and 5 are connected by CNTNLSUB.

    If subcases 1 and 5 have VISCO entry while Subcase 3 does not have the VISCO entry, then:
    • TIMEC will indicate the accumulative time from Subcases 1 and 5 only.
    • TIMET will indicate the accumulative time from Subcases 1, 3 and 5.

    If CNTNLSUB is not used, then both TIMEC and TIMET have the same effect of denoting the time for a specific subcase (only for subcases with the VISCO entry).

  8. The material parameters must be specified according to the chosen creep law. For example, the parameter B is used in both Hyperbolic Sine and the Darveaux models, but their meanings are different.

    For the Anand model, if the ratio dH/R is the only available unit, set R as 1.0 and use dH/R as the value of dH. If s 0 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4CamaaBa aaleaacaaIWaaabeaaaaa@37D1@ and h 0 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiAamaaBa aaleaacaaIWaaabeaaaaa@37C6@ are known, set them as the values of s 1 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4CamaaBa aaleaacaaIXaaabeaaaaa@37D2@ and A 0 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyqamaaBa aaleaacaaIWaaabeaaaaa@379F@ and set all other s i MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4CamaaBa aaleaacaWGPbaabeaaaaa@3805@ and A i MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyqamaaBa aaleaacaWGPbaabeaaaaa@37D3@ as zeroes.

  9. Format B can be used for a basic material parameter calibration functionality based on experimental creep test data. The calibration is based on a time hardening formulation. The upper and lower bounds can be used for searching the suitable parameter values during the calibration process.
  10. There are no default values for ALB and AUB. The following are example values:
    • ALB=1.0e-25, AUB=1.0e-20
    • ALB=1.0e-20, AUB=1.0e-15
    • ALB=1.0e-15, AUB=1.0e-10
    • ALB=1.0e-10, AUB=1.0e-5
    • ALB=1.0e-5, AUB=1.0