MATVP

Bulk Data Entry Defines material properties for nonlinear creep materials.

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

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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@+=feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqOVdGhaaa@37B6@ R dH
thetaZ a s^ MathType@MTEF@5@5@+=feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabm4Cayaaja aaaa@36FB@ A0 A1 A2 A3 A4
  S1 S2 S3            

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

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MATVP MID DARVEAU Css MathType@MTEF@5@5@+=feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4qamaaBaaaleaacaWGZbGaam4Caaqabaaaaa@38D7@ n   α MathType@MTEF@5@5@+=feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqySdegaaa@3792@ R dH
thetaZ εT MathType@MTEF@5@5@+=feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyTdu2aaSbaaSqaaiaadsfaaeqaaaaa@389F@ B          

Example A

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MATVP 101 STRAIN 3.28e-11 3.15 -0.2        

Example B

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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)

 
Css MathType@MTEF@5@5@+=feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4qamaaBaaaleaacaWGZbGaam4Caaqabaaaaa@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@+=feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqySdegaaa@3792@ Material parameter.

No default (Real > 0.0)

 
ξ MathType@MTEF@5@5@+=feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=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)

 
εT MathType@MTEF@5@5@+=feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyTdu2aaSbaaSqaaiaadsfaaeqaaaaa@389F@ Material parameter.

No default (Real)

 
a Material parameter.

No default (Real)

 
s^ MathType@MTEF@5@5@+=feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=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=A1m+1σ¯nm+1((m+1)ε¯c)mm+1 MathType@MTEF@5@5@+=feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGafqyTduMbaeHbaiaadaahaaWcbeqaaiaadogaaaGccqGH9aqpcaWGbbWaaWbaaSqabeaadaWcaaqaaiaaigdaaeaacaWGTbGaey4kaSIaaGymaaaaaaGccuaHdpWCgaqeamaaCaaaleqabaWaaSaaaeaacaWGUbaabaGaamyBaiabgUcaRiaaigdaaaaaaOWaaeWaaeaadaqadaqaaiaad2gacqGHRaWkcaaIXaaacaGLOaGaayzkaaGafqyTduMbaebadaahaaWcbeqaaiaadogaaaaakiaawIcacaGLPaaadaahaaWcbeqaamaalaaabaGaamyBaaqaaiaad2gacqGHRaWkcaaIXaaaaaaaaaa@501B@
    TIME hardening formulation:(2)
    ε¯˙c=Aσ¯ntm MathType@MTEF@5@5@+=feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGafqyTduMbaeHbaiaadaahaaWcbeqaaiaadogaaaGccqGH9aqpcaWGbbGafq4WdmNbaebadaahaaWcbeqaaiaad6gaaaGccaWG0bWaaWbaaSqabeaacaWGTb aaaaaa@3FC6@
    Where,
    ε¯˙c=23ε˙c:ε˙c MathType@MTEF@5@5@+=feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGafqyTduMbaeHbaiaadaahaaWcbeqaaiaadogaaaGccqGH9aqpdaGcaaqaamaalaaabaGaaGOmaaqaaiaaiodaaaGafqyTduMbaiaadaahaaWcbeqaaiaadogaaaGccaGG6aGafqyTduMbaiaadaahaaWcbeqaaiaadogaaaaabeaa aaa@41CE@
    Equivalent creep strain rate
    σ¯ MathType@MTEF@5@5@+=feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGafq4WdmNbae baaaa@37D2@
    Equivalent deviatoric stress
    t MathType@MTEF@5@5@+=feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiDaaaa@36F0@
    Total time
    HYPERB material model formulation:(3)
    ε¯˙c=Asinhn(Bσ¯)exp(dHR(θθz)) MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGafqyTduMbaeHbaiaadaahaaWcbeqaaiaadogaaaGcqaaaaaaaaaWdbiabg2da9iaabgeacaqGZbGaaeyAaiaab6gacaqGObWdamaaCaaaleqabaWdbiaad6gaaaGccaGGOaGaamOqaiqbeo8aZzaaraGaaiykaiaabwgacaqG4bGaaeiCamaabmaabaGaeyOeI0YaaSaaaeaacaWGKbGaamisaaqaaiaadkfadaqadaqaaiabeI7aXjabgkHiTiabeI7aXnaaCaaaleqabaGaamOEaaaaaOGaayjkaiaawMcaaaaaaiaawIcacaGLPaaaaaa@52C9@
    Where,
    θ and θz MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcqaaaaaaaaaWdbeaacqaH4oqCdaahaaWcbeqaaiaadQhaaaaaaa@38F8@
    The current and absolute zero temperatures, respectively.
    If dH MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcqaaaaaaaaaWdbeaacaWGKbGaamisaaaa@37CC@ is set to zero, the temperature dependence is absent.
    Anand material model formulation:(4)
    ˙¯c=Asinh1mξσ¯sexpdHRθθZ MathType@MTEF@5@5@+=feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa0aaaeaacuGHiiIZgaGaaaaadaahaaWcbeqaaiaadogaaaGccqGH9aqpcaWGbbGaci4CaiaacMgacaGGUbGaaiiAamaaCaaaleqabaWaaSaaaeaacaaIXaaabaGaamyBaaaaaaGcdaqadaqaaiabe67a4naalaaabaWaa0aaaeaacqaHdpWCaaaabaGaam4CaaaaaiaawIcacaGLPaaaciGGLbGaaiiEaiaacchadaqadaqaaiabgkHiTmaalaaabaGaamizaiaadIeaaeaacaWGsbWaaeWaaeaacqaH4oqCcqGHsislcqaH4oqCdaahaaWcbeqaaiaadQfaaaaakiaawIcacaGLPaaaaaaacaGLOaGaayzkaaaaaa@5542@
    (5)
    s˙=ho1ss*asign1ss*˙¯c MathType@MTEF@5@5@+=feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabm4CayaacaGaeyypa0JaamiAamaaBaaaleaacaWGVbaabeaakmaaemaabaGaaGymaiabgkHiTmaalaaabaGaam4CaaqaaiaadohadaahaaWcbeqaaiaacQcaaaaaaaGccaGLhWUaayjcSdWaaWbaaSqabeaacaWGHbaaaOGaam4CaiaadMgacaWGNbGaamOBamaabmaabaGaaGymaiabgkHiTmaalaaabaGaam4CaaqaaiaadohadaahaaWcbeqaaiaacQcaaaaaaaGccaGLOaGaayzkaaWaa0aaaeaacuGHiiIZgaGaaaaadaahaaWcbeqaaiaadogaaa aaaa@4F6B@
    (6)
    s*=s^1A˙¯cexpdHRθθZn MathType@MTEF@5@5@+=feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4CaiaacQcacqGH9aqpceWGZbGbaKaadaWadaqaamaalaaabaGaaGymaaqaaiaadgeaaaWaa0aaaeaacuGHiiIZgaGaaaaadaahaaWcbeqaaiaadogaaaGcciGGLbGaaiiEaiaacchadaqadaqaamaalaaabaGaamizaiaadIeaaeaacaWGsbWaaeWaaeaacqaH4oqCcqGHsislcqaH4oqCdaahaaWcbeqaaiaadQfaaaaakiaawIcacaGLPaaaaaaacaGLOaGaayzkaaaacaGLBbGaayzxaaWaaWbaaSqabeaacaWGUbaaaaaa@4F00@
    (7)
    h0=A0+A1θθZ+A2θθZ2+A3˙¯c+A4˙¯c2 MathType@MTEF@5@5@+=feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=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@5BC5@
    (8)
    s0=S1+S2θθZ+A3θθZ2 MathType@MTEF@5@5@+=feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4CamaaBaaaleaacaaIWaaabeaakiabg2da9iaadofadaWgaaWcbaGaaGymaaqabaGccqGHRaWkcaWGtbWaaSbaaSqaaiaaikdaaeqaaOWaaeWaaeaacqaH4oqCcqGHsislcqaH4oqCdaahaaWcbeqaaiaadQfaaaaakiaawIcacaGLPaaacqGHRaWkcaWGbbWaaSbaaSqaaiaaiodaaeqaaOWaaeWaaeaacqaH4oqCcqGHsislcqaH4oqCdaahaaWcbeqaaiaadQfaaaaakiaawIcacaGLPaaadaahaaWcbeqaaiaaikdaaaaaaa@4ECA@
    Where,
    s MathType@MTEF@5@5@+=feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4Caaaa@36EB@
    Deformation resistance
    s0 MathType@MTEF@5@5@+=feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4CamaaBaaaleaacaaIWaaabeaaaaa@37D1@
    Initial deformation resistance
    Darveaux material model formulation:(9)
    ˙¯sc=Csssinhnασ¯expdHRθθZ˙¯c=˙¯sc1+TBexpB˙¯sct MathType@MTEF@5@5@+=feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=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@6F31@
  5. The units of various CTYPE material parameters:
    • STRAIN, TIMEC, TIMET
      Material Parameter
      Units
      A
      FnL2nT(m+1) MathType@MTEF@5@5@+=feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOramaaCaaaleqabaGaeyOeI0IaamOBaaaakiaadYeadaahaaWcbeqaaiaaikdacaWGUbaaaOGaamivamaaCaaaleqabaGaeyOeI0Iaaiikaiaad2gacqGHRaWkcaaIXaGaaiykaaaaaaa@4168@
    • HYPERB
      Material Parameter
      Units
      A
      T1 MathType@MTEF@5@5@+=feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamivamaaCaaaleqabaGaeyOeI0IaaGymaaaaaaa@38A2@
      B
      F1L2 MathType@MTEF@5@5@+=feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOramaaCaaaleqabaGaeyOeI0IaaGymaaaakiaadYeadaahaaWcbeqaaiaaikda aaaaaa@3A58@
      dH
      JM1 MathType@MTEF@5@5@+=feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOsaiaad2eadaahaaWcbeqaaiabgkHiTiaaigdaaaaaaa@396A@
      R
      JM1θ1 MathType@MTEF@5@5@+=feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOsaiaad2eadaahaaWcbeqaaiabgkHiTiaaigdaaaGccqaH4oqCdaahaaWcbeqaaiabgkHiTiaaigdaaaaaaa@3CFF@
      thetaZ
      θ MathType@MTEF@5@5@+=feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqiUdehaaa@37AA@
    • ANAND
      Material Parameter
      Units
      A
      T1 MathType@MTEF@5@5@+=feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamivamaaCaaaleqabaGaeyOeI0IaaGymaaaaaaa@38A2@
      B
      F1L2 MathType@MTEF@5@5@+=feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOramaaCaaaleqabaGaeyOeI0IaaGymaaaakiaadYeadaahaaWcbeqaaiaaikda aaaaaa@3A58@
      dH
      JM1 MathType@MTEF@5@5@+=feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOsaiaad2eadaahaaWcbeqaaiabgkHiTiaaigdaaaaaaa@396A@
      R
      JM1θ1 MathType@MTEF@5@5@+=feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOsaiaad2eadaahaaWcbeqaaiabgkHiTiaaigdaaaGccqaH4oqCdaahaaWcbeqaaiabgkHiTiaaigdaaaaaaa@3CFF@
      thetaZ
      θ MathType@MTEF@5@5@+=feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqiUdehaaa@37AA@
      A0
      FL2 MathType@MTEF@5@5@+=feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOraiaadYeadaahaaWcbeqaaiabgkHiTiaaikdaaaaaaa@3966@
      s^ MathType@MTEF@5@5@+=feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabm4Cayaaja aaaa@36FB@
      FL2 MathType@MTEF@5@5@+=feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOraiaadYeadaahaaWcbeqaaiabgkHiTiaaikdaaaaaaa@3966@
      S1
      FL2 MathType@MTEF@5@5@+=feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOraiaadYeadaahaaWcbeqaaiabgkHiTiaaikdaaaaaaa@3966@
      S2
      FL2θ1 MathType@MTEF@5@5@+=feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOraiaadYeadaahaaWcbeqaaiabgkHiTiaaikdaaaGccqaH4oqCdaahaaWcbeqaaiabgkHiTiaaigdaaaaaaa@3CFB@
      S3
      FL2θ2 MathType@MTEF@5@5@+=feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOraiaadYeadaahaaWcbeqaaiabgkHiTiaaikdaaaGccqaH4oqCdaahaaWcbeqaaiabgkHiTiaaikdaaaaaaa@3CFC@
      A1
      FL2θ1 MathType@MTEF@5@5@+=feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOraiaadYeadaahaaWcbeqaaiabgkHiTiaaikdaaaGccqaH4oqCdaahaaWcbeqaaiabgkHiTiaaigdaaaaaaa@3CFB@
      A2
      FL2θ2 MathType@MTEF@5@5@+=feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOraiaadYeadaahaaWcbeqaaiabgkHiTiaaikdaaaGccqaH4oqCdaahaaWcbeqaaiabgkHiTiaaikdaaaaaaa@3CFC@
      A3
      FL2T MathType@MTEF@5@5@+=feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOraiaadYeadaahaaWcbeqaaiabgkHiTiaaikdaaaGccaWGubaaaa@3A49@
      A4
      FL2T2 MathType@MTEF@5@5@+=feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOraiaadYeadaahaaWcbeqaaiabgkHiTiaaikdaaaGccaWGubWaaWbaaSqabeaacaaIYaaaaaaa@3B32@
    • DARVEAU
      Material Parameter
      Units
      Css MathType@MTEF@5@5@+=feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4qamaaBaaaleaacaWGZbGaam4Caaqabaaaaa@38D7@
      T1 MathType@MTEF@5@5@+=feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamivamaaCaaaleqabaGaeyOeI0IaaGymaaaaaaa@38A2@
      dH
      JM1 MathType@MTEF@5@5@+=feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOsaiaad2eadaahaaWcbeqaaiabgkHiTiaaigdaaaaaaa@396A@
      R
      JM1θ1 MathType@MTEF@5@5@+=feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOsaiaad2eadaahaaWcbeqaaiabgkHiTiaaigdaaaGccqaH4oqCdaahaaWcbeqaaiabgkHiTiaaigdaaaaaaa@3CFF@
      α MathType@MTEF@5@5@+=feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqySdegaaa@3792@
      F1L2 MathType@MTEF@5@5@+=feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOramaaCaaaleqabaGaeyOeI0IaaGymaaaakiaadYeadaahaaWcbeqaaiaaikda aaaaaa@3A58@
    Where,
    F MathType@MTEF@5@5@+=feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOraaaa@36C2@
    Force
    L MathType@MTEF@5@5@+=feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOraaaa@36C2@
    Length
    T MathType@MTEF@5@5@+=feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=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 s0 MathType@MTEF@5@5@+=feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4CamaaBaaaleaacaaIWaaabeaaaaa@37D1@ and h0 MathType@MTEF@5@5@+=feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiAamaaBaaaleaacaaIWaaabeaaaaa@37C6@ are known, set them as the values of s1 MathType@MTEF@5@5@+=feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4CamaaBaaaleaacaaIXaaabeaaaaa@37D2@ and A0 MathType@MTEF@5@5@+=feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyqamaaBaaaleaacaaIWaaabeaaaaa@379F@ and set all other si MathType@MTEF@5@5@+=feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4CamaaBaaaleaacaWGPbaabeaaaaa@3805@ and Ai MathType@MTEF@5@5@+=feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyqamaaBaaaleaacaWGPbaabeaaaaa@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