/MAT/LAW87 (BARLAT2000)

Block Format Keyword This elasto-plastic law is developed for anisotropic materials, especially aluminum alloys.

Yield stresses can be defined either by user-defined functions (plastic strain versus stress) or analytically by a combination of Swift-Voce model. The model is based on Barlat YLD2000 criterion. 1

Format

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
/MAT/LAW87/mat_ID/unit_ID or /MAT/BARLAT2000/mat_ID/unit_ID
mat_title
ρ i                
E ν   Iflag VP c p
If Ifit =0, insert the following two lines
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
α 1 α 2 α 3 α 4 Ifit  
α 5 α 6 α 7 α 8  
If Ifit =1, insert the following two lines.
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
σ 00 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaa Wdbiabeo8aZ9aadaWgaaWcbaWdbiaaicdacaaIWaaapaqabaaaaa@3A0D@ σ 45 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaa Wdbiabeo8aZ9aadaWgaaWcbaWdbiaaisdacaaI1aaapaqabaaaaa@3A16@ σ 90 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaa Wdbiabeo8aZ9aadaWgaaWcbaWdbiaaiMdacaaIWaaapaqabaaaaa@3A16@ σ b MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaa Wdbiabeo8aZ9aadaWgaaWcbaWdbiaadkgaa8aabeaaaaa@3980@ Ifit
r 00 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaa WdbiaadkhapaWaaSbaaSqaa8qacaaIWaGaaGimaaWdaeqaaaaa@3941@ r 45 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaa WdbiaadkhapaWaaSbaaSqaa8qacaaI0aGaaGynaaWdaeqaaaaa@394A@ r 90 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaa WdbiaadkhapaWaaSbaaSqaa8qacaaI5aGaaGimaaWdaeqaaaaa@394A@ r b MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaa WdbiaadkhapaWaaSbaaSqaa8qacaWGIbaapaqabaaaaa@38B4@
Hardening parameter.
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
Chard
Input for material yield and hardening. If Iflag=0 read:
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
  a MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyyaaaa@36D9@         Fcut Fsmooth Nrate
Blank line
If Iflag=0, Nrate read line(s):
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
fct_IDi Fscalei ε ˙ i MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGafqyTduMbai aadaWgaaWcbaGaamyAaaqabaaaaa@38BE@
If Iflag=1 read:
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
a MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyyaaaa@36D9@ α s v MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqySde2aaS baaSqaaiaadohacaWG2baabeaaaaa@39B2@ n Fcut Fsmooth
A ε 0 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyTdu2aaS baaSqaaiaaicdaaeqaaaaa@3881@ Q B K0
If Iflag=2 read:
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
  a MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyyaaaa@36D9@        
Am Bm Cm Dm Pm
Qm ε 0 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyTdu2aaS baaSqaaiaaicdaaeqaaaaa@3881@ mart VM0    
A H S MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyqamaaBa aaleaacaWGibGaam4uaaqabaaaaa@388B@ B H S MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOqamaaBa aaleaacaWGibGaam4uaaqabaaaaa@388C@ MHS NHS EPS0HS
HMART K 1 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4samaaBa aaleaacaaIXaaabeaaaaa@37AB@ K 2 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4samaaBa aaleaacaaIYaaabeaaaaa@37AC@    
T0   Cp Eta  
Read if Chard > 0:
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
CRC1 CRA1 CRC2 CRA2
CRC3 CRA3 CRC4 CRA4

Definition

Field Contents SI Unit Example
mat_ID Material identifier

(Integer, maximum 10 digits)

 
unit_ID Unit Identifier

(Integer, maximum 10 digits)

 
mat_title Material title

(Character, maximum 100 characters)

 
ρ i Initial density

(Real)

[ kg m 3 ]
E Young's modulus

(Real)

[ Pa ]
ν Poisson's ratio

(Real)

 
Iflag Yield stress definition flag.
= 0 (Default)
Tabulated input and function numbers defined in Nrate.
= 1
Swift-Voce analytic formulation and then Nrate = 0.
= 2
Hansel hardening model.

(Integer)

 
VP Strain rate choice flag. 4
= 0 (Default)
Strain rate effect on yield stress depends on the total strain rate.
= 1
Strain rate effect on yield depends on the plastic strain rate.

(Integer)

 
Ifit Material parameter fit flag.
=0 (Default)
Input Barlat parameters in α 1 through α 8 .
=1
Barlat parameters are calculated from the test data which is input as σ 00 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaa Wdbiabeo8aZ9aadaWgaaWcbaWdbiaaicdacaaIWaaapaqabaaaaa@3A10@ , σ 45 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaa Wdbiabeo8aZ9aadaWgaaWcbaWdbiaaicdacaaIWaaapaqabaaaaa@3A10@ , σ 90 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaa Wdbiabeo8aZ9aadaWgaaWcbaWdbiaaicdacaaIWaaapaqabaaaaa@3A10@ , σ b MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaa Wdbiabeo8aZ9aadaWgaaWcbaWdbiaadkgaa8aabeaaaaa@3983@ , r 00 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaa WdbiaadkhapaWaaSbaaSqaa8qacaaIWaGaaGimaaWdaeqaaaaa@3944@ , r 45 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaa WdbiaadkhapaWaaSbaaSqaa8qacaaIWaGaaGimaaWdaeqaaaaa@3944@ , r 90 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaa WdbiaadkhapaWaaSbaaSqaa8qacaaIWaGaaGimaaWdaeqaaaaa@3944@ , r b MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaa WdbiaadkhapaWaaSbaaSqaa8qacaWGIbaapaqabaaaaa@38B7@ .
(Integer)
 
α i Barlat material parameters with i=1~8.

(Real)

 
σ 00 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaa Wdbiabeo8aZ9aadaWgaaWcbaWdbiaaicdacaaIWaaapaqabaaaaa@3A10@ Yield strength in 00 direction (rolling direction).

(Real)

[ Pa ]
σ 45 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaa Wdbiabeo8aZ9aadaWgaaWcbaWdbiaaicdacaaIWaaapaqabaaaaa@3A10@ Yield strength in 45 direction.

(Real)

[ Pa ]
σ 90 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaa Wdbiabeo8aZ9aadaWgaaWcbaWdbiaaicdacaaIWaaapaqabaaaaa@3A10@ Yield strength in 90 direction.

(Real)

[ Pa ]
σ b MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaa Wdbiabeo8aZ9aadaWgaaWcbaWdbiaadkgaa8aabeaaaaa@3983@ Yield strength biaxial loading.

(Real)

[ Pa ]
r 00 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaa WdbiaadkhapaWaaSbaaSqaa8qacaaIWaGaaGimaaWdaeqaaaaa@3944@ Lankford r-value in 00 direction (rolling direction).

(Real)

 
r 45 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaa WdbiaadkhapaWaaSbaaSqaa8qacaaIWaGaaGimaaWdaeqaaaaa@3944@ Lankford r-value in 45 direction.

(Real)

 
r 90 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaa WdbiaadkhapaWaaSbaaSqaa8qacaaIWaGaaGimaaWdaeqaaaaa@3944@ Lankford r-value in 90 direction.

(Real)

 
r b MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaa WdbiaadkhapaWaaSbaaSqaa8qacaWGIbaapaqabaaaaa@38B7@ Lankford r-value in biaxial loading.

(Real)

 
Chard Hardening coefficient.
=0
Hardening is a full isotropic model.
=1
Hardening uses the kinematic Chaboche Roussilier model.
= value between 0 and 1
Weight for the combined isotropic kinematic hardening.
(Integer)
 
a Exponent in yield function. 2

Default = 2 (Integer)

 
α s v MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqySde2aaS baaSqaaiaadohacaWG2baabeaaaaa@39B5@ Swift-Voce weighting coefficient. 2
= 1
Swift hardening law.
= 0
Voce hardening law.

Default = 0.0 (Real)

 
Q Voce hardening coefficient.

(Real)

[ Pa ]
K0 Voce hardening parameter.

(Real)

[ Pa ]
B Voce plastic strain coefficient.

Default = 0.0 (Real)

 
A Swift hardening coefficient.

(Real)

[ Pa ]
n Swift hardening exponent.

Default = 1.0 (Real)

 
ε 0 Swift hardening parameter.

Default = 0.00 (Real)

 
Fsmooth Smooth strain rate option flag when VP=0. 4
= 0 (Default)
No strain rate smoothing.
= 1
Strain rate smoothing active.

(Integer)

 
Fcut Cutoff frequency for strain rate filtering, Appendix: Filtering. 7

Default = 10KHz (Real)

[Hz]
c Cowper-Seymonds reference strain rate.

(Real)

[ 1 s ]
p Cowper-Seymonds strain rate exponent. 5

(Real)

 
Nrate Number of yield functions. 2
Nrate > 0
Used only if Iflag = 0.

(Integer)

 
fct_IDi Yield stress versus plastic strain identifier.

(Integer)

 
Fscalei Scale factor for ordinate for fct_IDi.

Default = 1.0 (Real)

[ Pa ]
ε ˙ i Strain rate i corresponding to fct_IDi.
VP =0
Total strain rate for fct_IDi.
VP =1
Plastic strain rate for fct_IDi.

Default = 1.0 (Real) 5

[ 1 s ]
Am Parameter A for martensite rate equation.

(Real)

 
Bm Parameter B for martensite rate equation.

(Real)

 
Cm Parameter C for martensite rate equation.

(Real)

 
Dm Parameter D for martensite rate equation.

(Real)

[ 1 K ] MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeaaciGaaiaabeqaamaabaabaaGcbaWaamWaaeaada WcaaqaaiaaigdaaeaacaWGlbaaaaGaay5waiaaw2faaaaa@3981@
Pm Parameter P for martensite rate equation.

(Real)

 
Qm Parameter Q for martensite rate equation.

(Real)

[ K ]
ε 0 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyTdu2aaS baaSqaaiaaicdaaeqaaaaa@3881@ mart Parameter ε 0 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyTdu2aaS baaSqaaiaaicdaaeqaaaaa@3881@ for martensite rate equation.

(Real)

 
VM0 Initial volume fraction VM0 for martensite rate equation.

(Real)

 
A H S MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyqamaaBa aaleaacaWGibGaam4uaaqabaaaaa@388B@ Parameter A H S MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyqamaaBa aaleaacaWGibGaam4uaaqabaaaaa@388B@ in Hansel hardening law.

(Real)

[ Pa ]
B H S MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOqamaaBa aaleaacaWGibGaam4uaaqabaaaaa@388C@ Parameter B H S MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOqamaaBa aaleaacaWGibGaam4uaaqabaaaaa@388C@ in Hansel hardening law.

(Real)

[ Pa ]
MHS Coefficient m MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyBaaaa@36E5@ in Hansel hardening law.

(Real)

 
NHS Exponent n MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOBaaaa@36E6@ in Hansel hardening law.

(Real)

 
EPS0HS Reference strain ε 0 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyTdu2aaS baaSqaaiaaicdaaeqaaaaa@3881@ in Hansel hardening law.

(Real)

 
HMART Martensite Δ H γ α MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeuiLdqKaam isamaaBaaaleaacqaHZoWzcqaHXoqyaeqaaaaa@3B99@ coefficient in Hansel hardening law. [ Pa ]
K 1 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4samaaBa aaleaacaaIXaaabeaaaaa@37AB@ Temperature parameter K 1 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4samaaBa aaleaacaaIXaaabeaaaaa@37AB@ in Hansel hardening law.

(Real)

 
K 2 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4samaaBa aaleaacaaIYaaabeaaaaa@37AC@ Temperature parameter K 2 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4samaaBa aaleaacaaIYaaabeaaaaa@37AC@ in Hansel hardening law.

(Real)

 
T0 Initial temperature.

(Real)

[ K ]
Cp Specific heat per mass unit.

(Real)

[ J kgK ] MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeaaciGaaiaabeqaamaabaabaaGcbaWaamWaaeaada WcaaqaaiaabQeaaeaacaqGRbGaae4zaiabgwSixlaabUeaaaaacaGL BbGaayzxaaaaaa@3DB3@
Eta Taylor-Quinney coefficient.

(Real)

 
CRCi Chaboche Rousselier kinematic parameter C i=1~4.

(Real) 3

 
CRAi Chaboche Rousselier kinematic parameter A i=1~4.

(Real) 3

[ Pa ]

Example 1 (with Barlat parameters input Iflag=0 and Ifit=0)

This example uses Barlat parameters input (Ifit=0) and tabulated yield stress-strain curve input (Iflag=0).
#RADIOSS STARTER
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/UNIT/1
unit for mat
                  kg                  mm                  ms
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#-  2. MATERIALS:
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/MAT/LAW87/1/1
Steel 
#              RHO_I
              7.8E-6                   0
#                  E                  Nu     IFlag        VP             coeff_c               exp_p              
                 210                 0.3         0         1             4.15401                3.57             
#                 a1                  a2                  a3                  a4     I_fit
                 1.0                 1.0                 1.0                 1.0         0
#                 a5                  a6                  a7                  a8
                 1.0                 1.0                 1.0                 1.0
#              Chard
                   0
#              exp_a               ALPHA                NEXP                Fcut   Fsmooth     NRATE
                   2                   0                   0                   0         1         1
# Blank

#  func_id                        YSCALE         strain rate
         4                           1.5                   1
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/FUNCT/4
Steel
#                  X                   Y
                   0                  .3
               0.007                  .5
                0.05                  .7
                 0.1                 .75
                 0.3                  .9
                   1                 1.2				 
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#ENDDATA
/END
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|

Example 2 (with experiment data input Ifit=1)

Here Ifit=1 is used to input material experiment data of yield strength and Lankford r-value in 00, 45, 90 directions and in biaxial loading. Then related Barlat parameters will be automatically fitted and used. Swift-Voce parameters input used with Iflag=1.
#RADIOSS STARTER
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/UNIT/1
unit for mat
                   g                  mm                  ms
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/MAT/LAW87/1/1
Aluminum
#              RHO_I
              2.7E-3                   0
#                  E                  Nu     IFlag        VP             coeff_c               exp_p 
               70000                 0.3         1         0                   0                   0
#              sig00               sig45               sig90                sigb     I_fit
          133.179899          133.102756          132.330693          162.330301         1
#                r00                 r45                 r90                  rb
         0.703242569         0.486264221         0.865336191         0.546807587
#              Chard
                   0
#              exp_a               ALPHA                NEXP                Fcut   Fsmooth
                   8                0.55                0.21                   0         1
#             ASwift                Eps0               Qvoce                Beta                  KO
                415.             0.00220               174.7               11.19               132.4
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#ENDDATA
/END
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|

Example 3 (with Hansel yield model (Iflag=2) and kinematic hardening model (Chard=1))

In this example use Barlat parameters input (Ifit=0) with Hansel yield model (Iflag=2) and kinematic hardening model (Chard=1).
#RADIOSS STARTER
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/UNIT/1
unit for mat
                  kg                  mm                  ms
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/MAT/BARLAT2000/2/1
Steel
#              RHO_I
            7.800E-6                   0
#                  E                  Nu     IFlag        VP                   c                   P
                 210                  .3         2         0                   0                   0
#                 a1                  a2                  a3                  a4     I_fit
              0.4865              1.3783              0.7536              1.0246         0
#                 a5                  a6                  a7                  a8
              1.0363              0.9036              1.2321              1.4858
#              Chard  
                   1
#              exp_a
                   8                                                                                
#                 AM                  BM                  CM                  DM                  PM
               0.578               0.185               -6.78                0.02                7.54
#                 QM              E0MART                 VM0
              1379.0                0.01              0.1690
#                AHS                 BHS                 MHS                 NHS              EPS0HS
              -0.261               9.170               0.118               0.401              0.0988
#              HMART                  K1                  K2
              0.5490                3.95            -0.00681
#              TEMP0                TREF                  CP                 ETA
                300.                293.                460.                 0.1
#               CRC1                CRA1                CRC2                CRA2
                  80               0.052                   0                  0. 
#               CRC3                CRA3                CRC4                CRA4
                   0                 0.0                   0                  0.  
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#ENDDATA
/END
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|

Comments

  1. The yield function is expressed as:(1)
    f = σ ¯ σ y
    (2)
    σ ¯ =   1 2 1 a ( φ ( X ) + φ ( X ) )   1 a
    (3)
    φ ( X ) = | X 1 X 2 | a  
    (4)
      φ ( X ) = | 2 X 2 + X 1 | a + | 2 X 1 + X 2 | a
    X ' and X " denote the principal values of the tensors X ' and X " which are a linear transformation of the stress deviator, which leads to:(5)
    φ ( X ) =   [ ( X x x X y y ) 2 + 4 ( X x y ) 2 ] a 2  
    (6)
      φ ( X ) = [ 3 2 ( X x x X y y ) + 1 2 ( X x x X y y ) 2 + 4 ( X x y ) 2 ] a + [ 3 2 ( X x x X y y ) 1 2 ( X x x X y y ) 2 + 4 ( X x y ) 2 ] a MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOabaeqabaaeaaaaaa aaa8qacaGGGcGafqOXdOMbayaadaqadaWdaeaapeGabmiwayaagaaa caGLOaGaayzkaaGaeyypa0ZaamWaa8aabaWdbmaalaaapaqaa8qaca aIZaaapaqaa8qacaaIYaaaamaabmaapaqaa8qaceWGybGbayaapaWa aSbaaSqaa8qacaWG4bGaamiEaaWdaeqaaOWdbiabgkHiTiqadIfaga Gba8aadaWgaaWcbaWdbiaadMhacaWG5baapaqabaaak8qacaGLOaGa ayzkaaGaey4kaSYaaSaaa8aabaWdbiaaigdaa8aabaWdbiaaikdaaa WaaOaaa8aabaWdbmaabmaapaqaa8qaceWGybGbayaapaWaaSbaaSqa a8qacaWG4bGaamiEaaWdaeqaaOWdbiabgkHiTiqadIfagaGba8aada WgaaWcbaWdbiaadMhacaWG5baapaqabaaak8qacaGLOaGaayzkaaWd amaaCaaaleqabaWdbiaaikdaaaGccqGHRaWkcaaI0aWaaeWaa8aaba WdbiqadIfagaGba8aadaWgaaWcbaGaamiEaiaadMhaaeqaaaGcpeGa ayjkaiaawMcaamaaCaaaleqabaGaaGOmaaaaaeqaaaGccaGLBbGaay zxaaWdamaaCaaaleqabaWdbiaadggaaaGccqGHRaWkaeaadaWadaWd aeaapeWaaSaaa8aabaWdbiaaiodaa8aabaWdbiaaikdaaaWaaeWaa8 aabaWdbiqadIfagaGba8aadaWgaaWcbaWdbiaadIhacaWG4baapaqa baGcpeGaeyOeI0IabmiwayaagaWdamaaBaaaleaapeGaamyEaiaadM haa8aabeaaaOWdbiaawIcacaGLPaaacqGHsisldaWcaaWdaeaapeGa aGymaaWdaeaapeGaaGOmaaaadaGcaaWdaeaapeWaaeWaa8aabaWdbi qadIfagaGba8aadaWgaaWcbaWdbiaadIhacaWG4baapaqabaGcpeGa eyOeI0IabmiwayaagaWdamaaBaaaleaapeGaamyEaiaadMhaa8aabe aaaOWdbiaawIcacaGLPaaapaWaaWbaaSqabeaapeGaaGOmaaaakiab gUcaRiaaisdadaqadaWdaeaapeGabmiwayaagaWaaSbaaSqaaiaadI hacaWG5baabeaaaOGaayjkaiaawMcaamaaCaaaleqabaGaaGOmaaaa aeqaaaGccaGLBbGaayzxaaWdamaaCaaaleqabaWdbiaadggaaaaaaa a@835B@

    The tensors X ' and X " are linear transformations of the stress tensor:

    X = L σ     a n d     X = L σ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GabCiwa8aagaqba8qacqGH9aqpceWHmbWdayaafaWdbiaaho8acaGG GcGaaiiOaiaadggacaWGUbGaamizaiaacckacaGGGcGabCiwa8aaga Gba8qacqGH9aqpceWHmbGbayaacaWHdpaaaa@4603@ (7)
    L = 1 3 [ 2 α 1 α 1 0 α 2 2 α 2 0 0 0 3 α 7 ] MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GabCita8aagaqba8qacqGH9aqpdaWcaaWdaeaapeGaaGymaaWdaeaa peGaaG4maaaadaWadaWdaeaafaqabeWadaaabaWdbiaaikdacqaHXo qypaWaaSbaaSqaa8qacaaIXaaapaqabaaakeaapeGaeyOeI0IaeqyS de2damaaBaaaleaapeGaaGymaaWdaeqaaaGcbaWdbiaaicdaa8aaba WdbiabgkHiTiabeg7aH9aadaWgaaWcbaWdbiaaikdaa8aabeaaaOqa a8qacaaIYaGaeqySde2damaaBaaaleaapeGaaGOmaaWdaeqaaaGcba Wdbiaaicdaa8aabaWdbiaaicdaa8aabaWdbiaaicdaa8aabaWdbiaa iodacqaHXoqypaWaaSbaaSqaa8qacaaI3aaapaqabaaaaaGcpeGaay 5waiaaw2faaaaa@5181@
    (8)
    L = 1 9 [ 2 α 3 + 2 α 4 + 8 α 5 2 α 6 α 3 4 α 4 4 α 5 + 4 α 6 0 4 α 3 4 α 4 4 α 5 + α 6 2 α 3 + 8 α 4 + 2 α 5 2 α 6 0 0 0 9 α 8 ] MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GabCita8aagaGba8qacqGH9aqpdaWcaaWdaeaapeGaaGymaaWdaeaa peGaaGyoaaaadaWadaWdaeaafaqabeWadaaabaWdbiabgkHiTiaaik dacqaHXoqypaWaaSbaaSqaa8qacaaIZaaapaqabaGcpeGaey4kaSIa aGOmaiabeg7aH9aadaWgaaWcbaWdbiaaisdaa8aabeaak8qacqGHRa WkcaaI4aGaeqySde2damaaBaaaleaapeGaaGynaaWdaeqaaOWdbiab gkHiTiaaikdacqaHXoqypaWaaSbaaSqaa8qacaaI2aaapaqabaaake aapeGaeqySde2damaaBaaaleaapeGaaG4maaWdaeqaaOWdbiabgkHi TiaaisdacqaHXoqypaWaaSbaaSqaa8qacaaI0aaapaqabaGcpeGaey OeI0IaaGinaiabeg7aH9aadaWgaaWcbaWdbiaaiwdaa8aabeaak8qa cqGHRaWkcaaI0aGaeqySde2damaaBaaaleaapeGaaGOnaaWdaeqaaa GcbaWdbiaaicdaa8aabaWdbiaaisdacqaHXoqypaWaaSbaaSqaa8qa caaIZaaapaqabaGcpeGaeyOeI0IaaGinaiabeg7aH9aadaWgaaWcba Wdbiaaisdaa8aabeaak8qacqGHsislcaaI0aGaeqySde2damaaBaaa leaapeGaaGynaaWdaeqaaOWdbiabgUcaRiabeg7aH9aadaWgaaWcba WdbiaaiAdaa8aabeaaaOqaa8qacqGHsislcaaIYaGaeqySde2damaa BaaaleaapeGaaG4maaWdaeqaaOWdbiabgUcaRiaaiIdacqaHXoqypa WaaSbaaSqaa8qacaaI0aaapaqabaGcpeGaey4kaSIaaGOmaiabeg7a H9aadaWgaaWcbaWdbiaaiwdaa8aabeaak8qacqGHsislcaaIYaGaeq ySde2damaaBaaaleaapeGaaGOnaaWdaeqaaaGcbaWdbiaaicdaa8aa baWdbiaaicdaa8aabaWdbiaaicdaa8aabaWdbiaaiMdacqaHXoqypa WaaSbaaSqaa8qacaaI4aaapaqabaaaaaGcpeGaay5waiaaw2faaaaa @872F@
  2. The yield stress could be defined either by tabulated input or using the analytic Swift-Voce model.
    • Iflag=0: Tabulated.
      • It is possible to add total strain rate dependency by defining a number Nrate of functions.
    • Iflag=1: The analytic Swift-Voce model is expressed as:(9)
      σ y = α s v [ A ( ε ¯ p + ε 0 ) n ] + ( 1 α s v ) [ K 0 + Q ( 1 exp ( B ε ¯ p ) ) ] MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Wdm3aaS baaSqaaiaadMhaaeqaaOGaeyypa0JaeqySde2aaSbaaSqaaiaadoha caWG2baabeaakmaadmaabaGaamyqamaabmaabaGafqyTduMbaebada WgaaWcbaGaamiCaaqabaGccqGHRaWkcqaH1oqzdaWgaaWcbaGaaGim aaqabaaakiaawIcacaGLPaaadaahaaWcbeqaaiaad6gaaaaakiaawU facaGLDbaacqGHRaWkdaqadaqaaiaaigdacqGHsislcqaHXoqydaWg aaWcbaGaam4CaiaadAhaaeqaaaGccaGLOaGaayzkaaWaamWaaeaaca WGlbWaaSbaaSqaaiaaicdaaeqaaOGaey4kaSIaamyuamaabmaabaGa aGymaiabgkHiTiGacwgacaGG4bGaaiiCamaabmaabaGaeyOeI0Iaam Oqaiqbew7aLzaaraWaaSbaaSqaaiaadchaaeqaaaGccaGLOaGaayzk aaaacaGLOaGaayzkaaaacaGLBbGaayzxaaaaaa@6301@
      Where,
      ε ¯ p
      Equivalent plastic strain.
    • Iflag=2: Hansel hardening model is considered.(10)
      σ y = B H S B H S A H S e m ε ¯ p + ε 0 n K 1 K 2 T + Δ H γ α V m MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Wdm3aaS baaSqaaiaadMhaaeqaaOGaeyypa0ZaaiWaaeaacaWGcbWaaSbaaSqa aiaadIeacaWGtbaabeaakiabgkHiTmaabmaabaGaamOqamaaBaaale aacaWGibGaam4uaaqabaGccqGHsislcaWGbbWaaSbaaSqaaiaadIea caWGtbaabeaaaOGaayjkaiaawMcaaiaadwgadaahaaWcbeqaamaabm aabaGaeyOeI0IaamyBamaadmaabaGafqyTduMbaebadaahaaadbeqa aiaadchaaaWccqGHRaWkcqaH1oqzdaWgaaadbaGaaGimaaqabaaali aawUfacaGLDbaadaahaaadbeqaaiaad6gaaaaaliaawIcacaGLPaaa aaaakiaawUhacaGL9baadaqadaqaaiaadUeadaWgaaWcbaGaaGymaa qabaGccqGHsislcaWGlbWaaSbaaSqaaiaaikdaaeqaaOGaamivaaGa ayjkaiaawMcaaiabgUcaRiabfs5aejaadIeadaWgaaWcbaGaeq4SdC MaeqySdegabeaakiaadAfadaWgaaWcbaGaamyBaaqabaaaaa@64D4@
      Temperature is updated in the law when adiabatic conditions:(11)
      Δ T = η σ ¯ d ε ¯ p ρ C p MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeuiLdqKaam ivaiabg2da9iabeE7aOnaalaaabaWaa0aaaeaacqaHdpWCaaGaamiz amaanaaabaGaeqyTdugaamaaBaaaleaacaWGWbaabeaaaOqaaiabeg 8aYjaadoeadaWgaaWcbaGaamiCaaqabaaaaaaa@443D@
      The martensite rate equation is computed as follows:(12)
      V m ε = 0 i f ε < ε 0 B A e Q T 1 V m V m B + 1 B V m p 2 1 tanh C + D T f ε ε 0 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaacq GHciITcaWGwbWaaSbaaSqaaiaad2gaaeqaaaGcbaGaeyOaIyRaeqyT dugaaiabg2da9maaceaabaqbaeqabiGaaaqaaiaaicdaaeaacaWGPb GaamOzaiabew7aLjabgYda8iabew7aLnaaBaaaleaacaaIWaaabeaa aOqaamaalaaabaGaamOqaaqaaiaadgeaaaGaeyyXICTaamyzamaaCa aaleqabaWaaeWaaeaadaWcaaqaaiaadgfaaeaacaWGubaaaaGaayjk aiaawMcaaaaakiabgwSixpaabmaabaWaaSaaaeaacaaIXaGaeyOeI0 IaamOvamaaBaaaleaacaWGTbaabeaaaOqaaiaadAfadaWgaaWcbaGa amyBaaqabaaaaaGccaGLOaGaayzkaaWaaWbaaSqabeaadaqadaqaam aalaaabaGaamOqaiabgUcaRiaaigdaaeaacaWGcbaaaaGaayjkaiaa wMcaaaaakiabgwSixpaalaaabaWaaeWaaeaacaWGwbWaaSbaaSqaai aad2gaaeqaaaGccaGLOaGaayzkaaWaaWbaaSqabeaacaWGWbaaaaGc baGaaGOmaaaacqGHflY1daqadaqaaiaaigdacqGHsislciGG0bGaai yyaiaac6gacaGGObWaamWaaeaacaWGdbGaey4kaSIaamiraiaadsfa aiaawUfacaGLDbaaaiaawIcacaGLPaaaaeaacaWGMbGaeqyTduMaey yzImRaeqyTdu2aaSbaaSqaaiaaicdaaeqaaaaaaOGaay5Eaaaaaa@7A8D@
  3. If Chard>0, a kinematic hardening model of Chaboche Rousselier is used:
    • The back stress is calculated as:(13)
      a = i = 1 4 a i MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyyaiabg2 da9maaqahabaGaamyyamaaBaaaleaacaWGPbaabeaaaeaacaWGPbGa eyypa0JaaGymaaqaaiaaisdaa0GaeyyeIuoaaaa@3F84@
      With,(14)
      a i = A i C i d ε p C i a i Δ ε ¯ p MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyyamaaBa aaleaacaWGPbaabeaakiabg2da9iaadgeadaWgaaWcbaGaamyAaaqa baGccaWGdbWaaSbaaSqaaiaadMgaaeqaaOGaamizaiabew7aLnaaBa aaleaacaWGWbaabeaakiabgkHiTiaadoeadaWgaaWcbaGaamyAaaqa baGccaWGHbWaaSbaaSqaaiaadMgaaeqaaOGaeuiLdqKafqyTduMbae badaWgaaWcbaGaamiCaaqabaaaaa@49BE@
    • The yield stress is computed as follows when combined isotropic kinematic hardening is chosen:(15)
      σ y = ( 1 C h a r d ) . σ i s o _ h a r d + C h a r d . σ k i n _ h a r d MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Wdm3aaS baaSqaaiaadMhaaeqaaOGaeyypa0JaaiikaiaaigdacqGHsislcaWG dbGaamiAaiaadggacaWGYbGaamizaiaacMcacaGGUaGaeq4Wdm3aaS baaSqaaiaadMgacaWGZbGaam4Baiaac+facaWGObGaamyyaiaadkha caWGKbaabeaakiabgUcaRiaadoeacaWGObGaamyyaiaadkhacaWGKb GaaiOlaiabeo8aZnaaBaaaleaacaWGRbGaamyAaiaad6gacaGGFbGa amiAaiaadggacaWGYbGaamizaaqabaaaaa@5AED@
  4. The strain rate filtering is available to smooth strain rates when tabulated input is chosen.
    List of Animation output (in /ANIM/SHELL/USRII/JJ):
    • USR 1= plastic strain
    • USR 2= effective stress
    • USR 3= increment of plastic strain
  5. When Iflag=1 (analytic Swift-Voce formulation is used) strain rates effect is taken into account using Cowper-Symonds expression:(16)
    σ y = σ y ( 1 + ( ε ˙ c ) 1 p )

    If VP=0: ε ˙ is the total strain rate.

    If VP=1: ε ˙ is the plastic strain rate.

    If c=0 or p=0, the strain rate effects are not taken into account.

  6. When Iflag=0 (tabulated formulation) then:

    If VP=0: ε ˙ i is the total strain rate.

    If VP =1: ε ˙ i is the plastic strain rate.

  7. Strain rate filtering:

    If VP=0 (dependency on strain rate), the default value of Fcut = 10KHz.

    If VP=1 (dependency on plastic strain rate), Fsmooth and Fcut are ignored.

  8. If Ifit=1, the coefficients α i will be automatically fit in the Radioss Starter. The tensile yield strengths σ 00 , σ 45 , σ 90 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaa Wdbiabeo8aZ9aadaWgaaWcbaWdbiaaicdacaaIWaaapaqabaGccaGG SaWdbiabeo8aZ9aadaWgaaWcbaWdbiaaisdacaaI1aaapaqabaGcca GGSaWdbiabeo8aZ9aadaWgaaWcbaWdbiaaiMdacaaIWaaapaqabaaa aa@42D8@ and Lankford ratios r 00 , r 45 , r 90 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaa WdbiaadkhapaWaaSbaaSqaa8qacaaIWaGaaGimaaWdaeqaaOGaaiil a8qacaWGYbWdamaaBaaaleaapeGaaGinaiaaiwdaa8aabeaakiaacY capeGaamOCa8aadaWgaaWcbaWdbiaaiMdacaaIWaaapaqabaaaaa@4074@ must be determined from uniaxial tension experiments along the rolling, diagonal and transverse directions at an amount of plastic work corresponding to a plastic strain equal to 0.2%. σ b MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaa Wdbiabeo8aZ9aadaWgaaWcbaWdbiaadkgaa8aabeaaaaa@3983@ and r b MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaa WdbiaadkhapaWaaSbaaSqaa8qacaWGIbaapaqabaaaaa@38B7@ should be determined from biaxial test, for the same amount of plastic strain.
1 Barlat F., Brem J.C., Yoon J.W, Chung K., Dick R.E., Lege D.J., Pourboghrat F., Choi, E. Chu S.-II, (2003), Plane stress yield function for aluminum alloy sheets part 1: Theory, International Journal of Plasticity, Volume 19, Issue 8, August, Pages 1215-1244.
2 J.L. Chaboche,G. Rousselier, (1983), On the Plastic and Viscoplastic Constitutive Equations-Part I: Rules Developed With Internal variable Concept, Journal of Pressure Vessel Technology, Volume 105, pages 153
3 A. H. C. Hänsel, P. Hora and J.Reissner, (1998), model for the kinetics of strain-induced martensitic phase transformation at nonisothermal conditions for the simulation of steel metal forming processes with metastable austenitic steels, Simulation of Materials Processing: Theory, methods, and Applications