/MAT/LAW71

Block Format Keyword This law describes the behavior of superelastic materials. It allows modeling the behavior of the shape memory alloys (such as Nitinol).

The particularity of these materials is that all of the strain is recovered upon unloading even when large deformations are reached. Besides, the material shows a hysteretic response in a complete loading-unloading cycle. The full recovery is due to phase change in the microstructure. The model is based on the work of Auricchio et al. 1997. This law is compatible with solid and shell elements.

Format

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
/MAT/LAW71/mat_ID/unit_ID
mat_title
ρ i                
E υ E_mart        
σ S AS MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaa Wdbiabeo8aZnaaDaaaleaacaWGtbaabaGaamyqaiaadofaaaaaaa@3AE5@ σ F AS MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaa Wdbiabeo8aZ9aadaqhaaWcbaGaamOraaqaaiaadgeacaWGtbaaaaaa @3AE7@ σ S SA MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaa Wdbiabeo8aZ9aadaqhaaWcbaGaam4uaaqaaiaadofacaWGbbaaaaaa @3AF4@ σ F SA MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaa Wdbiabeo8aZ9aadaqhaaWcbaGaamOraaqaaiaadofacaWGbbaaaaaa @3AE7@ α
EpsL CAS CSA TS_AS TF_AS
TS_SA TF_SA Cp Tini  

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 ]
υ Poisson's ratio.

(Real)

 
E_mart Martensite Young's modulus

Default = 0.0 (Real)

[ Pa ]
σ S AS MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaa Wdbiabeo8aZnaaDaaaleaacaWGtbaabaGaamyqaiaadofaaaaaaa@3AE5@ Material parameter defining the start of phase transformation from austenite to martensite (AS). 1

(Real)

[ Pa ]
σ F A S MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaa Wdbiabeo8aZ9aadaqhaaWcbaGaamOraaqaaiaadgeacaWGtbaaaaaa @3AE7@ Material parameter defining the end of phase transformation from austenite to martensite (AS). 1

(Real)

[ Pa ]
σ S S A MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaa Wdbiabeo8aZ9aadaqhaaWcbaGaam4uaaqaaiaadofacaWGbbaaaaaa @3AF4@ Material parameter defining the start of phase transformation from martensite to austenite (SA). 1

(Real)

[ Pa ]
σ F S A MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaa Wdbiabeo8aZ9aadaqhaaWcbaGaamOraaqaaiaadofacaWGbbaaaaaa @3AE7@ Material parameter defining the end of phase transformation from martensite to austenite (SA). 1

(Real)

[ Pa ]
α Material parameter measuring the difference in response between tension and compression.

Default = 0 (Real)

 
EpsL Maximum residual strain. 2

(Real)

 
CAS Stress-Temperature rate during loading.

Default = 0 (Real)

[ Pa K ] MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaamWaaeaada WcaaqaaiGaccfacaGGHbaabaGaci4saaaaaiaawUfacaGLDbaaaaa@3A85@
CSA Stress-Temperature rate during unloading.

Default = 0 (Real)

[ Pa K ] MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaamWaaeaada WcaaqaaiGaccfacaGGHbaabaGaci4saaaaaiaawUfacaGLDbaaaaa@3A85@
TS_AS Reference temperature for start of transformation (AS).

Default = 298K (Real)

[ K ]
TF_AS Reference temperature for rend of transformation (AS).

Default = 298K (Real)

[ K ]
TS_SA Reference temperature for start of transformation (SA).

Default = 298K (Real)

[ K ]
TF_SA Reference temperature for end of transformation (SA).

Default = 298K (Real)

[ K ]
Cp Specific heat capacity.

Default = 1030 (Real)

[ J kgK ] MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeaaciGaaiaabeqaamaabaabaaGcbaWaamWaaeaada WcaaqaaiaabQeaaeaacaqGRbGaae4zaiabgwSixlaabUeaaaaacaGL BbGaayzxaaaaaa@3DB3@
Tini Initial temperature.

Default = 360 K (Real)

[ K ]

Example (Metal)

#RADIOSS STARTER
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/UNIT/1
unit for mat
                  Mg                  mm                   s
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#-  2. MATERIALS:
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/MAT/LAW71/1/1
metal
#              RHO_I
             6.50E-9
#                  E                  Nu              E_mart
               62500                  .3               51000
#           sig_AS_s            sig_AS_f            sig_SA_s            sig_SA_f              alpha
                 450                 600                 300                 200                0.20
#               EpsL                 CAS                 CSA               TS_AS               TF_AS
               0.045                   1                   1                 383                 343
#              TS_SA               TF_SA                  CP                TINI
                 363                 403                 837                 360
#ENDDATA
/END
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|

Comments

  1. If E_mart=0, then Young's modulus is considered constant, equal to E, and not dependent on the phase fraction of the material.
  2. The different stresses σ S S A MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaa Wdbiabeo8aZ9aadaqhaaWcbaGaam4uaaqaaiaadofacaWGbbaaaaaa @3AF4@ , σ F A S MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaa Wdbiabeo8aZ9aadaqhaaWcbaGaamOraaqaaiaadgeacaWGtbaaaaaa @3AE7@ , σ S S A MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaa Wdbiabeo8aZ9aadaqhaaWcbaGaam4uaaqaaiaadofacaWGbbaaaaaa @3AF4@ and σ F S A MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaa Wdbiabeo8aZ9aadaqhaaWcbaGaamOraaqaaiaadofacaWGbbaaaaaa @3AE7@ , defining the start and the end of phase transfomation, as well as the residual strain EpsL, correspond to the case of a uniaxial tensile test:

    law71_transformation
    Figure 1.
  3. The parameter α is computed from the initial value of the austenite to martensite phase transformation in tension ( σ S A S ) T MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaa Wdbmaabmaapaqaa8qacqaHdpWCpaWaa0baaSqaaiaadofaaeaacaWG bbGaam4uaaaaaOWdbiaawIcacaGLPaaapaWaaSbaaSqaa8qacaWGub aapaqabaaaaa@3DE9@ and compression ( σ S A S ) C MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaa Wdbmaabmaapaqaa8qacqaHdpWCpaWaa0baaSqaaiaadofaaeaacaWG bbGaam4uaaaaaOWdbiaawIcacaGLPaaapaWaaSbaaSqaa8qacaWGub aapaqabaaaaa@3DE9@ from the relation.(1)
    α= 2 3 ( σ S AS ) C ( σ S AS ) T ( σ S AS ) C + ( σ S AS ) T MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaa Wdbiabeg7aHjabg2da9maakaaapaqaa8qadaWcaaWdaeaapeGaaGOm aaWdaeaapeGaaG4maaaaaSqabaGcdaWcaaWdaeaapeWaaeWaa8aaba Wdbiabeo8aZnaaDaaaleaacaWGtbaabaGaamyqaiaadofaaaaakiaa wIcacaGLPaaapaWaaSbaaSqaaiaadoeaaeqaaOWdbiabgkHiTmaabm aapaqaa8qacqaHdpWCdaqhaaWcbaGaam4uaaqaaiaadgeacaWGtbaa aaGccaGLOaGaayzkaaWdamaaBaaaleaapeGaamivaaWdaeqaaaGcba Wdbmaabmaapaqaa8qacqaHdpWCdaqhaaWcbaGaam4uaaqaaiaadgea caWGtbaaaaGccaGLOaGaayzkaaWdamaaBaaaleaacaWGdbaabeaak8 qacqGHRaWkdaqadaWdaeaapeGaeq4Wdm3aa0baaSqaaiaadofaaeaa caWGbbGaam4uaaaaaOGaayjkaiaawMcaa8aadaWgaaWcbaWdbiaads faa8aabeaaaaaaaa@5A47@
  4. The Drucker-Prager-type loading function F MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGgbaaaa@3833@ is introduced using the stress deviator s MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGgbaaaa@3833@ , the pressure p MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGgbaaaa@3833@ and the temperature.(2)
    F = s + 3 α p MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGgbGaey ypa0ZaauWaaeaacaWGZbaacaGLjWUaayPcSdGaey4kaSIaaG4maiab eg7aHjaadchaaaa@418B@
    Two functions are defined for the start and the final point of transformation from austenite to martensite (A → S) or from martensite to austenite (S → A).
    (A→S) (S →A)
    Start point of transformation F S A S = F R S A S MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGgbWaa0 baaSqaaiaadofaaeaacaWGbbGaam4uaaaakiabg2da9iaadAeacqGH sislcaWGsbWaa0baaSqaaiaadofaaeaacaWGbbGaam4uaaaaaaa@4118@

    R S A S = σ S A S ( 2 3 + α ) C A S ( T T S A S ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGsbWaa0 baaSqaaiaadofaaeaacaWGbbGaam4uaaaakiabg2da9iabeo8aZnaa DaaaleaacaWGtbaabaGaamyqaiaadofaaaGcdaqadaqaamaakaaaba WaaSaaaeaacaaIYaaabaGaaG4maaaaaSqabaGccqGHRaWkcqaHXoqy aiaawIcacaGLPaaacqGHsislcaWGdbWaaWbaaSqabeaacaWGbbGaam 4uaaaakmaabmaabaGaamivaiabgkHiTiaadsfadaqhaaWcbaGaam4u aaqaaiaadgeacaWGtbaaaaGccaGLOaGaayzkaaaaaa@5079@

    F S S A = F R S S A MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGgbWaa0 baaSqaaiaadofaaeaacaWGtbGaamyqaaaakiabg2da9iaadAeacqGH sislcaWGsbWaa0baaSqaaiaadofaaeaacaWGtbGaamyqaaaaaaa@4118@

    R S S A = σ S S A ( 2 3 + α ) C S A ( T T S S A ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGsbWaa0 baaSqaaiaadofaaeaacaWGtbGaamyqaaaakiabg2da9iabeo8aZnaa DaaaleaacaWGtbaabaGaam4uaiaadgeaaaGcdaqadaqaamaakaaaba WaaSaaaeaacaaIYaaabaGaaG4maaaaaSqabaGccqGHRaWkcqaHXoqy aiaawIcacaGLPaaacqGHsislcaWGdbWaaWbaaSqabeaacaWGtbGaam yqaaaakmaabmaabaGaamivaiabgkHiTiaadsfadaqhaaWcbaGaam4u aaqaaiaadofacaWGbbaaaaGccaGLOaGaayzkaaaaaa@5079@

    Final point of transformation F F A S = F R F A S MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGgbWaa0 baaSqaaiaadAeaaeaacaWGbbGaam4uaaaakiabg2da9iaadAeacqGH sislcaWGsbWaa0baaSqaaiaadAeaaeaacaWGbbGaam4uaaaaaaa@40FE@

    R F A S = σ F A S ( 2 3 + α ) C A S ( T T F A S ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGsbWaa0 baaSqaaiaadAeaaeaacaWGbbGaam4uaaaakiabg2da9iabeo8aZnaa DaaaleaacaWGgbaabaGaamyqaiaadofaaaGcdaqadaqaamaakaaaba WaaSaaaeaacaaIYaaabaGaaG4maaaaaSqabaGccqGHRaWkcqaHXoqy aiaawIcacaGLPaaacqGHsislcaWGdbWaaWbaaSqabeaacaWGbbGaam 4uaaaakmaabmaabaGaamivaiabgkHiTiaadsfadaqhaaWcbaGaamOr aaqaaiaadgeacaWGtbaaaaGccaGLOaGaayzkaaaaaa@5052@

    F F S A = F R F S A MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGgbWaa0 baaSqaaiaadAeaaeaacaWGtbGaamyqaaaakiabg2da9iaadAeacqGH sislcaWGsbWaa0baaSqaaiaadAeaaeaacaWGtbGaamyqaaaaaaa@40FE@

    R F S A = σ F S A ( 2 3 + α ) C S A ( T T F S A ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGsbWaa0 baaSqaaiaadAeaaeaacaWGtbGaamyqaaaakiabg2da9iabeo8aZnaa DaaaleaacaWGgbaabaGaam4uaiaadgeaaaGcdaqadaqaamaakaaaba WaaSaaaeaacaaIYaaabaGaaG4maaaaaSqabaGccqGHRaWkcqaHXoqy aiaawIcacaGLPaaacqGHsislcaWGdbWaaWbaaSqabeaacaWGtbGaam yqaaaakmaabmaabaGaamivaiabgkHiTiaadsfadaqhaaWcbaGaamOr aaqaaiaadofacaWGbbaaaaGccaGLOaGaayzkaaaaaa@5052@

    Condition F S A S > 0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGgbWaa0 baaSqaaiaadofaaeaacaWGbbGaam4uaaaakiabg6da+iaaicdaaaa@3CA2@

    F F A S < 0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGgbWaa0 baaSqaaiaadAeaaeaacaWGbbGaam4uaaaakiabgYda8iaaicdaaaa@3C91@

    F ˙ > 0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaaceWGgbGbai aacqGH+aGpcaaIWaaaaa@39FE@

    F S S A < 0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGgbWaa0 baaSqaaiaadofaaeaacaWGtbGaamyqaaaakiabgYda8iaaicdaaaa@3C9E@

    F F S A > 0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGgbWaa0 baaSqaaiaadAeaaeaacaWGtbGaamyqaaaakiabg6da+iaaicdaaaa@3C95@

    F ˙ < 0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaaceWGgbGbai aacqGH8aapcaaIWaaaaa@39FA@

    Evolution equation of martensite During loading:

    X ˙ m = ( 1 X m ) F ˙ F R F A S MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaaceWGybGbai aadaWgaaWcbaGaamyBaaqabaGccqGH9aqpcaGGOaGaaGymaiabgkHi TiaadIfadaWgaaWcbaGaamyBaaqabaGccaGGPaWaaSaaaeaaceWGgb GbaiaaaeaacaWGgbGaeyOeI0IaamOuamaaDaaaleaacaWGgbaabaGa amyqaiaadofaaaaaaaaa@458B@

    During unloading:

    X ˙ m = X m F ˙ F R F S A MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaaceWGybGbai aadaWgaaWcbaGaamyBaaqabaGccqGH9aqpcaWGybWaaSbaaSqaaiaa d2gaaeqaaOWaaSaaaeaaceWGgbGbaiaaaeaacaWGgbGaeyOeI0Iaam OuamaaDaaaleaacaWGgbaabaGaam4uaiaadgeaaaaaaaaa@428A@

    σ S A S , σ F A S , T S A S , T F A S , α , C A S , σ S S A , σ F S A , T S S A , T F S A , C S A MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaHdpWCda qhaaWcbaGaam4uaaqaaiaadgeacaWGtbaaaOGaaiilaiabeo8aZnaa DaaaleaacaWGgbaabaGaamyqaiaadofaaaGccaGGSaGaamivamaaDa aaleaacaWGtbaabaGaamyqaiaadofaaaGccaGGSaGaamivamaaDaaa leaacaWGgbaabaGaamyqaiaadofaaaGccaGGSaGaeqySdeMaaiilai aadoeadaahaaWcbeqaaiaadgeacaWGtbaaaOGaaiilaiabeo8aZnaa DaaaleaacaWGtbaabaGaam4uaiaadgeaaaGccaGGSaGaeq4Wdm3aa0 baaSqaaiaadAeaaeaacaWGtbGaamyqaaaakiaacYcacaWGubWaa0ba aSqaaiaadofaaeaacaWGtbGaamyqaaaakiaacYcacaWGubWaa0baaS qaaiaadAeaaeaacaWGtbGaamyqaaaakiaacYcacaWGdbWaaWbaaSqa beaacaWGtbGaamyqaaaaaaa@64BB@ are the material parameters. The conversion of austenite to martensite takes place when above conditions (in table) are verified.

  5. List of Animation output (/ANIM/BRICK/USRI):
    • USR 1= Martensite phase fraction
    • USR 2= Loading function
    • USR 3= Unloading function