/MAT/LAW117

Block Format Keyword This law represents the constitutive relation of ductile adhesive materials in 2 modes for normal and tangential directions. This law models the elastic and failure response of the material.

This material is only compatible with solid hexahedron elements (/BRICK) and the TYPE43 property (cohesive solid). This material is not compatible with any failure model. All damage and failure are defined inside of the material directly.


Figure 1. Representative scheme of the mixed mode model

Format

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
/MAT/LAW117/mat_ID/unit_ID
mat_title
ρ i                
EN ET Imass Idel Irupt      
Fct_TN Fct_TT TN TT Fscale_x  
GIC GIIC EXP_G EXP_BK Gamma

Definition

Field Contents SI Unit Example
mat_ID Material identifier.

(Integer, maximum 10 digits)

unit_ID (Optional) Unit Identifier.

(Integer, maximum 10 digits)

mat_title Material title.

(Character, maximum 100 characters)

ρ i Initial density.

(Real)

[ kg m 3 ]
EN Stiffness normal to the plane of the cohesive element.

(Real)

[ P a m ] MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeaaciGaaiaabeqaamaabaabaaGcbaWaamWaaeaada WcaaqaaiaadcfacaWGHbaabaGaamyBaaaaaiaawUfacaGLDbaaaaa@3AA3@
ET Stiffness in the plane of the cohesive element.

(Real)

[ P a m ] MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeaaciGaaiaabeqaamaabaabaaGcbaWaamWaaeaada WcaaqaaiaadcfacaWGHbaabaGaamyBaaaaaiaawUfacaGLDbaaaaa@3AA3@
Imass Mass calculation flag.
= 1 (Default)
Element mass is calculated using density and mean area.
= 2
Element mass is calculated using density and volume.

(Integer)

 
Idel Failure flag indicating the number of integration points to delete the element (between 1 and 4).

Default = 1 (Integer)

 
Irupt Mixed mode displacement law flag.
= 1 (Default)
Power law
= 2
Benzeggage-Kenane

(Real)

 
Fct_TN Function identifier of the peak traction in normal direction versus element mesh size.

(Integer)

 
Fct_TT Function identifier of the peak traction in tangential direction versus element mesh size.

(Integer)

 
TN Peak traction in normal direction (default = 0)

or, Fct_TN ordinate scale factor (default = 1)

(Real)

[ Pa ]
TT Peak traction in tangential direction (default = 0)

or, Fct_TT ordinate scale factor (default = 1)

(Real)

[ Pa ]
Fscale_x Fct_TN and Fct_TT abscissa scale factor.

Default = 1 (Real)

[ m ]
GIC Energy release rate for mode I.

(Real)

[ Pa.m ] MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaa WdbmaadmaabaGaciiuaiaacggacaGGUaGaamyBaaGaay5waiaaw2fa aaaa@3BD0@
GIIC Energy release rate for mode II.

(Real)

[ Pa . m ] MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaa WdbmaadmaabaGaciiuaiaacggacaGGUaGaamyBaaGaay5waiaaw2fa aaaa@3BD0@
EXP_B Power law exponent for the mixed mode.

Default = 2 (Real)

EXP_BK Benzeggage-Kenane exponent for the mixed mode.

(Real)

Gamma Gamma exponent for Benzeggage-Kenane law.

Default = 1 (Real)

Example (Connect Material)

#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/UNIT/1
Units
                  kg                  mm                  ms
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/MAT/LAW117/1/1
CONNECT MATERIAL
#              RHO_I
              7.8E-6
#                 EN                  ET     Imass      Idel     Irupt
                   5                 1.2         0         1         0
#   Fct_TN    Fct_TT                  TN                  TT            Fscale_x
         0         0                   2                 0.7                   0
#                GIC                GIIC               EXP_B              EXP_BK               Gamma
                   1                1.75                   2                   2                   1
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#ENDDATA
/END
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|

Comments

  1. Mode I refers to the normal direction and mode II refers to the shear direction. δ I MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqiTdq2aaS baaSqaaiaadMeaaeqaaaaa@3895@ is the separation in normal direction equal to δ z z MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqiTdq2aaS baaSqaaiaadQhacaWG6baabeaaaaa@39C6@ direction. δ I I MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqiTdq2aaS baaSqaaiaadMeacaWGjbaabeaaaaa@3964@ is equal to the separation in tangential direction δ I I = δ y z + δ z x MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqiTdq2aaS baaSqaaiaadMeacaWGjbaabeaakiabg2da9maakaaabaGaeqiTdq2a aSbaaSqaaiaadMhacaWG6baabeaakiabgUcaRiabes7aKnaaBaaale aacaWG6bGaamiEaaqabaaabeaaaaa@430B@ . The mixed mode displacement is referred to by δ m MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqiTdq2aaS baaSqaaiaad2gaaeqaaaaa@38BA@ .
  2. The damage initiation displacement in mode I and mode II are respectively, δ I 0 = T N E N MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqiTdq2aa0 baaSqaaiaadMeaaeaacaaIWaaaaOGaeyypa0ZaaSaaaeaacaWGubWa aSbaaSqaaiaad6eaaeqaaaGcbaGaamyraiaad6eaaaaaaa@3DF0@ and δ I I 0 = T T E T MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqiTdq2aa0 baaSqaaiaadMeacaWGjbaabaGaaGimaaaakiabg2da9maalaaabaGa amivamaaBaaaleaacaWGubaabeaaaOqaaiaadweacaWGubaaaaaa@3ECA@ and for the mixed mode:(1)
    δ m 0 = δ I 0 δ I I 0 1 + β 2 ( δ I I 0 ) 2 + ( β δ I 0 ) 2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqiTdq2aa0 baaSqaaiaad2gaaeaacaaIWaaaaOGaeyypa0JaeqiTdq2aa0baaSqa aiaadMeaaeaacaaIWaaaaOGaeyyXICTaeqiTdq2aa0baaSqaaiaadM eacaWGjbaabaGaaGimaaaakiabgwSixpaakaaabaWaaSaaaeaacaaI XaGaey4kaSIaeqOSdi2aaWbaaSqabeaacaaIYaaaaaGcbaWaaeWaae aacqaH0oazdaqhaaWcbaGaamysaiaadMeaaeaacaaIWaaaaaGccaGL OaGaayzkaaWaaWbaaSqabeaacaaIYaaaaOGaey4kaSYaaeWaaeaacq aHYoGycqGHflY1cqaH0oazdaqhaaWcbaGaamysaaqaaiaaicdaaaaa kiaawIcacaGLPaaadaahaaWcbeqaaiaaikdaaaaaaaqabaaaaa@5C50@

    With the mode mix β = δ I I δ I MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqOSdiMaey ypa0ZaaSaaaeaacqaH0oazdaWgaaWcbaGaamysaiaadMeaaeqaaaGc baGaeqiTdq2aaSbaaSqaaiaadMeaaeqaaaaaaaa@3EC4@ .

  3. The maximum displacement at failure δ m F MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqiTdq2aa0 baaSqaaiaad2gaaeaacaWGgbaaaaaa@3985@ can be calculated using either a Power law for Irupt=1:(2)
    δ m F = 2 ( 1 + β 2 ) δ 0 [ ( E N G I C ) E X P _ G + ( β E T G I I C ) E X P _ G ] ( 1 E X P _ G ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqiTdq2aa0 baaSqaaiaad2gaaeaacaWGgbaaaOGaeyypa0ZaaSaaaeaacaaIYaWa aeWaaeaacaaIXaGaey4kaSIaeqOSdi2aaWbaaSqabeaacaaIYaaaaa GccaGLOaGaayzkaaaabaGaeqiTdq2aaWbaaSqabeaacaaIWaaaaaaa kiabgwSixpaadmaabaWaaeWaaeaadaWcaaqaaiaadweacaWGobaaba Gaam4raiaadMeacaWGdbaaaaGaayjkaiaawMcaamaaCaaaleqabaGa amyraiaadIfacaWGqbGaai4xaiaadEeaaaGccqGHRaWkdaqadaqaam aalaaabaGaeqOSdiMaeyyXICTaamyraiaadsfaaeaacaWGhbGaamys aiaadMeacaWGdbaaaaGaayjkaiaawMcaamaaCaaaleqabaGaamyrai aadIfacaWGqbGaai4xaiaadEeaaaaakiaawUfacaGLDbaadaahaaWc beqaaiabgkHiTmaabmaabaWaaSaaaeaacaaIXaaabaGaamyraiaadI facaWGqbGaai4xaiaadEeaaaaacaGLOaGaayzkaaaaaaaa@691C@
    or, a Benzeggage-Kenane law for Irupt =2:(3)
    δ m F = 2 δ 0 ( 1 1 + β 2 E N γ + β 2 1 + β 2 E T γ ) 1 γ [ G I C + ( G I I C G I C ) ( β 2 E T E N + β 2 E T ) E X P _ B K ] MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqiTdq2aa0 baaSqaaiaad2gaaeaacaWGgbaaaOGaeyypa0ZaaSaaaeaacaaIYaaa baGaeqiTdq2aaWbaaSqabeaacaaIWaaaaOWaaeWaaeaadaWcaaqaai aaigdaaeaacaaIXaGaey4kaSIaeqOSdi2aaWbaaSqabeaacaaIYaaa aaaakiabgwSixlaadweacaWGobWaaWbaaSqabeaacqaHZoWzaaGccq GHRaWkdaWcaaqaaiabek7aInaaCaaaleqabaGaaGOmaaaaaOqaaiaa igdacqGHRaWkcqaHYoGydaahaaWcbeqaaiaaikdaaaaaaOGaeyyXIC TaamyraiaadsfadaahaaWcbeqaaiabeo7aNbaaaOGaayjkaiaawMca amaaCaaaleqabaWaaSaaaeaacaaIXaaabaGaeq4SdCgaaaaaaaGccq GHflY1daWadaqaaiaadEeacaWGjbGaam4qaiabgUcaRmaabmaabaGa am4raiaadMeacaWGjbGaam4qaiabgkHiTiaadEeacaWGjbGaam4qaa GaayjkaiaawMcaamaabmaabaWaaSaaaeaacqaHYoGydaahaaWcbeqa aiaaikdaaaGccqGHflY1caWGfbGaamivaaqaaiaadweacaWGobGaey 4kaSIaeqOSdi2aaWbaaSqabeaacaaIYaaaaOGaeyyXICTaamyraiaa dsfaaaaacaGLOaGaayzkaaWaaWbaaSqabeaacaWGfbGaamiwaiaadc facaGGFbGaamOqaiaadUeaaaaakiaawUfacaGLDbaaaaa@803B@
  4. GIC and GIIC are the energy release rates between the peak traction and the maximum displacement for mode I and mode II, respectively.

    G I C = T N δ I F 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4raiaadM eacaWGdbGaeyypa0ZaaSaaaeaacaWGubGaamOtaiabgwSixlabes7a KnaaDaaaleaacaWGjbaabaGaamOraaaaaOqaaiaaikdaaaaaaa@4196@ and G I I C = T T δ I I F 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4raiaadM eacaWGjbGaam4qaiabg2da9maalaaabaGaamivaiaadsfacqGHflY1 cqaH0oazdaqhaaWcbaGaamysaiaadMeaaeaacaWGgbaaaaGcbaGaaG Omaaaaaaa@4338@