/FAIL/INIEVO

Block Format Keyword This criterion allows a two-step failure approach, divided into an initiation phase, in which damage has no effect on the stress computation, and a damage evolution phase, in which a stress softening can be generated. Initiation is based on plastic strain as function of several stress state quantities.

When the initiation criterion is reached, stress softening damage variable evolution is triggered. This evolution can be based on a plastic displacement at the time of failure or on a certain value of fracture energy. In addition, the shape can be chosen between a classic linear stress reduction or an exponential drop of the load-carrying capacity. Multiple pairs of initiation/evolution criterion can be combined in the same input card. This criterion is compatible with both solids and shells and can be used with non-local regularization.

Format

Card 1 - Number of initiation/evolution criterion, shear components effect, element deletion control
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
/FAIL/INIEVO/mat_ID/unit_ID
NINIEVO ISHEAR ILEN   FAILIP PTHICKFAIL
Card 2 - Read NINIEVO (Number of initiation/evolution couples, at least 1) cards
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
INITYPE EVOTYPE EVOSHAP COMPTYP
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
TAB_ID SR_REF FSCALE PARAM
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
TAB_EL EL_REF ELSCAL
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
DISP ALPHA ENER
Card 6 - Optional line
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
fail_ID        

Definition

Field Contents SI Unit Example
mat_ID Material identifier.

(Integer, maximum 10 digits)

unit_ID (Optional) Unit identifier.

(Integer, maximum 10 digits)

NINIEVO Number of initiation/evolution criteria.

Default = 1 (Integer)

ISHEAR Flag to take transverse shear components into account (shells only).
= 0 (Default)
Transverse components not considered.
= 1
Transverse components considered.

(Integer)

ILEN Element characteristic length formulation flag.
= 0 (Default)
Initial geometric formulation.
= 1
Initial critical timestep formulation.
= 2
Current geometric formulation (for shells only).

(Integer)

 
FAILIP Number of failed integration point prior to solid element deletion.

Default = 1 (Integer)

PTHICKFAIL Percentage of failed layers prior to shell element deletion.

0.0 ≤ PTHICKFAIL ≤ 1.0

Default = 0.0 (Real)

INITYPE Damage initiation tabulated criterion type. 2
= 1 (Default)
Plastic strain versus stress triaxiality (versus strain rate).
= 2
Plastic strain versus shear influence (versus strain rate).
= 3
Modified plastic strain versus principal plastic strain rate ratio (versus strain rate) MSFLD.
= 4
Plastic strain versus principal plastic strain rate ratio (versus strain rate) FLD.
= 5
Plastic strain versus stress state parameter (versus strain rate).

(Integer)

EVOTYPE Damage evolution type.
= 1 (Default)
Plastic displacement at failure based.
= 2
Fracture energy based.

(Integer)

EVOSHAP Shape of the damage evolution.
= 1 (Default)
Linear
= 2
Exponential

(Integer)

COMPTYP Criterion combination type (only if NINIEVO > 0).
= 1 (Default)
Maximum
= 2
Multiplication

(Integer)

TAB_ID Failure initiation criterion table identifier.

(Integer)

SR_REF Reference strain rate for table identifier.

Default = 1.0 (Real)

[ 1 s ]
FSCALE Scale factor for failure initiation criterion table.

Default = 1.0 (Real)

PARAM Parameter for failure initiation criterion.
If INITYPE = 1
Not used.
If INITYPE = 2
Pressure dependency parameter.
If INITYPE = 3
= 0.0
Direct formulation.
= 1.0
Incremental formulation
If INITYPE = 4
Not used
= 0.0
Direct formulation.
= 1.0
Incremental formulation
If INITYPE = 5
Triaxiality influence parameter.

Default = 0.0 (Real)

TAB_EL Element size scaling for failure initiation criterion.

(Integer)

EL_REF Reference element size for size scaling table.

Default = 1.0 (Real)

[ m ]
ELSCAL Scale factor for element size scaling function.

Default = 1.0 (Real)

DISP Plastic displacement at failure.

Default = 0.0 (Real)

[ m ]
ALPHA Exponential shape parameter (not applicable for exponential energy- based evolution).

Default = 1.0

ENER Fracture energy.

Default = 0.0

[ J m 2 ]
fail_ID (Optional) Failure criteria identifier.

(Integer, maximum 10 digits)

Comments

  1. The INIEVO failure criterion is a two-step failure criterion based on plastic strain and stress state. These two steps consist in the computation of two successive damage variables:
    • 1st step: the damage initiation phase, in which an internal variable evolution denoted is computed. This variable is a purely internal value that has no influence on the stress computation. Once this initiation variable reaches the value 1.0, the second stage of the failure is triggered by the computation of the damage variable evolution denoted D MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiraaaa@36BD@ .
    • 2nd step: The damage variable D MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiraaaa@36BD@ evolution is computed, generating a stress softening effect until the complete failure of the element and its deletion.
  2. Different types of failure initiation criterion can be used depending on the INITYPE parameter value.
    • If INITYPE = 1: A tabulated plastic strain at failure initiation map is given with respect to stress triaxiality and, optionally, with strain rate.

      ε p i n i t = f η , ε ˙ with η = p σ V M MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqbaeqabeWaaa qaaiabew7aLnaaDaaaleaacaWGWbaabaGaamyAaiaad6gacaWGPbGa amiDaaaakiabg2da9iaadAgadaqadaqaaiabeE7aOjaacYcacuaH1o qzgaGaaaGaayjkaiaawMcaaaqaaiaabEhacaqGPbGaaeiDaiaabIga aeaacqaH3oaAcqGH9aqpcqGHsisldaWcaaqaaiaadchaaeaacqaHdp WCdaWgaaWcbaGaamOvaiaad2eaaeqaaaaaaaaaaa@502C@

      Where,
      p MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiCaaaa@36E9@
      Hydrostatic pressure Tr σ / 3 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyOeI0Iaae ivaiaabkhadaqadaqaaiaaho8aaiaawIcacaGLPaaacaGGVaGaaG4m aaaa@3CF5@
      σ V M MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Wdm3aaS baaSqaaiaadAfacaWGnbaabeaaaaa@3990@
      von Mises stress
    • If INITYPE = 2: A tabulated plastic strain at failure initiation map is given with respect to a shear influence variable denoted as and, optionally, with strain rate.

      ε p i n i t = f θ , ε ˙ with θ = σ V M + k s p τ MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqbaeqabeWaaa qaaiabew7aLnaaDaaaleaacaWGWbaabaGaamyAaiaad6gacaWGPbGa amiDaaaakiabg2da9iaadAgadaqadaqaaiabeI7aXjaacYcacuaH1o qzgaGaaaGaayjkaiaawMcaaaqaaiaabEhacaqGPbGaaeiDaiaabIga aeaacqaH4oqCcqGH9aqpdaWcaaqaaiabeo8aZnaaBaaaleaacaWGwb GaamytaaqabaGccqGHRaWkcaWGRbWaaSbaaSqaaiaadohaaeqaaOGa amiCaaqaaiabes8a0baaaaaaaa@5421@

      Where,
      k s MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4AamaaBa aaleaacaWGZbaabeaaaaa@3808@
      Pressure influence parameter
      τ
      Maximum shear stress
      τ = σ major σ minor 2 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqiXdqNaey ypa0ZaaSaaaeaacqaHdpWCdaWgaaWcbaGaaeyBaiaabggacaqGQbGa ae4BaiaabkhaaeqaaOGaeyOeI0Iaeq4Wdm3aaSbaaSqaaiaab2gaca qGPbGaaeOBaiaab+gacaqGYbaabeaaaOqaaiaaikdaaaaaaa@47C5@
    • If INITYPE = 3: A tabulated modified plastic strain at failure initiation map is given with respect to principal strain rate ratio and, optionally, with strain rate. This initiation criterion is also denoted as MSFLD.

      ε p init =f α, ε ˙ with α= ε ˙ minor p ε ˙ minor p s minor s major MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqbaeqabeWaaa qaaiabew7aLnaaDaaaleaacaWGWbaabaGaamyAaiaad6gacaWGPbGa amiDaaaakiabg2da9iaadAgadaqadaqaaiabeg7aHjaacYcacuaH1o qzgaGaaaGaayjkaiaawMcaaaqaaiaabEhacaqGPbGaaeiDaiaabIga aeaacqaHXoqycqGH9aqpdaWcaaqaaiqbew7aLzaacaWaa0baaSqaai aab2gacaqGPbGaaeOBaiaab+gacaqGYbaabaGaamiCaaaaaOqaaiqb ew7aLzaacaWaa0baaSqaaiaab2gacaqGPbGaaeOBaiaab+gacaqGYb aabaGaamiCaaaaaaGccqGHijYUdaWcaaqaaiaadohadaWgaaWcbaGa aeyBaiaabMgacaqGUbGaae4BaiaabkhaaeqaaaGcbaGaam4CamaaBa aaleaacaqGTbGaaeyyaiaabQgacaqGVbGaaeOCaaqabaaaaaaaaaa@6722@

      Where, s i MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4CamaaBa aaleaacaWGPbaabeaaaaa@3805@ are the principal deviatoric stress component.

    • If INITYPE = 4: A tabulated plastic strain at failure initiation map is given with respect to principal strain rate ratio and, optionally, with strain rate. This initiation criterion is also denoted as FLD.

      ε p init =f α, ε ˙ with α= ε ˙ minor p ε ˙ minor p s minor s major MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqbaeqabeWaaa qaaiabew7aLnaaDaaaleaacaWGWbaabaGaamyAaiaad6gacaWGPbGa amiDaaaakiabg2da9iaadAgadaqadaqaaiabeg7aHjaacYcacuaH1o qzgaGaaaGaayjkaiaawMcaaaqaaiaabEhacaqGPbGaaeiDaiaabIga aeaacqaHXoqycqGH9aqpdaWcaaqaaiqbew7aLzaacaWaa0baaSqaai aab2gacaqGPbGaaeOBaiaab+gacaqGYbaabaGaamiCaaaaaOqaaiqb ew7aLzaacaWaa0baaSqaaiaab2gacaqGPbGaaeOBaiaab+gacaqGYb aabaGaamiCaaaaaaGccqGHijYUdaWcaaqaaiaadohadaWgaaWcbaGa aeyBaiaabMgacaqGUbGaae4BaiaabkhaaeqaaaGcbaGaam4CamaaBa aaleaacaqGTbGaaeyyaiaabQgacaqGVbGaaeOCaaqabaaaaaaaaaa@6722@

    • If INITYPE = 5: A tabulated plastic strain at failure initiation map is given with respect to a stress state parameter denoted as β and, optionally, with strain rate. This initiation criterion is also denoted as FLD.
      ε p init =f β, ε ˙ with β= σ VM + k d p σ major MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqbaeqabeWaaa qaaiabew7aLnaaDaaaleaacaWGWbaabaGaamyAaiaad6gacaWGPbGa amiDaaaakiabg2da9iaadAgadaqadaqaaiabek7aIjaacYcacuaH1o qzgaGaaaGaayjkaiaawMcaaaqaaiaabEhacaqGPbGaaeiDaiaabIga aeaacqaHYoGycqGH9aqpaaWaaSaaaeaacqaHdpWCdaWgaaWcbaGaam Ovaiaad2eaaeqaaOGaey4kaSIaam4AamaaBaaaleaacaWGKbaabeaa kiaadchaaeaacqaHdpWCdaWgaaWcbaGaaeyBaiaabggacaqGQbGaae 4Baiaabkhaaeqaaaaaaaa@58BA@
      Important: The strain rate dependency applied to the failure criterion can only be used with material laws that are strain rate dependent. The strain rate used for the constitutive law (total strain rate, deviatoric strain rate or plastic strain rate), will be the same used for the failure criterion.
  3. The damage initiation variable, ω D MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyYdC3aaS baaSqaaiaadseaaeqaaaaa@38B6@ is computed incrementally as:(1)
    ω D = t = 0 Δ ε p ε p i n i t MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyYdC3aaS baaSqaaiaadseaaeqaaOGaeyypa0ZaaabCaeaadaWcaaqaaiabfs5a ejabew7aLnaaBaaaleaacaWGWbaabeaaaOqaaiabew7aLnaaDaaale aacaWGWbaabaGaamyAaiaad6gacaWGPbGaamiDaaaaaaaabaGaamiD aiabg2da9iaaicdaaeaacqGHEisPa0GaeyyeIuoaaaa@4B00@
    • If INITYPE = 3 (MSFLD), a modified plastic strain is used, which only evolves when η > 0 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4TdGMaey Opa4JaaGimaaaa@3961@ :(2)
      ω D = t = 0 Δ ε p ε p i n i t MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyYdC3aaS baaSqaaiaadseaaeqaaOGaeyypa0ZaaabCaeaadaWcaaqaaiabfs5a ejabew7aLnaaBaaaleaacaWGWbaabeaaaOqaaiabew7aLnaaDaaale aacaWGWbaabaGaamyAaiaad6gacaWGPbGaamiDaaaaaaaabaGaamiD aiabg2da9iaaicdaaeaacqGHEisPa0GaeyyeIuoaaaa@4AFF@
    • If INITYPE = 3 (MSFLD) and INITYPE = 4 (FLD) criteria, depending on PARAM value, a direct formulation can be used instead of the incremental one:(3)
      ω D = ε p ε p init MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyYdC3aaS baaSqaaiaadseaaeqaaOGaeyypa0ZaaSaaaeaacqaH1oqzdaWgaaWc baGaamiCaaqabaaakeaacqaH1oqzdaqhaaWcbaGaamiCaaqaaiaadM gacaWGUbGaamyAaiaadshaaaaaaaaa@4339@
  4. To take into account regularization of the element size, a table (TAB_EL) can be defined describing a scale factor for the element size denoted as f s i z e MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOzamaaBa aaleaacaWGZbGaamyAaiaadQhacaWGLbaabeaaaaa@3ADA@ map with respect to initial element size L e MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamitamaaBa aaleaacaWGLbaabeaaaaa@37DA@ and, optionally, the stress state variable used in the failure initiation criterion depending on INITYPE value. For instance, if INITYPE = 2, f s i z e = f ( L e , θ ) MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOzamaaBa aaleaacaWGZbGaamyAaiaadQhacaWGLbaabeaakiabg2da9iaadAga caGGOaGaamitamaaBaaaleaacaaIWaaabeaakiaacYcacqaH4oqCca GGPaaaaa@4255@ . The element size factor is introduced into the damage initiation variable computation as:(4)
    ω D = t = 0 Δ ε p ε p i n i t f s i z e MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyYdC3aaS baaSqaaiaadseaaeqaaOGaeyypa0ZaaabCaeaadaWcaaqaaiabfs5a ejabew7aLnaaBaaaleaacaWGWbaabeaaaOqaaiabew7aLnaaDaaale aacaWGWbaabaGaamyAaiaad6gacaWGPbGaamiDaaaakiabgwSixlaa dAgadaWgaaWcbaGaam4CaiaadMgacaWG6bGaamyzaaqabaaaaaqaai aadshacqGH9aqpcaaIWaaabaGaeyOhIukaniabggHiLdaaaa@523A@
  5. When the damage initiation variable ω D MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyYdC3aaS baaSqaaiaadseaaeqaaaaa@38B6@ reaches the value 1, the damage variable evolution D MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiraaaa@36BD@ is triggered, generating a stress softening. This evolution can be either based on:
    • Plastic displacement at failure (DISP), denoted u p f MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyDamaaDa aaleaacaWGWbaabaGaamOzaaaaaaa@38FB@ , if EVOTYPE = 1.
    • Dissipated fracture energy (ENER) denoted G f MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4ramaaBa aaleaacaWGMbaabeaaaaa@37D7@ , if EVOTYPE = 2.
  6. EVOSHAP parameter allows to define the shape of the damage evolution. For both evolution type (plastic displacement or fracture energy), a linear and an exponential shape can be chosen.
    • If EVOSHAP = 1, the damage evolution is linear:
      • If EVOTYPE = 1: plastic displacement at failure is directly input with DISP:(5)
        Δ D = L e Δ ε p u p f MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyiLdqKaam iraiabg2da9maalaaabaGaamitamaaBaaaleaacaWGLbaabeaakiab gs5aejabew7aLnaaBaaaleaacaWGWbaabeaaaOqaaiaadwhadaqhaa WcbaGaamiCaaqaaiaadAgaaaaaaaaa@426B@
        Where, L e MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamitamaaBa aaleaacaWGLbaabeaaaaa@37DB@ is the initial element length.


        Figure 1. Linear damage evolution with plastic displacement DISP at failure
      • If EVOTYPE = 2: plastic displacement at failure is deduced from the fracture energy input, which is calculated with ENER:

        ΔD= L e Δ ε p u p f with u p f = 2 G f σ Y 0 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqbaeqabeWaaa qaaiabgs5aejaadseacqGH9aqpdaWcaaqaaiaadYeadaWgaaWcbaGa amyzaaqabaGccqGHuoarcqaH1oqzdaWgaaWcbaGaamiCaaqabaaake aacaWG1bWaa0baaSqaaiaadchaaeaacaWGMbaaaaaaaOqaaiaabEha caqGPbGaaeiDaiaabIgaaeaacaWG1bWaa0baaSqaaiaadchaaeaaca WGMbaaaOGaeyypa0ZaaSaaaeaacaaIYaGaam4ramaaBaaaleaacaWG MbaabeaaaOqaaiabeo8aZnaaDaaaleaacaWGzbaabaGaaGimaaaaaa aaaaaa@50A3@

        Where, σ Y 0 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Wdm3aa0 baaSqaaiaadMfaaeaacaaIWaaaaaaa@397B@ is the yield stress at damage evolution triggering.
        Note: This expression considers that the plastic behavior is almost perfect at the onset of damage to ensure a dissipated energy equal to G f MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4ramaaBa aaleaacaWGMbaabeaaaaa@37D7@ .


        Figure 2. Linear damage evolution with fracture energy input ENER
    • If EVOSHAP = 2, the damage evolution is exponential.
      • If EVOTYPE = 1: plastic displacement at failure is directly input with DISP and shape of the exponential can be modified with ALPHA.(6)
        D= 1 e α L e ( ε p ε p 0 ) u p f 1 e α MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiraiabg2 da9maalaaabaGaaGymaiabgkHiTiaadwgadaahaaWcbeqaaiabgkHi Tiabeg7aHnaalaaabaGaamitamaaBaaameaacaWGLbaabeaaliaacI cacqaH1oqzdaWgaaadbaGaamiCaaqabaWccqGHsislcqaH1oqzdaqh aaadbaGaamiCaaqaaiaaicdaaaWccaGGPaaabaGaamyDamaaDaaame aacaWGWbaabaGaamOzaaaaaaaaaaGcbaGaaGymaiabgkHiTiaadwga daahaaWcbeqaaiabgkHiTiabeg7aHbaaaaaaaa@5026@


        Figure 3. Exponential damage evolution with plastic displacement DISP. at failure with different alpha parameter value
      • If EVOTYPE = 2: the area between the stress – plastic displacement curve of the exponential function corresponds to the failure energy ENER.

        D=1 e E dis G f with E dis = D=0 D=1 σ Y L e Δ ε p MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqbaeqabeWaaa qaaiaadseacqGH9aqpcaaIXaGaeyOeI0IaamyzamaaCaaaleqabaGa eyOeI0YaaSaaaeaacaWGfbWaaSbaaWqaaiaadsgacaWGPbGaam4Caa qabaaaleaacaWGhbWaaSbaaWqaaiaadAgaaeqaaaaaaaaakeaacaqG 3bGaaeyAaiaabshacaqGObaabaGaamyramaaBaaaleaacaWGKbGaam yAaiaadohaaeqaaOGaeyypa0Zaa8qCaeaacqaHdpWCdaWgaaWcbaGa amywaaqabaGccqGHflY1caWGmbWaaSbaaSqaaiaadwgaaeqaaOGaey iLdqKaeqyTdu2aaSbaaSqaaiaadchaaeqaaaqaaiaadseacqGH9aqp caaIWaaabaGaamiraiabg2da9iaaigdaa0Gaey4kIipaaaaaaa@5C9B@



        Figure 4. Exponential damage evolution with fracture energy input ENER
  7. For the same material, several pairs of Initiation/Evolution criteria can be defined in the same input card, setting a value NINIEVO > 1. In this case, another parameter COMPTYP can be used to choose the way the different criteria are combined to create the softening effect.
    • If COMPTYP = 1: the damage variable of the criterion concerned, denoted as D i MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiramaaBa aaleaacaWGPbaabeaaaaa@37D7@ , is compared with the maximum value among all the criteria using COMPTYP = 1.

      D MAX =max D i , D MAX with i N MAX MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqbaeqabeWaaa qaaiaadseadaWgaaWcbaGaamytaiaadgeacaWGybaabeaakiabg2da 9iGac2gacaGGHbGaaiiEamaabmaabaGaamiramaaBaaaleaacaWGPb aabeaakiaacYcacaWGebWaaSbaaSqaaiaad2eacaWGbbGaamiwaaqa baaakiaawIcacaGLPaaaaeaacaWG3bGaamyAaiaadshacaWGObaaba GaamyAaiabgIGiodaacaWGobWaaSbaaSqaaiaad2eacaWGbbGaamiw aaqabaaaaa@4EA0@

      Where, N MAX MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOtamaaBa aaleaacaWGnbGaamyqaiaadIfaaeqaaaaa@3967@ is the number of initiation/evolution card using COMPTYP = 1.

    • If COMPTYP = 2: the damage variable of the criterion concerned, denoted as D i MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiramaaBa aaleaacaWGPbaabeaaaaa@37D7@ , is accumulated by a multiplicative formula among all the criteria using COMPTYP = 2.(7)
      D M U L T = 1 i N m u l t ( 1 D i ) MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiramaaBa aaleaacaWGnbGaamyvaiaadYeacaWGubaabeaakiabg2da9iaaigda cqGHsisldaqeqbqaaiaacIcacaaIXaGaeyOeI0IaamiramaaBaaale aacaWGPbaabeaakiaacMcaaSqaaiaadMgacqGHiiIZcaWGobWaaSba aWqaaiaad2gacaWG1bGaamiBaiaadshaaeqaaaWcbeqdcqGHpis1aa aa@4B49@

      Where, N M U L T MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOtamaaBa aaleaacaWGnbGaamyvaiaadYeacaWGubaabeaaaaa@3A48@ is the number of initiation/evolution card using COMPTYP = 2.

    Finally, the global damage variable used to calculate the damaged stress tensor is defined as the following maximum value:(8)
    D=max D MAX , D MULT σ=(1D) σ eff MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaacaWGeb Gaeyypa0JaciyBaiaacggacaGG4bWaaeWaaeaacaWGebWaaSbaaSqa aiaad2eacaWGbbGaamiwaaqabaGccaGGSaGaamiramaaBaaaleaaca WGnbGaamyvaiaadYeacaWGubaabeaaaOGaayjkaiaawMcaaaqaaiaa ho8acqGH9aqpcaGGOaGaaGymaiabgkHiTiaadseacaGGPaGaaC4Wdm aaBaaaleaacaWGLbGaamOzaiaadAgaaeqaaaaaaa@4EF9@
    Where,
    σ MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaC4Wdaaa@3742@
    Final damaged stress tensor
    σ eff MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaC4WdmaaBa aaleaacaWGLbGaamOzaiaadAgaaeqaaaaa@3A2E@
    Effective stress tensor (obtained from the material law after plastic return mapping)
  8. FAILIP is an integer value used only for higher order or fully-integrated solid elements. It defines the number of failed integration points before deletion of the solid element.
  9. The parameter PTHICKFAIL is a real parameter used for shell elements. If PTHICKFAIL is blank or set to 0.0, the value of PTHICKFAIL from the shell property is used. If PTHICKFAIL > 0.0, any PTHICKFAIL value defined in the shell properties are ignored and the value entered in this failure model is used. For values of PTHICKFAIL > 0.0, shell elements fail and are deleted when the ratio of through thickness failed integration points equals or exceeds PTHICKFAIL.
  10. ILEN is a flag parameter for you to choose between two possible formulas for computing the element characteristic length L e MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamitamaaBa aaleaacaWGLbaabeaaaaa@37DA@ .
    ILEN=0
    Initial geometrical formulation, where the characteristic length corresponds to the square root of the initial area for shells L e = A 0 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamitamaaBa aaleaacaWGLbaabeaakiabg2da9maakaaabaGaamyqamaaBaaaleaa caaIWaaabeaaaeqaaaaa@3AA6@ and the cubic root of initial volume for solids L e = V 0 3 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamitamaaBa aaleaacaWGLbaabeaakiabg2da9maakeaabaGaamOvamaaBaaaleaa caaIWaaabeaaaeaadaahaaadbeqaaiaaiodaaaaaaaaa@3BA6@ .
    ILEN = 1
    Initial critical timestep formulation where the characteristic length corresponds to the one used to compute the initial element critical timestep. The formula used may vary between the different formulations of shells or solids.
    ILEN = 2
    Current geometrical formulation, where the characteristic length corresponds to the square root of the current area for shells L e = A MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamitamaaBa aaleaacaWGLbaabeaakiabg2da9maakaaabaGaamyqaaWcbeaaaaa@39CB@ .
  11. If the non-local regularization is used (/NONLOCAL/MAT), the non-local plastic strain is used to compute the damage initiation variable and the damage variable (and the instability variable if used). Also, in this case, the initial element length L e MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamitamaaBa aaleaacaWGLbaabeaaaaa@37DA@ in all formula is replaced by the non-local parameter L M A X MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamitamaaBa aaleaacaWGnbGaamyqaiaadIfaaeqaaaaa@3966@ .