/FAIL/SYAZWAN

Block Format Keyword This simplified failure criterion is based on a fracture surface with linear damage accumulation. It also provides the initialization of damage value using strain histories with linear strain path assumptions.

Format

Card 1 – Fracture surface parameters 1
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
/FAIL/SYAZWAN/mat_ID/unit_ID
Icard MathType@MTEF@5@5@+=feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamysaiaadogacaWGHbGaamOCaiaadsgaaaa@3A70@ εpfMIN MathType@MTEF@5@5@+=feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyTdu2aa0baaSqaaiaadchaaeaacaWGMbaaaOWaaSbaaSqaaiaad2eacaWGjbGaamOtaaqabaaaaa@3C51@      
If Icard MathType@MTEF@5@5@+=feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamysaiaadogacaWGHbGaamOCaiaadsgaaaa@3A70@ = 1: classical input / Card 2 – Fracture surface parameters
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
C1 C2 C3 C4 C5
C6        
If Icard MathType@MTEF@5@5@+=feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamysaiaadogacaWGHbGaamOCaiaadsgaaaa@3A70@ = 2: plastic strain input / Card 2 – Failure plastic strains
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
εfcomp MathType@MTEF@5@5@+=feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyTdu2aa0baaSqaaiaadAgaaeaacaWGJbGaam4Baiaad2gacaWGWbaaaaaa@3C75@ εfshear MathType@MTEF@5@5@+=feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyTdu2aa0baaSqaaiaadAgaaeaacaWGJbGaam4Baiaad2gacaWGWbaaaaaa@3C75@ εftens MathType@MTEF@5@5@+=feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyTdu2aa0baaSqaaiaadAgaaeaacaWGJbGaam4Baiaad2gacaWGWbaaaaaa@3C75@ εfplane MathType@MTEF@5@5@+=feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyTdu2aa0baaSqaaiaadAgaaeaacaWGJbGaam4Baiaad2gacaWGWbaaaaaa@3C75@ εfbiax MathType@MTEF@5@5@+=feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyTdu2aa0baaSqaaiaadAgaaeaacaWGJbGaam4Baiaad2gacaWGWbaaaaaa@3C75@
Card 3 – Damage initialization parameters
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
Dinit Dsf Dmax
Card 4 – Instability and softening parameters
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
Inst Iform Nvalue Softexp
Card 5 – Element size scaling
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
fct_IDEl El_ref Fscale_El
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)

Icard MathType@MTEF@5@5@+=feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamysaiaadogacaWGHbGaamOCaiaadsgaaaa@3A70@ Card input format flag. 3
= 1 (Default)
Fracture surface parameters input.
= 2
Plastic strain at failure input.

(Integer)

εpfMIN MathType@MTEF@5@5@+=feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyTdu2aa0baaSqaaiaadchaaeaacaWGMbaaaOWaaSbaaSqaaiaad2eacaWGjbGaamOtaaqabaaaaa@3C51@ Minimum plastic strain at failure.

Default = 0.0 (Real)

C1 First constant for failure surface.

(Real)

C2 Second constant for failure surface.

(Real)

C3 Third constant for failure surface.

(Real)

C4 Fourth constant for failure surface.

(Real)

C5 Fifth constant for failure surface.

(Real)

C6 Sixth constant for failure surface.

(Real)

εfcomp MathType@MTEF@5@5@+=feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyTdu2aa0baaSqaaiaadAgaaeaacaWGJbGaam4Baiaad2gacaWGWbaaaaaa@3C75@ Plastic strain at failure for uniaxial compression.

(Real)

εfshear MathType@MTEF@5@5@+=feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyTdu2aa0baaSqaaiaadAgaaeaacaWGJbGaam4Baiaad2gacaWGWbaaaaaa@3C75@ Plastic strain at failure for shearing.

(Real)

εftens MathType@MTEF@5@5@+=feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyTdu2aa0baaSqaaiaadAgaaeaacaWGJbGaam4Baiaad2gacaWGWbaaaaaa@3C75@ Plastic strain at failure for uniaxial tension.

(Real)

εfplane MathType@MTEF@5@5@+=feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyTdu2aa0baaSqaaiaadAgaaeaacaWGJbGaam4Baiaad2gacaWGWbaaaaaa@3C75@ Plastic strain at failure for plane strain.

(Real)

εfbiax MathType@MTEF@5@5@+=feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyTdu2aa0baaSqaaiaadAgaaeaacaWGJbGaam4Baiaad2gacaWGWbaaaaaa@3C75@ Plastic strain at failure for biaxial tension.

(Real)

Dinit Damage value initialization from strain tensors flag.
= 0 (Default)
Damage is not initialized.
= 1
Damage is initialized.

(Integer)

Dsf Damage initialization scale factor.

Default = 1.0 (Real)

Dmax Damage initialization maximum value.

Default = 1.0 (Real)

Inst Necking instability flag.
= 0 (Default)
Instability is not activated.
= 1
Instability is activated.

(Integer)

Iform Necking instability formulation flag.
= 1 (Default)
Incremental formulation (loading path history).
= 2
Direct formulation (no loading path history).

(Integer)

Nvalue The N-value derived from Hollomon’s Law.

Default = 0.25 (Real)

Softexp Stress softening exponent.

Default = 1.0 (Real)

fct_IDEl Element size factor function identifier.

(Integer)

El_ref Reference element size.

Default = 1.0 (Real)

[m]
Fscale_El Element size factor function scale factor.

Default = 1.0

fail_ID (Optional) Failure criteria identifier.

(Integer, maximum 10 digits)

Example

Comments

  1. It is highly recommended to set the value of Iplas MathType@MTEF@5@5@+=feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamysamaaBaaaleaacaWGWbGaamiBaiaadggacaWGZbaabeaaaaa@3AB2@ in /PROP/SHELL to 1. This will allow accurate calculation of the principal strain ratio β .
  2. The value of C1, C2, C3, C4, C5, and C6 is based on:(1)
    εpf=C1+C2η+C3θ¯+C4η2+C5θ¯2+C6ηθ¯ MathType@MTEF@5@5@+=feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyTdu2aa0baaSqaaiaadchaaeaacaWGMbaaaOGaeyypa0Jaam4qamaaBaaaleaacaaIXaaabeaakiabgUcaRiaadoeadaWgaaWcbaGaaGOmaaqabaGccqaH3oaAcqGHRaWkcaWGdbWaaSbaaSqaaiaaiodaaeqaaOGafqiUdeNbaebacqGHRaWkcaWGdbWaaSbaaSqaaiaaisdaaeqaaOGaeq4TdG2aaWbaaSqabeaacaaIYaaaaOGaey4kaSIaam4qamaaBaaaleaacaaI1aaabeaakiqbeI7aXzaaraWaaWbaaSqabeaacaaIYaaaaOGaey4kaSIaam4qamaaBaaaleaacaaI2aaabeaakiabeE7aOjqbeI7aXzaaraaaaa@55DB@
    Where,
    εpf MathType@MTEF@5@5@+=feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaH1oqzdaqhaaWcbaGaamiCaaqaaiaadAgaaaaaaa@3B18@
    Plastic strain at failure.
    η
    Stress triaxiality with η=13σxx+σyyσVM MathType@MTEF@5@5@+=feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaH3oaAcqGH9aqpdaWcaaqaamaalaaabaGaaGymaaqaaiaaiodaaaWaaeWaceaacqaHdpWCdaWgaaWcbaGaamiEaiaadIhaaeqaaOGaey4kaSIaeq4Wdm3aaSbaaSqaaiaadMhacaWG5baabeaaaOGaayjkaiaawMcaaaqaaiabeo8aZnaaBaaaleaacaWGwbGaamytaaqabaaaaaaa@499F@
    with 23η23 MathType@MTEF@5@5@+=feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqGHsisldaWcaaqaaiaaikdaaeaacaaIZaaaaiabgsMiJkabeE7aOjabgsMiJoaalaaabaGaaGOmaaqaaiaaiodaaaaaaa@4079@
    θ¯ MathType@MTEF@5@5@+=feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacuaH4oqCgaqeaaaa@3932@
    Normalized Lode angle θ¯=12πarcosζ MathType@MTEF@5@5@+=feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacuaH4oqCgaqeaiabg2da9iaaigdacqGHsisldaWcaaqaaiaaikdaaeaacqaHapaCaaGaamyyaiaadkhaciGGJbGaai4BaiaacohacqaH2oGEaaa@44D6@
    with Lode angle ( θ ) parameter ζ=cos3θ=272ηη213 MathType@MTEF@5@5@+=feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaH2oGEcqGH9aqpciGGJbGaai4BaiaacohadaqadaqaaiaaiodacqaH4oqCaiaawIcacaGLPaaacqGH9aqpcqGHsisldaWcaaqaaiaaikdacaaI3aaabaGaaGOmaaaacqaH3oaAdaqadaqaaiabeE7aOnaaCaaaleqabaGaaGOmaaaakiabgkHiTmaalaaabaGaaGymaaqaaiaaiodaaaaacaGLOaGaayzkaaaaaa@4D7B@

    Where, σVM MathType@MTEF@5@5@+=feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaHdpWCdaWgaaWcbaGaamOvaiaad2eaaeqaaaaa@3B00@ is the von Mises stress.

    Figure 1 shows the example of curve fit of plane stress failure curve into failure surface criteria.


    Figure 1. Example of Syazwan failure criterion fit
  3. Two different parameter input card formats are available for /FAIL/SYAZWAN depending on the value of Icard MathType@MTEF@5@5@+=feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamysaiaadogacaWGHbGaamOCaiaadsgaaaa@3A70@ .
    • If Icard MathType@MTEF@5@5@+=feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamysaiaadogacaWGHbGaamOCaiaadsgaaaa@3A70@ = 1: you must directly input the Ci parameters
    • If Icard MathType@MTEF@5@5@+=feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamysaiaadogacaWGHbGaamOCaiaadsgaaaa@3A70@ = 2: you can specify some plastic strain at failure for several commonly tested loading conditions: uniaxial compression εfcomp MathType@MTEF@5@5@+=feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyTdu2aa0baaSqaaiaadAgaaeaacaWGJbGaam4Baiaad2gacaWGWbaaaaaa@3C75@ , shearing εfshear MathType@MTEF@5@5@+=feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyTdu2aa0baaSqaaiaadAgaaeaacaWGZbGaamiAaiaadwgacaWGHbGaamOCaaaaaaa@3D5E@ , uniaxial tension εftens MathType@MTEF@5@5@+=feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyTdu2aa0baaSqaaiaadAgaaeaacaWG0bGaamyzaiaad6gacaWGZbaaaaaa@3C80@ , plane strain εfplane MathType@MTEF@5@5@+=feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyTdu2aa0baaSqaaiaadAgaaeaacaWGWbGaamiBaiaadggacaWGUbGaamyzaaaaaaa@3D5B@ and biaxial tension εfbiax MathType@MTEF@5@5@+=feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyTdu2aa0baaSqaaiaadAgaaeaacaWGIbGaamyAaiaadggacaWG4baaaaaa@3C6A@ . In that case, the Ci parameter will be automatically computed by solving the set of equations below:(2)
      C113C2C3+19C4+C5+13C6=εfcompC1=εfshearC1+13C2+C3+19C4+C5+13C6=εftensC1+13C2+13C4=εfplaneC1+23C2C3+49C4+C523C6=εfbiaxC218πC3+23C418π3C6=0 MathType@MTEF@5@5@+=feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=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@B9A9@
    Note: The last equation imposes that the plane strain condition corresponds to a local minimum of the failure criterion.
  4. In some cases, the criterion may have negative or very low values for some loading conditions. In that case, it will be bounded by the minimum plastic strain at failure parameter εpfMIN MathType@MTEF@5@5@+=feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyTdu2aa0baaSqaaiaadchaaeaacaWGMbaaaOWaaSbaaSqaaiaad2eacaWGjbGaamOtaaqabaaaaa@3C51@ that must be positive or null (by default = 0.0). All values under εpfMIN MathType@MTEF@5@5@+=feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyTdu2aa0baaSqaaiaadchaaeaacaWGMbaaaOWaaSbaaSqaaiaad2eacaWGjbGaamOtaaqabaaaaa@3C51@ are then ignored.
    Figure 2 shows an example with a minimum value (orange curve) of 0.2.


    Figure 2. Failure criterion (blue curve) bounded by plastic strain at failure minimum value. εpfMIN MathType@MTEF@5@5@+=feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyTdu2aa0baaSqaaiaadchaaeaacaWGMbaaaOWaaSbaaSqaaiaad2eacaWGjbGaamOtaaqabaaaaa@3C51@ (orange curve) of 0.2
  5. The damage variable evolution is computed incrementally as:(3)
    D=t=0Δεpεpf MathType@MTEF@5@5@+=feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiraiabg2da9maaqahabaWaaSaaaeaacqGHuoarcqaH1oqzdaWgaaWcbaGaamiCaaqabaaakeaacqaH1oqzdaqhaaWcbaGaamiCaaqaaiaadAgaaaaaaaqaaiaadshacqGH9aqpcaaIWaaabaGaeyOhIukaniabggHiLdaaaa@4621@
  6. You may want to realize a simulation starting from existing total and plastic strains fields (after a previous forming simulation for instance). In the case where the failure criterion is not computed during the first simulation, it is possible to estimate a damage field from the total strain tensor and the plastic strain values obtained at the end of the first simulation (using .sta files). If the Dinit flag is set to 1, the damage field will be computed if the plastic strain ≠ 0. /INISHE/STRA_F, /INISHE/STRA_F, /INISHE/EPSP_F and /INISH3/EPSP_F must be present in the keywords of the status file. The initial stress tensors are not incorporated into the simulation model; thus, the stress triaxiality is derived using:(4)
    η=131+β1+β+β2 MathType@MTEF@5@5@+=feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4TdGMaeyypa0ZaaSaaaeaacaaIXaaabaWaaOaaaeaacaaIZaaaleqaaaaakmaalaaabaGaaGymaiabgUcaRiabek7aIbqaamaakaaabaGaaGymaiabgUcaRiabek7aIjabgUcaRiabek7aInaaCaaaleqabaGaaGOmaaaaaeqaaaaaaaa@445B@
    The β value can be recovered from the stress triaxiality value using the first root of Equation 4:(5)
    β=(23η2)3η249η223η21 MathType@MTEF@5@5@+=feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqOSdiMaeyypa0ZaaSaaaeaacaGGOaGaaGOmaiabgkHiTiaaiodacqaH3oaAdaahaaWcbeqaaiaaikdaaaGccaGGPaGaeyOeI0YaaOaaaeaacaaIZaGaeq4TdG2aaWbaaSqabeaacaaIYaaaaOWaaeWaaeaacaaI0aGaeyOeI0IaaGyoaiabeE7aOnaaCaaaleqabaGaaGOmaaaaaOGaayjkaiaawMcaaaWcbeaaaOqaaiaaikdadaqadaqaaiaaiodacqaH3oaAdaahaaWcbeqaaiaaikdaaaGccqGHsislcaaIXaaacaGLOaGaayzkaaaaaaaa@5156@
    Then, an initial damage value can be estimated as:(6)
    Dt=0=εpt=0εpf MathType@MTEF@5@5@+=feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiramaaBaaaleaacaWG0bGaeyypa0JaaGimaaqabaGccqGH9aqpdaWcaaqaaiabew7aLnaaDaaaleaacaWGWbaabaGaamiDaiabg2da9iaaicdaaaaakeaacqaH1oqzdaqhaaWcbaGaamiCaaqaaiaadAgaaaaaaaaa@4402@
    Figure 3 shows an example of initialized damage field in one-step after a forming simulation performed without failure criterion computation. Damage field is then deduced using the plastic strain and the strain tensor as presented above.


    Figure 3. Example of damage field “one-step” initialization after a forming simulation
  7. A controlled necking instability can be used if the flag Inst is set to 1. To trigger this instability, a criterion variable denoted f MathType@MTEF@5@5@+=feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOzaaaa@36DF@ is computed based on the Nvalue specified by you, using:(7)
    ε1=2(2α)(1α+α2)43α3α2+4αNvalueε2=2(2α1)(1α+α2)43α3α2+4αNvalue MathType@MTEF@5@5@+=feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaacqaH1oqzdaWgaaWcbaGaaGymaaqabaGccqGH9aqpdaWcaaqaaiaaikdacaGGOaGaaGOmaiabgkHiTiabeg7aHjaacMcacaGGOaGaaGymaiabgkHiTiabeg7aHjabgUcaRiabeg7aHnaaCaaaleqabaGaaGOmaaaakiaacMcaaeaacaaI0aGaeyOeI0IaaG4maiabeg7aHjabgkHiTiaaiodacqaHXoqydaahaaWcbeqaaiaaikdaaaGccqGHRaWkcaaI0aGaeqySdegaaiaad6eadaWgaaWcbaGaamODaiaadggacaWGSbGaamyDaiaadwgaaeqaaaGcbaGaeqyTdu2aaSbaaSqaaiaaikdaaeqaaOGaeyypa0ZaaSaaaeaacaaIYaGaaiikaiaaikdacqaHXoqycqGHsislcaaIXaGaaiykaiaacIcacaaIXaGaeyOeI0IaeqySdeMaey4kaSIaeqySde2aaWbaaSqabeaacaaIYaaaaOGaaiykaaqaaiaaisdacqGHsislcaaIZaGaeqySdeMaeyOeI0IaaG4maiabeg7aHnaaCaaaleqabaGaaGOmaaaakiabgUcaRiaaisdacqaHXoqyaaGaamOtamaaBaaaleaacaWG2bGaamyyaiaadYgacaWG1bGaamyzaaqabaaaaaa@7B6C@
    Where, α MathType@MTEF@5@5@+=feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqySdegaaa@3793@ ratio between the minor principal and major principal stress computed from β using:(8)
    α=2β+12+β MathType@MTEF@5@5@+=feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqySdeMaeyypa0ZaaSaaaeaacaaIYaGaeqOSdiMaey4kaSIaaGymaaqaaiaaikdacqGHRaWkcqaHYoGyaaaaaa@3FE2@
    You can then compute an effective plastic strain at necking instability:(9)
    εpinst=ε1431+β+β2 MathType@MTEF@5@5@+=feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyTdu2aa0baaSqaaiaadchaaeaacaWGPbGaamOBaiaadohacaWG0baaaOGaeyypa0JaeqyTdu2aaSbaaSqaaiaaigdaaeqaaOGaeyyXIC9aaOaaaeaadaWcaaqaaiaaisdaaeaacaaIZaaaamaabmaabaGaaGymaiabgUcaRiabek7aIjabgUcaRiabek7aInaaCaaaleqabaGaaGOmaaaaaOGaayjkaiaawMcaaaWcbeaaaaa@4C63@

    The parameter Nvalue is the value of the instability plastic strain taken in uniaxial tension (for which η=1/3 MathType@MTEF@5@5@+=feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4TdGMaeyypa0ZaaSGbaeaacaaIXaaabaGaaG4maaaaaaa@3A34@ and θ¯=1 MathType@MTEF@5@5@+=feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGafqiUdeNbaebacqGH9aqpcaaIXaaaaa@3983@ ). You can then use the relation linking β and the stress triaxiality described above to plot the instability strain evolution.

    Using the instability plastic strain, an instability criterion variable denoted f MathType@MTEF@5@5@+=feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOzaaaa@36DF@ is either computed:
    • Incrementally (if Iform = 1) to take into account the loading history(10)
      f=t=0Δεpεpinst MathType@MTEF@5@5@+=feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOzaiabg2da9maaqahabaWaaSaaaeaacqGHuoarcqaH1oqzdaWgaaWcbaGaamiCaaqabaaakeaacqaH1oqzdaqhaaWcbaGaamiCaaqaaiaadMgacaWGUbGaam4CaiaadshaaaaaaaqaaiaadshacqGH9aqpcaaIWaaabaGaeyOhIukaniabggHiLdaaaa@492A@
    • Directly (if Iform = 2) to ignore the loading path history(11)
      f=εpεpinst MathType@MTEF@5@5@+=feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOzaiabg2da9maalaaabaGaeqyTdu2aaSbaaSqaaiaadchaaeqaaaGcbaGaeqyTdu2aa0baaSqaaiaadchaaeaacaWGPbGaamOBaiaadohacaWG0baaaaaaaaa@4161@
    If the criterion is reached ( f=1 MathType@MTEF@5@5@+=feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOzaiabg2da9iaaigdaaaa@38A0@ ), the instant value of the damage variable D MathType@MTEF@5@5@+=feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiraaaa@36BC@ is saved in the value Dcrit MathType@MTEF@5@5@+=feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiramaaBaaaleaacaWGJbGaamOCaiaadMgacaWG0baabeaaaaa@3AAF@ that becomes an element history variable. The necking instability can then be triggered by a stress softening whose equation is:(12)
    D=ΔDf=ΔfDcrit=1whilef<1Dwhenf1σ=σeff1DDcrit1DcritSoftexp MathType@MTEF@5@5@+=feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=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@797B@
    Where,
    σ
    Damaged stress tensor.
    σeff MathType@MTEF@5@5@+=feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Wdm3aaSbaaSqaaiaadwgacaWGMbGaamOzaaqabaaaaa@3AA3@
    Undamaged effective stress tensor.
    Dcrit MathType@MTEF@5@5@+=feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiramaaBaaaleaacaWGJbGaamOCaiaadMgacaWG0baabeaaaaa@3AAE@
    Critical damage value that triggers stress softening.
    Softexp MathType@MTEF@5@5@+=feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4uaiaad+gacaWGMbGaamiDamaaBaaaleaaciGGLbGaaiiEaiaacchaaeqaaaaa@3CAA@
    Exponent parameter.
    For visualization purposes, the instability curve ( εpinst MathType@MTEF@5@5@+=feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyTdu2aa0baaSqaaiaadchaaeaacaWGPbGaamOBaiaadohacaWG0baaaaaa@3C8E@ versus η ) can be obtained from all the equations above. For instance, if the Nvalue is set to 0.175, the following curve (Figure 4) is obtained.


    Figure 4. Example of instability curve (orange) and its position with respect to failure criterion (blue)

    The effect of instability curve is restricted to positive stress triaxiality (as necking only occurs in tension) and only has an effect when it is under the failure criterion curve.

    Figure 5 shows several instability curves obtained with different Nvalue parameter values.


    Figure 5. Instability curves obtained with different Nvalue parameters
  8. Element size scaling can be used to regularize the failure and ensure to obtain an almost constant fracture energy dissipated with different mesh sizes. This element size dependency is introduced by computing a size scale factor denoted fsize MathType@MTEF@5@5@+=feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaeOzamaaBaaaleaacaWGZbGaamyAaiaadQhacaWGLbaabeaaaaa@3AD8@ defined by the function fct_IDEl. The size scaling factor evolution is given with respect to the ratio of initial element characteristic length divided by a reference size El_ref (by default = 1.0): fsizeLe0Lref MathType@MTEF@5@5@+=feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaeOzamaaBaaaleaacaWGZbGaamyAaiaadQhacaWGLbaabeaakmaabmaabaWaaSaaaeaacaWGmbWaa0baaSqaaiaadwgaaeaacaaIWaaaaaGcbaGaamitamaaBaaaleaacaWGYbGaamyzaiaadAgaaeqaaaaaaOGaayjkaiaawMcaaaaa@42F9@ . An additional scale factor Fscale_El can also be applied to the entire regularization function. The element size scale factor fsize MathType@MTEF@5@5@+=feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaeOzamaaBaaaleaacaWGZbGaamyAaiaadQhacaWGLbaabeaaaaa@3AD8@ thus computed is introduced in the damage variable evolution equation (and if defined, the instability variable evolution equation) as:(13)
    D=t=0ΔεpεpffsizeLe0Lreffscaleel MathType@MTEF@5@5@+=feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiraiabg2da9maaqahabaWaaSaaaeaacqGHuoarcqaH1oqzdaWgaaWcbaGaamiCaaqabaaakeaacqaH1oqzdaqhaaWcbaGaamiCaaqaaiaadAgaaaGccqGHflY1caqGMbWaaSbaaSqaaiaadohacaWGPbGaamOEaiaadwgaaeqaaOWaaeWaaeaadaWcaaqaaiaadYeadaqhaaWcbaGaamyzaaqaaiaaicdaaaaakeaacaWGmbWaaSbaaSqaaiaadkhacaWGLbGaamOzaaqabaaaaaGccaGLOaGaayzkaaGaeyyXICTaaeOzamaaDaaaleaacaWGZbGaam4yaiaadggacaWGSbGaamyzaaqaaiaadwgacaWGSbaaaaaaaeaacaWG0bGaeyypa0JaaGimaaqaaiabg6HiLcqdcqGHris5aaaa@5F57@
  9. Alternatively, the /NONLOCAL/MAT option which is compatible with Syazwan failure criterion (Figure 6) can be used to regularize the solution according to mesh size and orientation. If the non-local regularization is used, the non-local plastic strain is used to compute the damage evolution (and the instability variable, if used). In that case, the maximum non-local length parameter LE_MAX is used instead of the initial element size if an element size scaling is defined through fct_IDEl. Also, the non-local regularization is also available with the “one-step” damage field initialization.


    Figure 6. Example of /NONLOCAL/MAT option cumulated with /FAIL/SYAZWAN on automotive DP450 steel