MATF

Bulk Data Entry Defines material properties and failure model parameters for Failure criteria calculations.

Attention: Valid for Implicit and Explicit Analysis

Format A - Implicit

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
MATF MID                
  CRI CRITERIA TID/V1 V2 V3 V4 V5 V6  
  V7 V8 V9   V10 V11 V12 W1  
  W2 W3 W4            
  etc.                

Format B - Explicit

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
MATF MID DAMAGE DC EXP          
  CRI CRITERIA EPS_TID/ MATER/ INI_ID V1/EVO_ID V2 V3 V4 V5  
      INST_ID V6 V7 V8      
    DEP_L E_TID EL_REF FE_SCL        
    DEP_SR V_TID V_REF VT_SCL JC      

Example A

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
MATF 100                
  CRI PUCK 3.E5 3.E5 3.E5 3.E5 3.E5    
                0.25  
  0.25 0.25              

Example B.1 (Non-linear partially coupled BIQUAD criterion with classic input)

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
MATF 1 DAMAGE 0.2 2.0          
  CRI BIQUAD   1.5 0.25 0.35 0.09 0.12  
        0.045          

Example B.2 (Coupled equivalent strain TSTRN criterion with strain-rate dependency)

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
MATF 1 DAMAGE 0.0 1.0          
  CRI TSTRN 0.05 50.0          
    DEP_SR 9 2.1 1.5        

Example B.3 (Coupled TAB criterion with controlled necking and element size dependency)

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
MATF 1 DAMAGE 0.0 2.5          
  CRI TAB 36 1.0 2.0        
      36 0.5 -0.33 0.66      
    DEP_L 9 5.2 0.8        

Definitions

Field Contents SI Unit Example
MID Material identification number.

(Integer > 0)

 
CRI Flag to indicate that the failure criterion input data are to follow. 3  
CRITERIA Character String representing the chosen failure criterion.
PUCK
Puck failure criterion
HILL
Hill failure criterion
HOFF
Hoffman failure criterion
TSAI
Tsai-Wu failure criterion
HASH
Hashin failure criterion
STRN
Maximum strain failure criterion
STRS
Maximum stress failure criterion
DUCTILE
Damage initiation criterion
PUCK3D
Puck failure criterion for continuum shell elements
HILL3D
Hill failure criterion for continuum shell elements/solid elements with anisotropic material
HOFF3D
Hoffman failure criterion for continuum shell elements/solid elements with anisotropic material
TSAI3D
Tsai-Wu Failure criterion for continuum shell elements/solid elements with anisotropic material
HASH3D
Hashin failure criterion for continuum shell elements
STRN3D
Maximum strain failure criterion for continuum shell elements/solid elements with anisotropic material
STRS3D
Maximum stress failure criterion for continuum shell elements/solid elements with anisotropic material
CNTZ3D
Cuntze failure criterion for continuum shell elements
BIQUAD
Bi-quadratic criterion
TSTRN
Tensile strain criterion
TAB
Tabulated criterion
INIEVO
Damage initiation/evolution criterion

No default

 
TID Identification number of a TABLEMD entry that identifies the equivalent plastic strain (Yi) at the onset of damage versus temperature (Xi). 6  
Vi Material limits. 1, 2

(Real > 0.0)

 
Wi Parameters for failure criteria calculations. 3
W1
Failure envelope factor 12(-).
W2
Failure envelope factor 12(+)
If blank, set to be equal to W1, W1 and W3 should be specified.
W3
Failure envelope factor 22(-).
W4
Failure envelope factor 22(+).
This is only used for PUCK3D.

(Real > 0.0)

 
DAMAGE Flag to activate element deletion and stress softening. 2, 8

By default, damage is only used as an output variable.

Default = blank

 
D C MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiramaaBa aaleaacaWGdbaabeaaaaa@37B0@ Critical damage value from which the stress softening is triggered. This is valid only if DAMAGE is activated. 2, 8
0
Stress softening from the beginning (fully coupled approach)
0 < DC < 1
Stress softening from a DC value (partially coupled approach)
1
No stress softening, the element is deleted when DC = 1 (failure criterion approach)
Default = 0.95 (95 percent damage) (Real)
 
EXP Nonlinear exponent for stress softening. This is valid only if DAMAGE is activated. 2, 8

Default = 1.0 (Real)

 
EPS_TID For CRI=TAB.

TABLEMD ID defining plastic strain at failure evolution with stress triaxiality and lode parameter.

No default (Integer)

 
MATER For CRI=BIQUAD.

Character string selector for partially automatic parameter setup.

This is optional and can be used when material data is unavailable.

Note: It is still recommended to provide at least c3 for accurate calculation.
MILD
Mild steel
HSS
HSS steel
UHSS
UHSS steel
AA5182
Aluminum AA5182
AA6082
Aluminum AA6082-T6
PA6GF30
Plastic PA6GF30
PPT40
Plastic PP T40
Default = blank (Character)
 
INST_ID For CRI=TAB.

TABLEMD ID defining plastic strain at necking instability evolution with stress triaxiality and Lode parameter.

Default = blank (Integer)

 
DEP_L Flag to activate element size dependency. 4

No default

 
E_TID (Optional) TABLEMD ID for tabulated element size dependency.

Default = blank (Integer)

 
EL_REF Reference element size.

Default = blank or 1.0 (when E_TID is defined (Real)

 
FE_SCALE Scale factor for element size dependency table.

This affects the rate of increase or decrease of values defined in the table.

Default = blank or 1.0 (when E_TID is defined) (Real)

 
DEP_SR Flag to activate strain rate dependency. 3  
V_TID TABLEMD ID for strain rate dependency.

Default = blank (Integer)

 
V_REF Reference strain rate.

Default = 1.0 (Real)

 
VT_SCALE Scale factor for strain rate dependency table.

This affects the rate of increase or decrease of values defined in the table.

Default = 1.0 (Real)

 
JC Johnson-Cook strain rate dependency factor.

Default = 0.0 (Real)

 
INI_ID For CRI=INIEVO. 7

ID of the DMGINI Bulk Data Entry.

 
EVO_ID For CRI=INIEVO

ID of the DMGEVO Bulk Data Entry.

Default = blank (Integer)

 

Comments

  1. MID field may refer to MAT1, MAT2, MAT8, MAT9 or MAT9OR entries.
  2. Support information for various failure criteria:
    Analysis Type Supported Criteria
    Implicit Analysis (Linear and Nonlinear (SMDISP/LGDISP) Static/Transient) Analysis) PUCK, HILL, HOFF, TSAI, HASH, STRN, STRS, DUCTILE, PUCK3D, HILL3D, HOFF3D, TSAI3D, HASH3D, STRN3D, STRS3D, CNTZ3D
    Explicit Dynamic Analysis BIQUAD, TSTRN, TAB, INIEVO
  3. Multiple different failure criteria can be defined on a single MATF Bulk Data Entry. Therefore, the CRI continuation line can be repeated, and multiple different failure criteria can be specified. However, a particular failure criterion can only appear once on the MATF entry and cannot be repeated. Different failure criteria for different materials can be defined by referencing the corresponding material entry (with the same ID as MATF) on MID# fields of the PCOMP(G) and PLY entries (for PCOMPP). If different failure criteria are required to be defined for a single composite property, then the MATF entry should be used.

Comments: Format A

  1. For laminated shells (PCOMP/PCOMPP/PCOMPG).
    V1, V2, through V5 specify material stress/strain limits.
    V1
    Tensile stress/strain limit in longitudinal direction
    V2
    Compressive stress/strain limit in longitudinal direction
    V3
    Tensile stress/strain limit in lateral direction
    V4
    Compressive stress/strain limit in lateral direction
    V5
    In-plane shear stress/strain limit

    For STRS failure criterion, the input allowables should be stress-allowables.

    For STRN failure criterion, the input allowables should be strain-allowables. OptiStruct will not conduct internal conversion for STRN failure criterion. The values defined are directly used as strain-allowables for STRN failure criterion on MATF.

    For STRN failure criterion, the STRN field on MAT8 entry has no effect on the allowable values defined on the MATF entry.

    For Solid Elements (MAT9/MAT9OR) and Continuum Shells (PCOMPLS).

    V1, V2 through V9 specify material stress/strain limits.
    V1
    Tensile stress/strain limit in 1-1 direction
    V2
    Compressive stress/strain limit in 1-1 direction
    V3
    Tensile stress/strain limit in 2-2 direction
    V4
    Compressive stress/strain limit in 2-2 direction
    V5
    Tensile stress/strain limit in 3-3 direction
    V6
    Compressive stress/strain limit in 3-3 direction
    V7
    Shear stress/strain limit in 1-2 direction
    V8
    Shear stress/strain limit in 2-3 direction
    V9
    Shear stress/strain limit in 1-3 direction

    Coordinate system 1-2-3 are user-defined for continuum shell elements or solid elements with MAT9.

    For STRS3D failure criterion, the input allowables should be stress-allowables.

    For STRN3D failure criterion, the input allowables should be strain-allowables. OptiStruct will not conduct internal conversion for STRN3D failure criterion. The values defined are directly used as strain-allowables for STRN3D failure criterion on MATF.

  2. V10, V11, and V12 are used for TSAI/TSAI3D criterion.
    • For TSAI:
      • V10: the coupling coefficient C 12 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4qamaaBa aaleaacaaIXaGaaGOmaaqabaaaaa@3862@ for the σ 1 σ 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Wdm3aaS baaSqaaiaaigdaaeqaaOGaeq4Wdm3aaSbaaSqaaiaaikdaaeqaaaaa @3B56@ term.
      • If V10 is blank, the coupling coefficient is calculated from W1.
      • If V10 and W1 are both blank, the coupling coefficient is 0.0.
    • For TSAI3D:
      • V10: the coupling coefficient C 12 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4qamaaBa aaleaacaaIXaGaaGOmaaqabaaaaa@3862@ for the σ 1 σ 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Wdm3aaS baaSqaaiaaigdaaeqaaOGaeq4Wdm3aaSbaaSqaaiaaikdaaeqaaaaa @3B56@ term.
      • V11: the coupling coefficient C 23 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4qamaaBa aaleaacaaIXaGaaGOmaaqabaaaaa@3862@ for the σ 2 σ 3 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Wdm3aaS baaSqaaiaaikdaaeqaaOGaeq4Wdm3aaSbaaSqaaiaaiodaaeqaaaaa @3B58@ term.
      • V12: the coupling coefficient C 12 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4qamaaBa aaleaacaaIXaGaaGOmaaqabaaaaa@3862@ for the σ 1 σ 3 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Wdm3aaS baaSqaaiaaigdaaeqaaOGaeq4Wdm3aaSbaaSqaaiaaikdaaeqaaaaa @3B56@ term.
      • If V10, V11, and V12 are all blank, the coupling coefficients are calculated from W1, W2, and W3.
      • If V10, V11, and V12 and W1, W2, and W3 are all blank, the coupling coefficients are 0.0.
  3. W1, W2, W3, and W4 definition is dependent on the failure criterion specified.
    • PUCK/PUCK3D specify failure envelope parameters:
      W1
      Failure envelope factor 12(-)
      W2
      Failure envelope factor 12(+)
      If W2 is blank, it is set to be equal to W1, W1 and W3 should be specified.
      W3
      Failure envelope factor 22(-)
      W4
      Failure envelope factor 22(+).
      This is only used for PUCK3D.
    • TSAI3D on anisotropic solid material

      If V10, V11 and V12 are blank, they are the tensile stress limits in equal-biaxial tension tests. W1 is the tensile stress limit in equal-biaxial tests where the two tensile loads are in directions 1 and 2. W1 is mandatory, while W2 and W3 are optional. If W2 and W3 are not specified, then they are set equal to W1. The definition of W2 and W3 is similar to W1. W2 is the tensile stress limit in equal-biaxial tension tests where the two tensile loads are in directions 2 and 3. W3 is the tensile stress limit in equal-biaxial tension tests where the two tensile loads are in directions 1 and 3.

      If V10, V11 and V12 are defined, W1, W2 and W3 are ignored for TSAI3D.

    • HASH3D

      When Hashin failure criteria is applied on continuum shell elements, W1 is defined as alpha, which takes the transverse shear stress (in 1-2 and 1-3 direction) into account in the tensile fiber check. When W1 is blank, alpha is assumed to be 1.0.

    • CNTZ3D
      When using Cuntze failure criterion, W1 and W2, corresponding to the two free curve parameters,   b | | MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaaiiOaiaadkgapaWaaSbaaSqaa8qacqGHLkIxcaGG8bGaaiiFaaWd aeqaaaaa@3C22@ and b T   MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamOya8aadaqhaaWcbaWdbiabgwQiEbWdaeaapeGaamivaaaakiaa cckaaaa@3B16@ should be provided. The two curve parameters can be determined from multi-axial test data from experiments. Bounds on the safe side for GFRP, CFRP and AFRP are assumed by Cuntze 1 to be:(1)
      0.0.5 < b | | < 0.15 , 1.0 < b | T < 1.6 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaaGimaiaac6cacaaIWaGaaiOlaiaaiwdacqGH8aapcaWGIbWdamaa BaaaleaapeGaeyyPI4LaaiiFaiaacYhaa8aabeaakiaaysW7cqGH8a apcaaIWaGaaiOlaiaaigdacaaI1aGaaiilaiaaysW7caaMc8UaaGym aiaac6cacaaIWaGaeyipaWZdbiaadkgapaWaa0baaSqaa8qacqGHLk IxcaGG8baapaqaa8qacaWGubaaaOWdaiabgYda8iaaigdacaGGUaGa aGOnaiaacYcacaaMc8UaaGjbVlaaicdacqGH8aapcaaMe8+dbiaadk gapaWaa0baaSqaa8qacqGHLkIxcaGG8bGaaiiFaaWdaeaapeGaeqiX dqhaaOWdaiabgYda8iaaicdacaGGUaGaaGinaaaa@6574@
  4. When some failure criteria are defined on both PCOMP(G/P) (allowables on MATi) and MATF, then:
    • If the same criterion type is defined in both PCOMP(G/P) property and the MATF entry, then the allowables defined on the MATF entry will be used in the failure criterion calculations. The MATF entry overwrites the allowables defined by the corresponding MATi entry (if any).
    • If some criteria are only defined on PCOMP(G/P) but not on MATF, then for such criteria, the allowables are taken from corresponding MATi entries.
    • If some criteria are defined on MATF, and PARAM,ALLFT,YES exists, then the criteria defined on MATF will use the allowables defined on MATF. However, the criteria not defined on MATF will be calculated based on allowables defined on the corresponding MATi entry.
  5. The following criteria can only be defined on the MATF entry.

    PUCK, DUCTILE, PUCK3D, HILL3D, HOFF3D, TSAI3D, HASH3D, STRN3D, and CNTZ3D.

    The rest of the criteria can also be defined on the FT field of the corresponding PCOMPP/PCOMPG/PCOMP entry.

    For the PUCK failure criterion, even though it is available on the FT field of the PCOMPP/PCOMPG/PCOMP entry, the corresponding failure envelope factors (W1, W2, W3) can only be defined on the MATF entry. Therefore, the MATF entry is mandatory when PUCK failure criterion is requested via the FT field of PCOMP/PCOMPG/PCOMPP entries, and additionally, the allowables should be defined on the MATF for PUCK criterion only. To use PUCK failure criteria, the MATF entry should be specified with MID referring to the corresponding material entry.

  6. If the CRITERIA field is set to DUCTILE, then the TID field should point to a TABLEMD entry with NDEP set to 1. The first data column (Yi) is the equivalent plastic strain at the onset of damage. The second data column (Xi) is the corresponding temperature. The second column should be specified in ascending order only.

    When the CRITERIA field is set to DUCTILE in OSTTS analysis, the temperature-based lookup is conducted for each temperature to identify the corresponding equivalent plastic strain from the TABLEMD entry. This plastic strain is used in conjunction with the calculated von Mises strain to calculate Damage (This can be output using the DAMAGE I/O Options Entry).

  7. The following tables summarize the supported failure criteria with different properties and materials.
    Table 1. Shell Elements
      PSHELL PCOMP/PCOMPG/PCOMPP
      MAT1/MAT2/MAT8
    HILL No Yes
    HOFF No Yes
    TSAI No Yes
    STRN No Yes
    STRS No Yes
    HASHIN No Yes
    PUCK No Yes
    DUCTILE No Yes
    Table 2. Solid Elements
    PSOLID PCOMPLS
    MAT9 MAT9OR MAT9 MAT9OR
    HILL3D Yes Yes Yes Yes
    HOFF3D Yes Yes Yes Yes
    TSAI3D Yes Yes Yes Yes
    STRN3D Yes Yes Yes Yes
    STRS3D Yes Yes Yes Yes
    HASH3D No Yes Yes Yes
    PUCH3D No Yes Yes Yes
    CNTZ3D No Yes Yes Yes

Comments: Format B

  1. The usage of V1 through V8 in difference criteria for Explicit Dynamic Analysis (Format B) is as follows:
    Vi BIQUAD TSTRN TAB
    V1 Failure plastic strain c1 in simple compression von Mises equivalent strain at which damage starts (eps_es) Scale factor for the EPS_TID table
    V2 Failure plastic strain c2 in pure shear von Mises equivalent strain at which damage ends (eps_ee) n exponent for the damage variable evolution
    V3 Failure plastic strain c3 in simple tension Major equivalent strain at which damage starts (eps_p1) -
    V4 Failure plastic strain c4 in plane strain Major equivalent strain at which damage ends (eps_p2) -
    V5 Failure plastic strain c5 in biaxial tension - -
    V6 Necking instability plastic strain in plane strain Scale factor for INST_TID table -
    V7 Stress triaxiality lower bound for element size regularization Stress triaxiality lower bound for element size regularization -
    V8 - Stress triaxiality upper bound for element size regularization -
  2. When the DAMAGE keyword is activated, the stress softening effect is defined by:(2)
    σ = σ e f f 1 D D C 1 D C E X P MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4WdmNaey ypa0Jaeq4Wdm3aaSbaaSqaaiaadwgacaWGMbGaamOzaaqabaGcdaWa daqaaiaaigdacqGHsisldaWadaqaamaalaaabaGaamiraiabgkHiTi aadseadaWgaaWcbaGaam4qaaqabaaakeaacaaIXaGaeyOeI0Iaamir amaaBaaaleaacaWGdbaabeaaaaaakiaawUfacaGLDbaadaahaaWcbe qaaiaadweacaWGybGaamiuaaaaaOGaay5waiaaw2faaaaa@4CB0@
    Where,
    σ
    Damaged stress tensor
    σ e f f MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Wdm3aaS baaSqaaiaadwgacaWGMbGaamOzaaqabaaaaa@3AA2@
    Undamaged effective stress tensor
    D MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiraaaa@36BC@
    Damage variable
    • If D C = 0 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiramaaBa aaleaacaWGdbaabeaakiabg2da9iaaicdaaaa@397A@ , the stress softening starts as soon as D 0 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiraiabgc Mi5kaaicdaaaa@393D@ and the stress softening is fully coupled (blue curve in Figure 1).
    • If 0 < D C < 1 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaGimaiabgY da8iaadseadaWgaaWcbaGaam4qaaqabaGccqGH8aapcaaIXaaaaa@3B37@ , the stress softening is partially coupled as it starts when D = D C MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiraiabg2 da9iaadseadaWgaaWcbaGaam4qaaqabaaaaa@397F@ (red curve).
    • If D C = 1 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiramaaBa aaleaacaWGdbaabeaakiabg2da9iaaigdaaaa@397B@ , the stress tensor rapidly drops to 0 when D = 1 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiraiabg2 da9iaaigdaaaa@387D@ and a failure criterion approach is then obtained (green curve).


    Figure 1. Effect of stress softening parameter DC on a single element behavior in uniaxial tension
    The EXP field can be used to add non-linearity in the stress softening effect and change the shape of the stress softening effect, as shown in Figure 2.


    Figure 2. Effect of stress softening exponent EXP on a single element behavior in uniaxial tension
    Note: If the DAMAGE keyword is not specified, the damage variable only becomes an output variable without triggering any element deletion of effect on stress computation. It can only show the critical spots of a structure where cracks are more likely to initiate.
  3. The DEP_SR flag can be used to introduce a strain rate dependency on the element failure. This makes the material’s ductility dependent on the loading velocity. Two possibilities are offered:
    • If V_TID is defined, a tabulated strain rate dependency is defined by TABLEMD, which defines the evolution of a dimensionless factor denoted by f s r ε ˙ ε 0 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOzamaaBa aaleaacaWGZbGaamOCaaqabaGcdaqadaqaamaalaaabaGafqyTduMb aiaaaeaacqaH1oqzdaWgaaWcbaGaaGimaaqabaaaaaGccaGLOaGaay zkaaaaaa@3EE3@ evolution with strain rate. Then the strain rate effect is introduced in the damage variable evolution by multiplication with the plastic strain at failure:(3)
      D = t = 0 Δ ε p ε p f η , ξ . f s r ε ˙ ε 0 . f s r s c a l e MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiraiabg2 da9maaqahabaWaaSaaaeaacqGHuoarcqaH1oqzdaWgaaWcbaGaamiC aaqabaaakeaadaqfWaqabSqaaiaadchaaeaacaWGMbaaneaacqaH1o qzaaGcdaqadaqaaiabeE7aOjaacYcacqaH+oaEaiaawIcacaGLPaaa caGGUaGaamOzamaaBaaaleaacaWGZbGaamOCaaqabaGcdaqadaqaam aalaaabaGafqyTduMbaiaaaeaacqaH1oqzdaWgaaWcbaGaaGimaaqa baaaaaGccaGLOaGaayzkaaGaaiOlaiaadAgadaWgaaWcbaGaam4Cai aadkhaaeqaaOWaaWbaaSqabeaacaWGZbGaam4yaiaadggacaWGSbGa amyzaaaaaaaabaGaamiDaiabg2da9iaaicdaaeaacqGHEisPa0Gaey yeIuoaaaa@5E3C@
      Where,
      η
      Stress triaxiality
      ξ
      Lode parameter
      ε ˙ 0
      V_REF
      f s r s c a l e MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaeOzamaaDa aaleaacaWGZbGaamOCaaqaaiaadohacaWGJbGaamyyaiaadYgacaWG Lbaaaaaa@3D9A@
      VT_SCALE
      ε p f MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaubmaeqale aacaWGWbaabaGaamOzaaqdbaGaeqyTdugaaaaa@39DF@
      Plastic strain at failure
      ε ˙
      Strain rate
    • If a continuous and analytical formula is desired, the Johnson-Cook strain rate dependency can be set up by specifying only a reference strain rate V_REF and the parameter JC (denoted as in the equation). Then, the damage variable evolution is given by:(4)
      D = t = 0 Δ ε p ε p f η , ξ . 1 + C J C ln ε ˙ ε 0 + MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiraiabg2 da9maaqahabaWaaSaaaeaacqGHuoarcqaH1oqzdaWgaaWcbaGaamiC aaqabaaakeaadaqfWaqabSqaaiaadchaaeaacaWGMbaaneaacqaH1o qzaaGcdaqadaqaaiabeE7aOjaacYcacqaH+oaEaiaawIcacaGLPaaa caGGUaWaaeWaaeaacaaIXaGaey4kaSIaam4qamaaBaaaleaacaWGkb Gaam4qaaqabaGcdaaadaqaaiGacYgacaGGUbWaaSaaaeaacuaH1oqz gaGaaaqaaiabew7aLnaaBaaaleaacaaIWaaabeaaaaaakiaawMYica GLQmcadaWgaaWcbaGaey4kaScabeaaaOGaayjkaiaawMcaaaaaaSqa aiaadshacqGH9aqpcaaIWaaabaGaeyOhIukaniabggHiLdaaaa@5BA5@
      Note: The strain-rate computation (total equivalent or plastic strain rate) depends on the choice made in the MATS1 Bulk Data Entry. In the absence of plasticity, the strain-rate dependency is not available.
  4. The DEP_L flag can be used introduce a mesh size dependency that can define the element’s ductile behavior dependent on its initial size. This can help to reduce the well-known mesh size dependency encountered when using coupled damage models or failure criteria. The TABLEMD defined in E_TID defines the evolution of a dimensionless scale factor with the initial element size given by, f s i z e L e 0 L r e f MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaeOzamaaBa aaleaacaWGZbGaamyAaiaadQhacaWGLbaabeaakmaabmaabaWaaSaa aeaacaWGmbWaa0baaSqaaiaadwgaaeaacaaIWaaaaaGcbaGaamitam aaBaaaleaacaWGYbGaamyzaiaadAgaaeqaaaaaaOGaayjkaiaawMca aaaa@42F9@ . The damage evolution then becomes:(5)
    D = t = 0 Δ ε p ε p f ( η , ξ ) f s i z e L e 0 L r e f f s i z e s c a l e MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiraiabg2 da9maaqahabaWaaSaaaeaacqGHuoarcqaH1oqzdaWgaaWcbaGaamiC aaqabaaakeaacqaH1oqzdaqhaaWcbaGaamiCaaqaaiaadAgaaaGcca GGOaGaeq4TdGMaaiilaiabe67a4jaacMcacqGHflY1caqGMbWaaSba aSqaaiaadohacaWGPbGaamOEaiaadwgaaeqaaOWaaeWaaeaadaWcaa qaaiaadYeadaqhaaWcbaGaamyzaaqaaiaaicdaaaaakeaacaWGmbWa aSbaaSqaaiaadkhacaWGLbGaamOzaaqabaaaaaGccaGLOaGaayzkaa GaeyyXICTaaeOzamaaDaaaleaacaWGZbGaamyAaiaadQhacaWGLbaa baGaam4CaiaadogacaWGHbGaamiBaiaadwgaaaaaaaqaaiaadshacq GH9aqpcaaIWaaabaGaeyOhIukaniabggHiLdaaaa@66C3@
    Where,
    L r e f MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamitamaaBa aaleaacaWGYbGaamyzaiaadAgaaeqaaaaa@39BC@
    EL_REF
    f s i z e s c a l e MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaeOzamaaDa aaleaacaWGZbGaamyAaiaadQhacaWGLbaabaGaam4CaiaadogacaWG HbGaamiBaiaadwgaaaaaaa@3F7A@
    FE_SCALE
  5. Both strain rate dependency and element size dependency can be used at the same time without creating any conflict.
  6. Element deletion from the mesh is activated differently depending on the element type (solid or shell) and the formulation (under-integrated or fully integrated).
    • For solid elements, deletion occurs only if all the integration points fail.
    • For shell elements, deletion occurs if more than half of the integration points (over thickness) fail.
  7. Damage initiation and evolution failure criterion (INIEVO) can also be defined using the DAMAGE continuation line in the MATS1 Bulk Data Entry.
  8. For the INIEVO criterion, strain rate dependency and element size dependency are not available as they are already considered through the DMGINI and DMGEVO Bulk Data Entries. The DAMAGE keyword, DC and EXP parameters are ignored for this criterion only. Element deletion is always turned on and stress softening is entirely controlled by the DMGEVO entry, if defined. If the DMGEVO entry is not specified, a failure criterion approach is used, and the element is deleted when the damage initiation criterion defined by the DMGINI entry is reached.
  9. For more information, refer to Material Failure Criterion in the Explicit Dynamic Analysis section of the User Guide.
1 Cuntze, R.G. and Freund, A., The predictive capability of failure mode concept-based strength criteria for multidirectional laminates in Failure Criteria in Fibre Reinforced Polymer Composites, 2004 QinetiQ Ltd. Published by Elsevier Ltd.