MATS1

Bulk Data Entry Specifies stress-dependent and temperature-dependent material properties for use in applications involving nonlinear materials.

This entry is used if a MAT1 entry is specified with the same MID in a nonlinear subcase.

Format

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
MATS1 MID TID TYPE H YF HR LIMIT1    
  TYPSTRN TSC              
  JHCOOK A B N C RSTRT      

Example

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
MATS1 17 28 PLASTIC 0.0 1 1 2.+4    

Definitions

Field Contents SI Unit Example
MID Identification entity of a MAT1 entry.
Integer
Specifies an identification number for this material.
<String>
Specifies a user-defined string label for this material entry. 1

No default (Integer > 0 or <String>)

 
TID Identification number of a TABLES1, TABLEST, TABLEG or TABLEMD entry. If H is given, this field must be blank. 4

(Integer ≥ 0 or blank)

 
TYPE Material nonlinearity type.
PLASTIC (Default)
Elastoplastic material.
NLELAST
Nonlinear elastic material.
blank
 
H Work hardening slope (slope of stress versus plastic strain) in units of stress. For elastic-perfectly plastic cases, H = 0.0. For more than a single slope in the plastic range, the stress-strain data must be supplied on a TABLES1 or TABLEG entry referenced by TID, and this field must be blank. 3

(Real)

 
YF Yield function criterion, selected by the following value. 11
1 (Default)
von Mises
2
Maximum principal stress

(Integer)

 
HR Hardening Rule, selected by the following value (Integer).
1 (Default)
Isotropic Hardening
2
Kinematic Hardening
3
Mixed Hardening with 30% contribution of the Kinematic Hardening and 70% contribution of the Isotropic Hardening
4
Johnson-Cook Hardening 12
5
Crushable Foam Hardening 13
Adjustable Mixed Hardening is selected by choosing (Real) value for HR:
0 < HR < 1
Indicates a mixed combination of Isotropic and Kinematic Hardening. The contribution of the Kinematic Hardening is HR whereas the contribution of the Isotropic Hardening is 1 - HR. 5

(1, 2, 3, 4, 5, or 0.0 < Real < 1.0)

 
LIMIT1 Initial yield point.

The LIMIT1 field can be blank, if the initial yield point value is defined via a referenced TABLES1 or TABLEG entries on the TID field. OptiStruct will error out if LIMIT1 is blank and TID does not reference a TABLES1 or TABLEG entry.

(Real > 0 or blank)

 
TYPSTRN Specifies the type of strain used on the x-axis of the table pointed to by TID. The strain type is selected by one of the following values. 6
0 (Default)
Total strain is used on the x-axis.
1
Plastic strain or volumetric strain is used on the x-axis. 12

(Integer)

 
TSC Tensile stress cutoff. A nonzero, positive value is recommended for realistic behavior. 6

Default = 0.0 (Real ≥ 0)

 
JHCOOK Flag that identifies that the Johnson-Cook hardening method parameters are to follow. For Johnson-Cook hardening, HR=4.

(Integer)

 
A Material yield stress.

No default (Real)

 
B Coefficinets to the plastic strain.

Default = 0.0 (Real)

 
N Exponent to the plastic strain.

Default = 1.0 (Real)

 
C Coefficient to the strain rate.

Default = 0.0 (Real)

 
RSTRT Reference strain rate.

Default = 1.0 (Real)

 

Comments

  1. String based labels allow for easier visual identification of materials, including when being referenced by other cards. (example, the MID field of properties). For more details, refer to String Label Based Input File in the Bulk Data Input File.
  2. For nonlinear elastic material, the stress-strain data given in the TABLES1 or TABLEG entry will be used to determine the stress for a given value of strain. The values H, YF, HR, and LIMIT1 will not be used in this case. Nonlinear elastic material is only available in EXPDYN subcases.
  3. For elastoplastic materials, the elastic stress-strain matrix is computed from a MAT1 entry, and the isotropic plasticity theory is used to perform the plastic analysis. In this case, either the table identification TID or the work hardening slope H may be specified, but not both. If the TID is omitted, the work hardening slope H must be specified, unless the material is perfectly plastic. The plasticity modulus ( H ) is related to the tangential modulus ( E T ) by:
    (1)
    H = E T 1 E T E
    Where, E is the elastic modulus and E T = d Y / d ε is the slope of the uniaxial stress-strain curve in the plastic region.


    Figure 1.
  4. If TID is given, TABLES1 or TABLEG entries (Xi,Yi) of stress-strain data ( ε x,Yx) must conform to the following rules:

    If TYPE=PLASTIC, the curve must be defined in the first quadrant. The data points must be in ascending order. If the table is defined in terms of total strain (TYPSTRN=0), the first point must be at the origin (X1=0, Y1=0) and the second point (X2, Y2) must be at the initial yield point (Y1) specified on the MATS1 entry. The slope of the line joining the origin to the yield stress must be equal to the value of E. If the table is defined in terms of plastic strain (TYPSTRN=1), the first point (X1, Y1), corresponding to yield point (Y1), must be at X1=0. TID may reference a TABLEST entry. In this case, the above rules apply to all TABLES1 tables pointed to by TABLEST.

    If TYPE=NLELAST, the full stress-strain curve may be defined in the first and third quadrants to accommodate different uniaxial compression data. If the curve is defined only in the first quadrant, then the curve must start at the origin (X1=0.0, Y1=0.0).

    For analysis where small deformations are assumed, there should be little or no difference between the true stress-strain curve and the engineering stress-strain curve, so either of them may be used in the TABLES1 definition. For analyses where small deformations are not assumed, the true stress-strain curve should be used.

    If the deformations go past the values defined in the table, the curve is extrapolated linearly.

  5. Kinematic hardening and Mixed hardening are supported only for solids.
  6. The conversion of the relation stress vs. total strain (TYPSTRN=0) into stress vs. plastic strain (TYPSTRN=1) is illustrated below. This is clearly different than simply shifting the entire table along the epsilon-axis.


    Figure 2.
  7. The temperature-dependence of the MATS1 material is defined by referencing a TABLEST entry via the TID field.
  8. Large strain elasto-plasticity can be activated using MATS1 (TYPE=PLASTIC) in conjunction with PARAM, LGDISP,1.
  9. MATS1 is not supported in conjunction with second order shell elements (CTRIA6 and CQUAD8).
  10. MATS1 is supported for CROD, CONROD, CBAR and CBEAM elements in the axial translational direction only. The behaviors in other directions remain elastic.

    The torsional deformation of CROD/CONROD elements or the shear, bending and torsional deformations of CBAR/CBEAM elements remain elastic.

  11. If Johnson-Cook is selected (HR=4), use the following formulations:(2)
    σ = ( a + b ε p n ) ( 1 + c ln ( ε ˙ ε ˙ 0 ) ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4WdmNaey ypa0ZaaeWaaeaacaWGHbGaey4kaSIaamOyaiabew7aLnaaDaaaleaa caWGWbaabaGaamOBaaaaaOGaayjkaiaawMcaamaabmaabaGaaGymai abgUcaRiaadogaciGGSbGaaiOBamaabmaabaWaaSaaaeaacuaH1oqz gaGaaaqaaiqbew7aLzaacaWaaSbaaSqaaiaaicdaaeqaaaaaaOGaay jkaiaawMcaaaGaayjkaiaawMcaaaaa@4C99@
    (3)
    σ ¯ = ( A + B ( ε ¯ p l ) n ) ( 1 + C ln ( ε ¯ ˙ p l ε ˙ 0 ) ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGafq4WdmNbae bacqGH9aqpdaqadaqaaiaadgeacqGHRaWkcaWGcbWaaeWaaeaacuaH 1oqzgaqeamaaCaaaleqabaGaamiCaiaadYgaaaaakiaawIcacaGLPa aadaahaaWcbeqaaiaad6gaaaaakiaawIcacaGLPaaadaqadaqaaiaa igdacqGHRaWkcaWGdbGaciiBaiaac6gadaqadaqaamaalaaabaGafq yTduMbaeHbaiaadaahaaWcbeqaaiaadchacaWGSbaaaaGcbaGafqyT duMbaiaadaWgaaWcbaGaaGimaaqabaaaaaGccaGLOaGaayzkaaaaca GLOaGaayzkaaaaaa@514E@
    Johnson-Cook strain rate dependence assumes that,(4)
    σ ¯ = σ 0 ( ε ¯ p l , θ ) R ( ε ¯ ˙ p l ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGafq4WdmNbae bacqGH9aqpcqaHdpWCdaahaaWcbeqaaiaaicdaaaGcdaqadaqaaiqb ew7aLzaaraWaaWbaaSqabeaacaWGWbGaamiBaaaakiaacYcacqaH4o qCaiaawIcacaGLPaaacaWGsbWaaeWaaeaacuaH1oqzgaqegaGaamaa CaaaleqabaGaamiCaiaadYgaaaaakiaawIcacaGLPaaaaaa@499B@
    and (5)
    ε ¯ ˙ p l = ε ˙ 0 exp ( 1 C ( R 1 ) ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGafqyTduMbae HbaiaadaahaaWcbeqaaiaadchacaWGSbaaaOGaeyypa0JafqyTduMb aiaadaWgaaWcbaGaaGimaaqabaGcciGGLbGaaiiEaiaacchadaqada qaamaalaaabaGaaGymaaqaaiaadoeaaaWaaeWaaeaacaWGsbGaeyOe I0IaaGymaaGaayjkaiaawMcaaaGaayjkaiaawMcaaaaa@4780@

    for σ ¯ σ 0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGafq4WdmNbae bacqGHLjYScqaHdpWCdaahaaWcbeqaaiaaicdaaaaaaa@3C42@

    Where,
    σ ¯ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGafq4WdmNbae baaaa@37D2@
    Yield stress for non-zero strain rate
    ε ¯ ˙ p l MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGafqyTduMbae HbaiaadaahaaWcbeqaaiaadchacaWGSbaaaaaa@39D1@
    Equivalent plastic strain rate
    ε ˙ 0 and C MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaacaGacmGadaWaaiqacaabaiaafaaake aacaWGdbaaaa@399F@
    Are material parameters measured at or below the transition temperature θ t r a n s i t i o n MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqiUde3aaS baaSqaaiaadshacaWGYbGaamyyaiaad6gacaWGZbGaamyAaiaadsha caWGPbGaam4Baiaad6gaaeqaaaaa@4156@
    σ 0 ( ε ¯ p l , θ ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Wdm3aaW baaSqabeaacaaIWaaaaOWaaeWaaeaacuaH1oqzgaqeamaaCaaaleqa baGaamiCaiaadYgaaaGccaGGSaGaeqiUdehacaGLOaGaayzkaaaaaa@4076@
    Static yield stress
    R ( ε ¯ ˙ p l ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOuamaabm aabaGafqyTduMbaeHbaiaadaahaaWcbeqaaiaadchacaWGSbaaaaGc caGLOaGaayzkaaaaaa@3C3B@
    Ratio of the yield stress at nonzero strain rate to the static yield stress (so that R ( ε ˙ 0 ) = 1.0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOuamaabm aabaGafqyTduMbaiaadaWgaaWcbaGaaGimaaqabaaakiaawIcacaGL PaaacqGH9aqpcaaIXaGaaiOlaiaaicdaaaa@3E24@ )
  12. When Crushable Foam is selected (HR=5), only maximum principal stress as yield criterion (YF=2) is used, and a table TID must be given.

    For rate independent table (TABLES1), first column is the volumetric strain, second column is the yield stress. The volumetric strain is defined as γ = 1 V V 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaacaGacmGadaWaaiqacaabaiaafaaake aacqaHZoWzcqGH9aqpcaaIXaGaeyOeI0YaaSaaaeaacaWGwbaabaGa amOvaiaaicdaaaaaaa@3FAC@ .

    The default for TSC (tensile stress cutoff) is zero, unless the user specifies a value. TSC is defined as a positive stress value which indicates the yield stress of crushable foam under tensile loading.

    The yield stress of crushable foam under compression loading can be given by a TABLES1 table.

    Where,
    x
    Values in the table is the volumetric strain (all positive values indicate the volume is compressed).
    y
    Value is the compression yield stress (all positive values).
    First entry in the TABLES1 entry will be x=0, y=y0, which indicates the initial compressive yield stress. All xi should be positive and in increasing order.

    For crushable foam, in place of the equivalent plastic strain in H3D file, the integrated volumetric strain (natural logarithm of the relative volume -ln(V/V0)) is output.

  13. If TID refers to TABLEMD, the first variable X1 is volumetric strain if HR=5 (Crushable foam), or plastic strain/full strain if HR=1, 2, 3. For rate-dependent problems, the second variable is strain rate.