/MAT/LAW121 (PLAS_RATE)

Block Format Keyword Elasto-plastic strain-rate dependent material with isotropic von Mises yield criterion. This material law is available for both solids and shells.

Format

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
/MAT/LAW121/mat_ID/unit_ID or /MAT/PLAS_RATE/mat_ID/unit_ID
mat_title
ρ i
E ν MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaH9oGBaa a@3817@ Ires Ivisc Fcut DTMIN
Fct_SIG0   Xscale_SIG0 Yscale_SIG0        
Fct_YOUN   Xscale_YOUN Yscale_YOUN        
Fct_TANG   Xscale_TANG TANG        
Fct_FAIL Ifail Xscale_FAIL Yscale_FAIL        

Definition

Field Contents SI Unit Example
mat_ID Material identifier.

(Integer, maximum 10 digits)

unit_ID (Optional) Unit identifier.

(Integer, maximum 10 digits)

mat_title Material title.

(Character, maximum 100 characters)

ρ i Initial density.

(Real)

[ kg m 3 ]
E Young’s modulus.

(Real)

[ Pa ]
ν MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaH9oGBaa a@3817@ Poisson’s ratio.

(Real)

Ires Resolution method for plasticity.
= 0
Set to 2.
= 1
NICE (Next Increment Correct Error) explicit method.
= 2 (Default)
Newton iterative semi-implicit method (Cutting plane).

(Integer)

Ivisc Strain rate dependency formulation.
= 0 (Default)
Scaled yield stress.
= 1
Visco-plastic formulation.

(Integer)

Ifail Failure criterion variable (used only Fct_FAIL > 0).
= 0 (Default)
Equivalent stress.
=1
Effective plastic strain.
= 2
Maximum principal stress or absolute value of minimum principal stress.
= 3
Maximum principal stress.

(Integer)

Fcut Cutoff frequency for strain rate filtering (used only Ivisc = 0).

Default = 10000 Hz (Real)

[Hz]
DTMIN Minimum time step size for automatic element deletion.

Default = 0.0 (Real)

[ s ]
Fct_SIG0 Yield stress versus effective strain rate function identifier.

(Integer)

Xscale_SIG0 Scale factor for abscissa (strain rate) in Fct_SIG0.

Default = 1.0 (Real)

[ 1 s ]
Yscale_SIG0 Scale factor for ordinate (stress) in Fct_SIG0.

Default = 1.0 (Real)

[ Pa ]
Fct_YOUN Young’s modulus versus effective strain rate function identifier (available only Ivisc = 0).

Default = 1.0 (Real)

Xscale_YOUN Scale factor for abscissa (strain rate) in Fct_YOUN.

Default = 1.0 (Real)

[ 1 s ]
Yscale_YOUN Scale factor for ordinate (stress) in Fct_YOUN.

Default = 1.0 (Real)

[ Pa ]
Fct_TANG Plastic tangent modulus versus effective strain rate function identifier.

(Integer)

Xscale_TANG Scale factor for abscissa (strain rate) in Fct_TANG.

Default = 1.0 (Real)

[ 1 s ]
TANG
If Fct_TANG > 0
Scale factor for ordinate (stress) in Fct_TANG.
Default = 1.0 (Real)
If Fct_TANG = 0
Plastic tangent TANG.
Default = 0.0 (Real)
[ Pa ]
Fct_FAIL Failure criterion variable versus effective strain rate function identifier.

(Integer)

Xscale_FAIL Scale factor for abscissa (strain rate) in Fct_FAIL.

Default = 1.0 (Real)

[ 1 s ]
Yscale_FAIL Scale factor for ordinate (stress) in Fct_FAIL.

Default = 1.0 (Real)

[ Pa ]

Example (Steel)

#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/UNIT/1
Unit system
                  Mg                  mm                   s
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/MAT/LAW121/1/1
Steel
#              RHO_I
             7.85E-9
#                  E                  Nu      Ires     Ivisc                Fcut               DTMIN
            194200.0                 0.3         1         0                1000                   0
# Fct_SIG0                   Xscale_SIG0         Yscale_SIG0
         5                             0                   0
# Fct_YOUN                   Xscale_YOUN         Yscale_YOUN
         6                             0                   0
# Fct_TANG                   Xscale_TANG                TANG
         7                             0                   0
# Fct_FAIL     Ifail         Xscale_FAIL         Yscale_FAIL
         8         1                   0                   0
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/FUNCT/5
Yield stress versus effective strain rate
                 0.0               272.2
              1000.0               572.2
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/FUNCT/6
Young’s modulus versus effective strain rate
                 0.0            192400.0
              1000.0            272400.0
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/FUNCT/7
Plastic tangent modulus versus effective strain rate
                 0.0              4500.0
              1000.0              6500.0
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/FUNCT/8
Failure criterion variable versus effective strain 
                 0.0                0.15
              1000.0                0.25
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#ENDDATA
/END
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|

Comments

  1. This material law considers isotropic and linear elasticity.
  2. The plastic behavior is described with a classical von Mises plasticity yield function described with:(1)
    f= σ VM σ Y MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOzaiabg2 da9iabeo8aZnaaBaaaleaacaWGwbGaamytaaqabaGccqGHsislcqaH dpWCdaWgaaWcbaGaamywaaqabaaaaa@3F48@
    With:(2)
    σ VM = 3 2 s:s MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Wdm3aaS baaSqaaiaadAfacaWGnbaabeaakiabg2da9maakaaabaWaaSaaaeaa caaIZaaabaGaaGOmaaaacaWHZbGaaiOoaiaahohaaSqabaaaaa@3EFD@

    Where, s MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaC4Caaaa@36F3@ is the deviatoric stress tensor.

  3. The yield stress is strain rate dependent and described as:(3)
    σ Y = σ 0 ( ε ˙ )+ E( ε ˙ ) E t ( ε ˙ ) E( ε ˙ ) E t ( ε ˙ ) ε p MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Wdm3aaS baaSqaaiaadMfaaeqaaOGaeyypa0Jaeq4Wdm3aaSbaaSqaaiaaicda aeqaaOGaaiikaiqbew7aLzaacaGaaiykaiabgUcaRmaalaaabaGaam yraiaacIcacuaH1oqzgaGaaiaacMcacaWGfbWaaSbaaSqaaiaadsha aeqaaOGaaiikaiqbew7aLzaacaGaaiykaaqaaiaadweacaGGOaGafq yTduMbaiaacaGGPaGaeyOeI0IaamyramaaBaaaleaacaWG0baabeaa kiaacIcacuaH1oqzgaGaaiaacMcaaaGaeqyTdu2aaSbaaSqaaiaadc haaeqaaaaa@55E1@
    Where,
    σ 0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Wdm3aaS baaSqaaiaaicdaaeqaaaaa@38A0@
    Strain rate dependent initial yield stress defined by function Fct_SIG0.
    E( ε ˙ ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyraiaacI cacuaH1oqzgaGaaiaacMcaaaa@39CA@
    Young’s modulus that may optionally depend on the strain rate (if Fct_YOUN is defined).
    E t ( ε ˙ ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyramaaBa aaleaacaWG0baabeaakiaacIcacuaH1oqzgaGaaiaacMcaaaa@3AF9@
    Plastic tangent modulus that may optionally depend on the strain rate (if Fct_TANG is defined).
    ε p
    Cumulative plastic strain.
    Note: The inequality E( ε ˙ )> E t ( ε ˙ ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyraiaacI cacuaH1oqzgaGaaiaacMcacqGH+aGpcaWGfbWaaSbaaSqaaiaadsha aeqaaOGaaiikaiqbew7aLzaacaGaaiykaaaa@3FD4@ must always be fulfilled. If not, the solver will automatically limit the value of the tangent modulus E t ( ε ˙ )=0.99×E( ε ˙ ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyramaaBa aaleaacaWG0baabeaakiaacIcacuaH1oqzgaGaaiaacMcacqGH9aqp caaIWaGaaiOlaiaaiMdacaaI5aGaey41aqRaamyraiaacIcacuaH1o qzgaGaaiaacMcaaaa@44DB@ .
  4. Two strain rate dependency formulations are available depending on the value of the flag Ivisc.
    • Ivisc = 0: scaled yield stress formulation. In this case, the strain rate corresponds to the total effective strain-rate computed as:(4)
      ε ˙ = 2 3 ε ˙ ' : ε ˙ ' MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGafqyTduMbai aacqGH9aqpdaGcaaqaamaalaaabaGaaGOmaaqaaiaaiodaaaGabCyT dyaacaGaai4jaiaacQdaceWH1oGbaiaacaGGNaaaleqaaaaa@3EF9@

      Where, ε ˙ ' MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabCyTdyaaca Gaai4jaaaa@37EC@ is the deviatoric total strain rate tensor.

      For this formulation, all strain rate dependent variables are updated at the beginning of the timestep and are constant during the return mapping algorithm. All strain rate dependent variables are allowed using this formulation. The strain rate is, in this case, filtered by default as: (5)
      ε ˙ f n = α ε ˙ n + ( 1 α ) ε ˙ f n 1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGafqyTduMbai aadaqhaaWcbaWaaSbaaWqaaiaadAgaaeqaaaWcbaGaamOBaaaakiab g2da9iabeg7aHjqbew7aLzaacaWaaWbaaSqabeaacaWGUbaaaOGaey 4kaSIaaiikaiaaigdacqGHsislcqaHXoqycaGGPaGafqyTduMbaiaa daqhaaWcbaGaamOzaaqaaiaad6gacqGHsislcaaIXaaaaaaa@4A57@

      Where, α = 2 π F c u t Δ t MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqySdeMaey ypa0JaaGOmaiabec8aWjaadAeadaWgaaWcbaGaam4yaiaadwhacaWG 0baabeaakiabfs5aejaadshaaaa@4150@ .

      You can then adapt the filtering by specifying a value for the cutoff frequency Fcut. This formulation is lighter and faster than the viscoplastic one described below.

    • Ivisc = 1: viscoplastic formulation. In this case, the strain rate corresponds to the plastic strain rate. (6)
      ε ˙ = ε ˙ p MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGafqyTduMbai aacqGH9aqpcuaH1oqzgaGaamaaBaaaleaacaWGWbaabeaaaaa@3B7E@

      In this case, the strain rate is initially null, and is computed and updated during the return mapping procedure. All strain rate dependent variable variations are taken into account leading to a heavier cost of computation. However, no strain rate filtering is needed, and you can speed up the simulation using the NICE explicit return mapping (Ires = 1). This formulation, the Young’s modulus is not allowed to vary with strain rate.

  5. You can choose the algorithm of return mapping to find a compromise between precision and cost. Two return mapping methods are available.
    • Ires = 1: the NICE explicit method (Next Increment Correct Error). This procedure only requires 1 iteration and uses a self-correcting ability to still preserve a good precision. This method can dramatically speed up the simulation.
    • Ires = 2: the Cutting-Plane (Newton iteration) method. This procedure requires several iterations (usually between 3 and 5) to solve the material behavior nonlinear equations. It is more expensive than the NICE explicit method but offers very good precision. This method is set by default.
  6. You can choose to add failure in the material behavior. To do so, a function Fct_FAIL must be defined to describe the evolution of the failure criterion variable with the strain rate. The nature of the failure criterion variable is chosen using the flag Ifail:
    • Ifail = 0: the criterion is fulfilled when the von Mises stress reaches the critical value defined in the function
    • Ifail = 1: the criterion is fulfilled when the cumulative plastic strain reaches the value defined in the function
    • Ifail = 2: the criterion is fulfilled when the maximum principal stress or the absolute value of the minimum principal stress reaches the critical value defined in the function
    • Ifail = 3: the criterion is fulfilled when the maximum principal stress reaches the critical value defined in the function
  7. Automatic element deletion can also be set if the element timestep decreases to reach a critical value defined by DTMIN.