/MAT/LAW36 (PLAS_TAB)

Block Format Keyword This law models an isotropic elasto-plastic material using user-defined functions for the work-hardening portion of the stress-strain curve (for example, stress versus plastic strain) for different strain rates.

Format

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
/MAT/LAW36/mat_ID/unit_ID or /MAT/PLAS_TAB/mat_ID/unit_ID
mat_title
ρi
E ν εmaxp εt εm
Nfunct Fsmooth Chard Fcut εf VP
fct_IDp Fscale fct_IDE Einf CE
Nfunct > 0: Read 1 + INT((Nfunct -1)/5) cards
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
fct_ID1 fct_ID2 fct_ID3 fct_ID4 fct_ID5
Nfunct > 0: Read 1 + INT((Nfunct -1)/5) cards
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
Fscale1 Fscale2 Fscale3 Fscale4 Fscale5
Nfunct > 0: Read 1 + INT((Nfunct -1)/5) cards
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
˙ε1 ˙ε2 ˙ε3 ˙ε4 ˙ε5

Definition

Field Contents SI Unit Example
mat_ID Material identifier.

(Integer, maximum 10 digits)
unit_ID Unit identifier.

(Integer, maximum 10 digits)
mat_title Material title.

(Character, maximum 100 characters)
ρi Initial density.

(Real)

 [kgm3]
E Young's modulus.

(Real)

 [Pa]
ν Poisson's ratio.

(Real)
εmaxp Failure plastic strain.

Default = 1020 (Real)
εt Tensile failure strain at which stress starts to reduce.

Default = 1020 (Real)
εm Maximum tensile failure strain at which the stress in element is set to zero.

Default = 2.0 x 1020 (Real)
Nfunct Number of functions (1≤Nfunct≤100 ).

(Integer)
Fsmooth Smooth strain rate option flag.
= 0 (Default)
No strain rate smoothing.
= 1
Strain rate smoothing active with linear interpolation.
= 2
Strain rate smoothing with natural logarithm interpolation.

(Integer)
Chard Hardening coefficient.
= 0
Hardening is a full isotropic model.
= 1
Hardening uses the kinematic Prager-Ziegler model.
= value between 0 and 1
Hardening is interpolated between the two models.

(Real)
Fcut Cutoff frequency for strain rate filtering. Only available for shell and solid elements, Appendix: Filtering.

Default = 1.0 x 1020 (Real)

 [Hz]
VP Strain rate choice flag.
= 0 (Default)
Strain rate effect on yield stress depends on the total strain rate.
= 1
Strain rate effect on yield depends on the plastic strain rate.
In this case, there is no strain rate filtering, so Fsmooth and Fcut are not used.

(Integer)
εf Tensile strain for element deletion.

Default = 3.0 x 1020 (Real)
fct_IDp Yield factor versus pressure function. 7

Default = 0 (Integer)
Fscale Scale factor for yield factor in fct_IDp.

Default = 1.0 (Real)

 [Pa]
fct_IDE Function identifier for the scale factor of Young's modulus, when Young's modulus is function of the plastic strain.

Default = 0: in this case the evolution of Young's modulus depends on Einf and CE.

(Integer)
Einf Saturated Young's modulus for infinitive plastic strain.

(Real)
CE Parameter for Young's modulus evolution.

(Real)
fct_ID1 Yield stress function identifier 1 corresponding to strain rate ˙ε1 .

(Integer)
fct_ID2 Yield stress function identifier 2 corresponding to strain rate ˙ε2 .

(Integer)
fct_ID3 Yield stress function identifier 3 corresponding to strain rate ˙ε3 .

(Integer)
fct_ID4 Yield stress function identifier 4 corresponding to strain rate ˙ε4 .

(Integer)
fct_ID5 Yield stress function identifier 5 corresponding to strain rate ˙ε5 .

(Integer)
Fscale1 Scale factor for ordinate (stress) in fct_ID1.

Default = 1.0 (Real)

 [Pa]
Fscale2 Scale factor for ordinate (stress) in fct_ID2.

Default = 1.0 (Real)

 [Pa]
Fscale3 Scale factor for ordinate (stress) in fct_ID3.

Default = 1.0 (Real)

 [Pa]
Fscale4 Scale factor for ordinate (stress) in fct_ID4.

Default = 1.0 (Real)

 [Pa]
Fscale5 Scale factor for ordinate (stress) in fct_ID5.

Default = 1.0 (Real)

 [Pa]
˙ε1 If VP =0 total strain rate for fct_ID1.

If VP =1 plastic strain rate for fct_ID1.

(Real)

 [1s]
˙ε2 If VP =0 total strain rate for fct_ID2.

If VP =1 plastic strain rate for fct_ID2.

(Real)

 [1s]
˙ε3 If VP =0 total strain rate for fct_ID3.

If VP =1 plastic strain rate for fct_ID3.

(Real)

 [1s]
˙ε4 If VP =0 total strain rate for fct_ID4.

If VP =1 plastic strain rate for fct_ID4.

(Real)

 [1s]
˙ε5 If VP =0 total strain rate for fct_ID5.

If VP =1 plastic strain rate for fct_ID5.

(Real)

 [1s]

▸Example (Aluminum)

Comments

  1. The first point of yield stress functions (plastic strain versus stress) should have a plastic strain value of zero. If the last point of the first (static) function equals 0 in stress, default value of εmaxp is set to the corresponding value of εp .
  2. Element deletion:
    • Once εp (plastic strain) reaches εmaxp , in one integration point, the element is deleted.
    • If ε1 reaches εt , the stress is reduced using the following relation:
      σ=σ(εm−ε1εm−εt)
    • If ε1 (largest principal strain) reaches εm ( ε1>εm ), the stress in element is reduced to 0 (but the element is not deleted).
    • Once ε1 (largest principal strain) reaches εf (maximum tensile failure strain), the element is deleted.
    • Once the yield stress value, interpolated or extrapolated from the curve(s) reaches 0, the element is deleted.
  3. The kinematic hardening model is not available in global formulation (N=0 in shell property keyword) that is, hardening is fully isotropic.
  4. In case of kinematic hardening and strain rate dependency, the yield stress depends on the strain rate.
  5. Strain rate filtering is used to smooth strain rates.
  6. The first function in fct_ID1 is used for strain rate values from 0 to its corresponding strain rate, strain rate 1. However, the last function used in the model does not extend to the maximum strain rate; for higher strain rates, a linear extrapolation will be applied. This could lead to instability and/or unusual deformation. This instability can be overcome by repeating the stress strain curve, corresponding to the last strain rate, again with a much higher strain rate.


    Figure 1.
  7. fct_IDp is used to distinguish the behavior in tension and compression for certain materials (pressure dependent yield). This is available for both shell and solid elements. The effective yield stress is then obtained by multiplying the nominal yield stress by the yield factor corresponding to the actual pressure.
  8. If ˙ε≤˙εn , the yield stress is interpolated between fn and fn−1 .
  9. If ˙ε≤˙ε1 , function f1 is used.
  10. Above ˙εmax , yield stress is extrapolated.

    mat_law36_yield_stress
    Figure 2.
    Where,
    ˙ε
    Total strain rate for VP =0
    ˙ε
    Plastic strain rate for VP =1
  11. Separate functions must be defined for different strain rates.
  12. Strain rate values must be given in strictly ascending order.
  13. The evolution of Young's modulus:
    • If fct_IDE > 0, the curve defines a scale factor for Young's modulus evolution with equivalent plastic strain, which means the Young's modulus is scaled by the function f(ˉεp) :
      E(t)=f(ˉεp)E

      The initial value of the scale factor should be equal to 1 and it decreases.

    • If fct_IDE = 0, the Young's modulus is calculated as:
      E(t)=E−(E−Einf)(1−exp(−CEˉεp))
      Where, E and Einf are respectively the initial and asymptotic value of Young's modulus, and ˉεp is the accumulated equivalent plastic strain.
      Note: If fct_IDE = 0 and CE = 0, Young's modulus E remains constant.
  14. When you specify εmaxp or εt and εm , a damage output variable is available using /ANIM/ELEM/DAMG or /H3D/ELEM/DAMG. This damage variable is computed as:
    D=max(εpεmaxp,1−εm−ε1εm−εt)
  15. When εmaxp is specified and the /NONLOCAL/MAT option is activated, non-local plastic strain is used to compute the damage variable.