/MAT/PLAS_ZERIL

Block Format Keyword This law defines an isotropic elasto-plastic material using the Zerilli-Armstrong plasticity model.

Format

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
/MAT/PLAS_ZERIL/mat_ID/unit_ID
mat_title
ρi                
E v            
C0 C5 n εpmax σmax0
C1 ε˙0 ICC Fsmooth Fcut    
C3 C4 ρCp Tr    

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]
v Poisson's ratio

(Real)

 
C0 Plasticity yield stress

(Real)

[Pa]
C5 Plasticity hardening parameter

(Real)

[Pa]
n Plasticity hardening exponent. 5

Default = 1.0 (Real)

 
εpmax Failure plastic strain.

Default = 1030 (Real)

 
σmax0 Plasticity maximum stress.

Default = 1030 (Real)

[Pa]
C1 Strain rate formulation coefficient.

(Real)

[Pa]
ε˙0 Reference strain rate (must be 1 s-1 converted into user's units).

(Real)

[1s]
ICC Strain rate computation flag. 7
= 0 (Default)
Set to 1
= 1
Strain rate effect on σmax .
= 2
No strain rate effect on σmax .

(Integer)

 
Fsmooth Smooth strain rate option flag.
= 0 (Default)
No strain rate smoothing.
= 1
Strain rate smoothing active.

(Integer)

 
Fcut Cutoff frequency for strain rate filtering. 8

Default = 1030 (Real)

[Hz]
C3 Temperature effect coefficient.

(Real)

[1K] MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeaaciGaaiaabeqaamaabaabaaGcbaWaamWaaeaadaWcaaqaaiaaigdaaeaacaWGlbaaaaGaay5waiaaw2faaaaa@3981@
C4 Temperature effect coefficient.
= 0
No strain rate effect.

(Real)

[1K] MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeaaciGaaiaabeqaamaabaabaaGcbaWaamWaaeaadaWcaaqaaiaaigdaaeaacaWGlbaaaaGaay5waiaaw2faaaaa@3981@
ρCp Specific heat per unit of volume.
= 0
Temperature is constant: T = Tr

(Real)

[Jm3K]
Tr Reference temperature.

Default = 298 K (Real)

[K]

Comments

  1. The Zerilli-Armstrong law is applicable only to shells and solids.
  2. The equation that describes stress during plastic deformation is: (1)
    σ=C0+(C1exp((C3T+C4Tln(ε˙ε˙0))))+C5εpn
    Where,
    εp
    Plastic strain
    ε˙
    Strain rate
    T MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKfMBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhiov2DaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9Ff0dmeaacaGacmGadaWaaiqacaabaiaafaaakeaacaWGubaaaa@39B0@
    Temperature
  3. Yield stress should be strictly positive.
  4. When ε¯p reaches εpmax in one integration point, then based on the element type:
    • Shell elements:

      The corresponding shell element is deleted.

    • Solid elements:

      The deviatoric stress of the corresponding integral point is permanently set to 0; however, the solid element is not deleted.

  5. n must be less than 1.
  6. If ε˙0 is 0, there is no strain rate effect.
  7. ICC is a flag of the strain rate effect on material maximum stress σmax :

    law_plaszeril
    σ=σy(1+cln(ε˙ε˙o)) σ=σy(1+cln(ε˙ε˙o))
    σmax=σmax0(1+cln(ε˙ε˙o)) σmax=σmax0
    Figure 1.
  8. Strain rate filtering input (Fcut) is only available for shell and solid elements.
  9. The strain rate filtering is used to smooth strain rates.
  10. Temperature is computed assuming adiabatic conditions:(2)
    Τ=Τr+EintρCρ(Volume)

    Where, Eint is the internal energy computed by Radioss.

  11. When the temperature is not initialized using /HEAT/MAT or /INITEMP, the reference temperature (Tr) is also the initial temperature.