Processing math: 100%

/MAT/LAW120 (TAPO)

Block Format Keyword This is a non-associated elasto-plastic model for polymer adhesives. The constitutive model is based on a I1-J2 criterion that can be reduced either to a von Mises or Drucker-Prager type in compression.

It can be used to represent the mechanical behavior of adhesives under complex loading paths with combined shear and tension. The material model includes a nonlinear damage model depending on plastic strain, triaxiality and strain rate. This material is applicable only to solid hexahedron elements (/BRICK).

Format

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
/MAT/LAW120/mat_ID/unit_ID or /MAT/TAPO/mat_ID/unit_ID
mat_title
ρi                
E ν Iform Itrx Idam      
Table_ID Xscale Yscale          
τ0 Q β H    
A1F A2F A1H A2H AS
C ˙εref ˙εmax        
D1c D2c D1f D2f    
Dtrx DJC Exp_n        

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)

ρi Initial density.

(Real)

[kgm3]
E Young’s (stiffness) modulus.

(Real)

[Pa]
ν Poisson's coefficient.

(Real)

 
Iform Yield criterion formulation flag.
= 1 (Default)
Drucker-Prager model in compression.
= 2
von Mises in compression.

(Integer)

Itrx Damage dependency on triaxiality in compression flag.
= 1
Damage depends on triaxiality in tension and compression.
= 2 (Default)
Damage depends on triaxiality in tension only.

(Integer)

Idam Strain rate definition in damage model flag.
= 1
Damage factor defined with undamaged plastic strain rate.
= 2 (Default)
Damage factor defined with damaged plastic strain rate.

(Integer)

Table_ID Table identifier to define yield stress as a function of plastic strain, strain rate and temperature.

(Integer)

 
Xscale Scale factor for strain rate variable in Table_ID.

(Real)

[Hz]
Yscale Scale factor for yield stress value defined by Table_ID.

(Real)

[Pa]
τ0 Initial shear yield stress.

(Real)

[Pa]
Q Voce hardening modulus.

(Real)

[Pa]
β Voce nonlinear hardening exponent.

Default = 1.0 (Real)

H Linear hardening exponent.

Default = 1.0 (Real)

[Pa]
A1F Yield function parameter.

(Real)

A2F Yield function parameter.

(Real)

A1H Yield function distortional hardening parameter.

(Real)

A2H Yield function distortional hardening parameter.

(Real)

AS Plastic flow function parameter for hydrostatic term.

(Real)

C Johnson-Cook strain rate coefficient for hardening.

(Real)

˙εref Quasi-static threshold strain rate in Johnson-Cook term.

(Real)

[Hz]
˙εmax Maximum dynamic threshold strain rate in Johnson-Cook term.

(Real)

[Hz]
D1c Johnson-Cook parameter for damage initiation.

(Real)

D2c Johnson-Cook parameter for damage initiation.

(Real)

D1f Johnson-Cook parameter for failure strain.

(Real)

D2f Johnson-Cook parameter for failure strain.

(Real)

Dtrx Johnson-Cook damage parameter for triaxiality term.

(Real)

DJC Johnson-Cook strain rate parameter for damage.

(Real)

Exp_n Exponential coefficient for damage strain rate dependency.

(Real)

Example (Adhesive Polymer)

Comments

  1. The yield function is described depending on the Iform flag:
    • Iform = 1: Drucker-Prager formulation:(1)
      f= J2+a13τ0I1+a23I12τ2y

      a1=A1F+A1Hεpl and a2=A2F+A2Hεpl

    • Iform = 2: von Mises formulation:(2)
      f= J2+A2F3I1+32A1FA2Fτ02(τ2y+A21FA2Fτ204)

    These 2 functions are written in terms of the damaged stress tensor: σd=σ/(1D)

    Where, D represents the isotropic damage.

  2. Plastic potential is expressed as:(3)
    f*= J2+AS3I12
  3. Yield stress is rate dependent:
    • Table_ID ≠ 0, the yield stress is tabulated.
    • Table_ID = 0, it is analytic.
    (4)
    τy=(τ0+R)g(˙ε)
    Where, R=Q(1exp(βεpl))+Hεpl .(5)
    g(˙ε)=1+C[ln(˙ε˙εref)ln(˙ε˙εmax)]
  4. Damage initiation and rupture are function of triaxiality σ*=σmˉσ with σm=I13 and ˉσeq=3J2 .(6)
    ˙D=nεplεcεfεcn1˙εplεfεc
    (7)
    εc=[D1c+D2cexp(Dtrxσ*)](1+DJCln(˙ε˙εref))
    (8)
    εf=[D1f+D2fexp(Dtrxσ*)](1+DJCln(˙ε˙εref))