/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.
(Integer) |
|
Itrx | Damage dependency on triaxiality in
compression flag.
(Integer) |
|
Idam | Strain rate definition in damage
model flag.
(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
- The yield function is described depending on the Iform flag:
- Iform = 1: Drucker-Prager formulation:
(1) f= J2+a1√3τ0I1+a23I12−τ2ya1=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/(1−D)
Where, D represents the isotropic damage.
- Iform = 1: Drucker-Prager formulation:
- Plastic potential is expressed as:
(3) f*= J2+AS3I12 - 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(1−exp(−βεpl))+Hεpl .(5) g(˙ε)=1+C[ln(˙ε˙εref)−ln(˙ε˙εmax)] - Damage initiation and rupture are function of triaxiality
σ*=σmˉσ
with
σm=I13
and
ˉσeq=√3J2
.
(6) ˙D=nεpl−εcεf−εcn−1˙εplεf−εc(7) εc=[D1c+D2cexp(Dtrxσ*)](1+DJCln(˙ε˙εref))(8) εf=[D1f+D2fexp(Dtrxσ*)](1+DJCln(˙ε˙εref))