/MAT/LAW120 (TAPO)
Block Format Keyword This is a nonassociated elastoplastic model for polymer adhesives. The constitutive model is based on a I1J2 criterion that can be reduced either to a von Mises or DruckerPrager 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  
${\rho}_{i}$  
E  $\nu $  I_{form}  Itrx  Idam  
Table_ID  Xscale  Yscale  
${\tau}_{0}$  Q  $\beta $  H  
A_{F1}  A_{F2}  A_{H1}  A_{H2}  A_{S}  
C  ${\dot{\epsilon}}_{ref}$  ${\dot{\epsilon}}_{max}$  
D_{1c}  D_{2c}  D_{1f}  D_{2f}  
D_{TRX}  D_{JC}  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) 

${\rho}_{i}$  Initial
density. (Real) 
$\left[\frac{\text{kg}}{{\text{m}}^{\text{3}}}\right]$ 
E  Young’s (stiffness)
modulus. (Real) 
$\left[\text{Pa}\right]$ 
$\nu $  Poisson's
coefficient. (Real) 

I_{form}  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) 
$\text{[Hz]}$ 
Yscale  Scale factor for yield stress value
defined by Table_ID. (Real) 
$\left[\text{Pa}\right]$ 
${\tau}_{0}$  Initial shear yield
stress. (Real) 
$\left[\text{Pa}\right]$ 
Q  Voce hardening
modulus. (Real) 
$\left[\text{Pa}\right]$ 
$\beta $  Voce nonlinear hardening
exponent. Default = 1.0 (Real) 

H  Linear hardening
exponent. Default = 1.0 (Real) 
$\left[\text{Pa}\right]$ 
A_{F1}  Yield function
parameter. (Real) 

A_{F2}  Yield function
parameter. (Real) 

A_{H1}  Yield function distortional
hardening parameter. (Real) 

A_{H2}  Yield function distortional
hardening parameter. (Real) 

A_{S}  Plastic flow function parameter for
hydrostatic term. (Real) 

C  JohnsonCook strain rate
coefficient for hardening. (Real) 

${\dot{\epsilon}}_{ref}$  Quasistatic threshold strain rate
in JohnsonCook term. (Real) 
$\text{[Hz]}$ 
${\dot{\epsilon}}_{max}$  Maximum dynamic threshold strain
rate in JohnsonCook term. (Real) 
$\text{[Hz]}$ 
D_{1c}  JohnsonCook parameter for damage
initiation. (Real) 

D_{2c}  JohnsonCook parameter for damage
initiation. (Real) 

D_{1f}  JohnsonCook parameter for failure
strain. (Real) 

D_{2f}  JohnsonCook parameter for failure
strain. (Real) 

D_{TRX}  JohnsonCook damage parameter for
triaxiality term. (Real) 

D_{JC}  JohnsonCook strain rate parameter
for damage. (Real) 

Exp_n  Exponential coefficient for damage
strain rate dependency. (Real) 
Example (Adhesive Polymer)
#12345678910
/UNIT/20
Material model units
Mg mm s
#12345678910
/MAT/TAPO/1/20
Adhesive polymer
# RHO_I
1.2E9 0
# E Nu Iform Itrx Idam
1588 .34 1 0 0
# TAU0 Q beta H
19.66 2.746 24.98 13.35
# A1F A2F A1H A2H AS
0.446 0.218 0.24 0.1 0.338
# CC Epsp_ref Epsp_max
0.1 0.002 1726
# D1c D2c D1f D2f
0.345 1.094 6.935 0.00
# D_trx D_JC Exp_n
0.001 1.044 0
Comments
 The yield function is described depending on the I_{form} flag:
 I_{form} = 1: DruckerPrager formulation:
(1) $$f={J}_{2}+\frac{{a}_{1}}{\sqrt{3}}{\tau}_{0}{I}_{1}+\frac{{a}_{2}}{3}{I}_{1}{}^{2}{\tau}_{y}^{2}$$${a}_{1}={a}_{f1}+{a}_{1h}{\epsilon}_{pl}$ and ${a}_{2}={a}_{f2}+{a}_{2h}{\epsilon}_{pl}$
 I_{form} = 2: von Mises formulation:
(2) $$f={J}_{2}+\frac{{a}_{f2}}{3}{I}_{1}+\frac{\sqrt{3}}{2}\frac{{a}_{f1}}{{a}_{f2}}{\tau}_{0}{}^{2}\left({\tau}_{y}^{2}+\frac{{a}_{f1}^{2}}{{a}_{f2}}\frac{{\tau}_{0}^{2}}{4}\right)$$
These 2 functions are written in terms of the damaged stress tensor: ${\sigma}_{d}=\sigma /\left(1D\right)$
Where, $D$ represents the isotropic damage.
 I_{form} = 1: DruckerPrager formulation:
 Plastic potential is expressed as:
(3) $${f}^{*}={J}_{2}+\frac{{a}_{s}}{3}{I}_{1}{}^{2}$$  Yield stress is rate dependent:
 Table_ID ≠ 0, the yield stress is tabulated.
 Table_ID = 0, it is analytic.
(4) $${\tau}_{y}=\left({\tau}_{0}+R\right)g\left(\dot{\epsilon}\right)$$Where, $R=Q\left(1\text{exp}\left(\beta {\epsilon}_{pl}\right)\right)+H{\epsilon}_{pl}$ .(5) $$g\left(\dot{\epsilon}\right)=1+C\left[ln\left(\frac{\dot{\epsilon}}{{\dot{\epsilon}}_{ref}}\right)ln\left(\frac{\dot{\epsilon}}{{\dot{\epsilon}}_{max}}\right)\right]$$  Damage initiation and rupture are function of triaxiality
${\sigma}^{*}=\frac{{\sigma}_{m}}{\overline{\sigma}}$
with
${\sigma}_{m}=\frac{{I}_{1}}{3}$
and
${\overline{\sigma}}_{eq}=\sqrt{3{J}_{2}}$
.
(6) $$\dot{D}=n{\frac{{\epsilon}_{pl}{\epsilon}_{c}}{{\epsilon}_{f}{\epsilon}_{c}}}^{n1}\frac{{\dot{\epsilon}}_{pl}}{{\epsilon}_{f}{\epsilon}_{c}}$$(7) $${\epsilon}_{c}=\left[{d}_{1c}+{d}_{2c}\text{exp}\left({d}_{trx}{\sigma}^{*}\right)\right]\left(1+{d}_{JC}ln\left(\frac{\dot{\epsilon}}{{\dot{\epsilon}}_{ref}}\right)\right)$$(8) $${\epsilon}_{f}=\left[{d}_{1f}+{d}_{2f}\text{exp}\left({d}_{trx}{\sigma}^{*}\right)\right]\left(1+{d}_{JC}ln\left(\frac{\dot{\epsilon}}{{\dot{\epsilon}}_{ref}}\right)\right)$$