/MAT/LAW117
Block Format Keyword This law represents the constitutive relation of ductile adhesive materials in 2 modes for normal and tangential directions. This law models the elastic and failure response of the material.
Format
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

/MAT/LAW117/mat_ID/unit_ID  
mat_title  
${\rho}_{i}$  
EN  ET  I_{mass}  I_{del}  I_{rupt}  
Fct_TN  Fct_TT  TN  TT  Fscale_x  
GIC  GIIC  EXP_G  EXP_BK  Gamma 
Definitions
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) 
$\left[\frac{\text{kg}}{{\text{m}}^{\text{3}}}\right]$ 
EN  Stiffness normal to the plane of the cohesive
element. (Real) 
$\left[\frac{\text{P}\text{a}}{\text{m}}\right]$ 
ET  Stiffness in the plane of the cohesive
element. (Real) 
$\left[\frac{\text{P}\text{a}}{\text{m}}\right]$ 
I_{mass}  Mass calculation flag.
(Integer) 

I_{del}  Failure flag indicating the number of
integration points to delete the element (between 1 and
4). Default = 1 (Integer) 

I_{rupt}  Mixed mode displacement law flag.
(Real) 

Fct_TN  Function identifier of the peak traction in
normal direction versus element mesh
size. (Integer) 

Fct_TT  Function identifier of the peak traction in
tangential direction versus element mesh
size. (Integer) 

TN  Peak traction in normal direction (default =
0) or, Fct_TN ordinate scale factor (default = 1) (Real) 
$\left[\text{Pa}\right]$ 
TT  Peak traction in tangential direction (default =
0) or, Fct_TT ordinate scale factor (default = 1) (Real) 
$\left[\text{Pa}\right]$ 
Fscale_x  Fct_TN and
Fct_TT abscissa scale factor. Default = 1 (Real) 
$\left[\text{m}\right]$ 
GIC  Energy release rate for mode I. (Real) 
$\left[\mathrm{Pa}.m\right]$ 
GIIC  Energy release rate for mode II. (Real) 
$\left[\mathrm{Pa}.m\right]$ 
EXP_B  Power law exponent for the mixed mode. Default = 2 (Real) 

EXP_BK  BenzeggageKenane exponent for the mixed
mode. (Real) 

Gamma  Gamma exponent for BenzeggageKenane
law. Default = 1 (Real) 
Example
#12345678910
/UNIT/1
Units
kg mm ms
#12345678910
/MAT/LAW117/1/1
CONNECT MATERIAL
# RHO_I
7.8E6
# EN ET Imass Idel Irupt
5 1.2 0 1 0
# Fct_TN Fct_TT TN TT Fscale_x
0 0 2 0.7 0
# GIC GIIC EXP_B EXP_BK Gamma
1 1.75 2 2 1
#12345678910
#ENDDATA
/END
#12345678910
Comments
 Mode I refers to the normal direction and mode II refers to the shear direction. ${\delta}_{I}$ is the separation in normal direction equal to ${\delta}_{zz}$ direction. ${\delta}_{II}$ is equal to the separation in tangential direction ${\delta}_{II}=\sqrt{{\delta}_{yz}+{\delta}_{zx}}$ . The mixed mode displacement is referred to by ${\delta}_{m}$ .
 The damage initiation
displacement in mode I and mode II are respectively,
${\delta}_{I}^{0}=\frac{{T}_{N}}{EN}$
and
${\delta}_{II}^{0}=\frac{{T}_{T}}{ET}$
and for the mixed mode:
(1) $${\delta}_{m}^{0}={\delta}_{I}^{0}\cdot {\delta}_{II}^{0}\cdot \sqrt{\frac{1+{\beta}^{2}}{{\left({\delta}_{II}^{0}\right)}^{2}+{\left(\beta \cdot {\delta}_{I}^{0}\right)}^{2}}}$$With the mode mix $\beta =\frac{{\delta}_{II}}{{\delta}_{I}}$ .
 The maximum displacement at
failure
${\delta}_{m}^{F}$
can be calculated using either a Power law
for
I_{rupt}=1:
(2) $${\delta}_{m}^{F}=\frac{2\left(1+{\beta}^{2}\right)}{{\delta}^{0}}\cdot {\left[{\left(\frac{EN}{GIC}\right)}^{EXP\_G}+{\left(\frac{\beta \cdot ET}{GIIC}\right)}^{EXP\_G}\right]}^{\left(\frac{1}{EXP\_G}\right)}$$or, a BenzeggageKenane law for I_{rupt} =2:(3) $${\delta}_{m}^{F}=\frac{2}{{\delta}^{0}{\left(\frac{1}{1+{\beta}^{2}}\cdot E{N}^{\gamma}+\frac{{\beta}^{2}}{1+{\beta}^{2}}\cdot E{T}^{\gamma}\right)}^{\frac{1}{\gamma}}}\cdot \left[GIC+\left(GIICGIC\right){\left(\frac{{\beta}^{2}\cdot ET}{EN+{\beta}^{2}\cdot ET}\right)}^{EXP\_BK}\right]$$  GIC and
GIIC are the energy release rates between the peak
traction and the maximum displacement for mode I and mode II, respectively.
$GIC=\frac{TN\cdot {\delta}_{I}^{F}}{2}$ and $GIIC=\frac{TT\cdot {\delta}_{II}^{F}}{2}$