#### CONNECTOR_GLUE_LINE

###### Connectors
*CONNECTOR_GLUE_LINE
"Optional title"
coid
entype${}_1$, enid${}_1$, entype${}_2$, enid${}_2$, pathid, $tol$, $\Delta$, $w$
$h$, $\rho$, $E$, $\nu$, $\sigma_f$, $\tau_f$, $G_I$, $G_{II}$
##### Parameter definition
VariableDescription
coid Command ID
entype${}_1$ Entity type of surface 1
options: P, PS, ALL
enid${}_1$ Entity ID of surface 1
entype${}_2$ Entity type of surface 2
options: P, PS, ALL
enid${}_2$ Entity ID of surface 2
pathid Path ID of glue line
$tol$ Maximum allowed distance between surfaces to be connected
$\Delta$ Discretization parameter (distance between glue connectors)
$w$ Glue line width
$h$ Glue film thickness
$\rho$ Density
$E$ Young's modulus
$\nu$ Poisson's ratio
$\sigma_f$ Failure stress in tension
$\tau_f$ Failure stress in shear
$G_I$ Delamination energy - modus I
$G_{II}$ Delamination energy - modus II
##### Description

This command is used to define the effect of an adhesive between two surfaces. The location of the glue is defined with a PATH. The glue line is represented by a series of generalized spring elements with spatial spacing $\Delta$. The picture below shows stresses building up in one spring element. The shear stress $\tau$ is defined as:

$\displaystyle{ \tau = \frac{E}{2(1+\nu)} \cdot \frac{\delta_t}{h} }$

The normal stress component is:

$\displaystyle{ \sigma = \frac{(1-\nu)E}{(1+\nu)(1-2\nu)} \cdot \frac{\delta_n}{h} }$

A resultant (effective) stress measure in the spring is defined as:

$\displaystyle{ \sigma_{eff} = \sqrt{\sigma^2 + \tau^2} = \frac{E_{eff} \delta}{h} }$

where $E_{eff}$ is a direction dependent stiffness:

$\displaystyle{ E_{eff} = \sqrt{ \frac{(1-\nu)^2}{((1+\nu)(1-2\nu))^2} \cdot \mathrm{cos}^2 \alpha + \frac{1}{4(1+\nu)^2} \cdot \mathrm{sin}^2 \alpha } \cdot E }$

The definition of the loading angle $\alpha$ is shown in the figure below. $\sigma_f$ is the maximum stress in pure vertical loading and $\tau_f$ is the capacity in shear. The maximum effective stress $\sigma_{max}$ in a general direction of stretching is defined as:

$\displaystyle{ \sigma_{max}(\alpha) = \sigma_f \cdot \mathrm{cos}^2 \alpha + \tau_f \cdot \mathrm{sin}^2 \alpha }$

That is, damage will grow and the stresses will drop once $\sigma_{eff}$ reaches $\sigma_{max}$. We refer to the normal and shear stress components at this point as $\sigma_p$ and $\tau_p$, respectively.

$\displaystyle{ \sqrt{\sigma_p^2 + \tau_p^2} = \sigma_f \cdot \mathrm{cos}^2 \alpha + \tau_f \cdot \mathrm{sin}^2 \alpha}$

Also the work of fracture $G$ is direction dependent. The elongation at complete fracture $\delta_{max}$ is adjusted such that:

$\displaystyle{ G(\alpha) = \frac{1}{2} ( \sigma_p \cdot \mathrm{cos} \alpha + \tau_p \cdot \mathrm{sin} \alpha ) \delta_{max} = G_I \cdot \mathrm{cos}^2 \alpha + G_{II} \cdot \mathrm{sin}^2 \alpha}$
##### Example

*UNIT_SYSTEM
SI
*PARAMETER
tol = 1.0e-4, "tolerance"
delta = 2.0e-3, "discretization"
w = 4.0e-3, "width"
h = 1.0e-4, "film thickness"
rho = 1000.0, "density"
E = 1.0e6, "Young's modulus"
pr = 0.45, "Poisson's ratio"
sig_f = 1.0e7, "failure stress in tension"
tau_f = 5.0e6, "failure stress in shear"
G_I = 1.0e4, "delamination energy - modus I"
G_II = 1.0e4, "delamination energy - modus II"
Lp = 0.1, "flange size"
hp = 0.002, "sheet thickness"
disp = 0.01, "pipe displacement"
tend = 0.01, "termination time"
*TIME
[%tend]
#
# MESH
*COMPONENT_BOX
"flange L"
1, 1, 1, 10, 10
[-%hp], [-%Lp/2], [-%Lp/2], 0, [%Lp/2], [%Lp/2]
*COMPONENT_BOX
"flange R"
2, 2, 1, 10, 10
0, [-%Lp/2], [-%Lp/2], [%hp], [%Lp/2], [%Lp/2]
*COMPONENT_PIPE
"pipe L"
3, 3, 10, 12, 1
[-%Lp-%hp], 0, 0, [-%hp], 0, 0, [%Rp], [%Rp+%hp]
*COMPONENT_PIPE
"pipe R"
4, 4, 10, 16, 1
[%hp], 0, 0, [%Lp+%hp], 0, 0, [%Rp], [%Rp+%hp]
*CHANGE_P-ORDER
ALL, 0, 3
*SMOOTH_MESH
ALL, 0, 45.0
#
# MATERIAL
*MAT_METAL
1, 2700.0, 70.0e9, 0.3
1
*FUNCTION
1
150.0e6 + 100.0e6*(1 - exp(-5*epsp))
#
# PARTS
*PART
"flange L"
1, 1
"flange R"
2, 1
"pipe L"
3, 1
"pipe R"
4, 1
#
# CONNECTIONS
*MERGE
"pipe L to flange L"
P, 3, P, 1
*MERGE
"pipe R to flange R"
P, 4, P, 2
*CONNECTOR_GLUE_LINE
"flange"
1
P, 1, P, 2, 22, [%tol], [%delta], [%w]
[%h], [%rho], [%E], [%pr], [%sig_f], [%tau_f], [%G_I], [%G_II]
*PATH
"glue line"
22
0, [-0.4*%Lp], [-0.4*%Lp]
0, [0.4*%Lp], [-0.4*%Lp]
0, [0.4*%Lp], [0.4*%Lp]
0, [-0.4*%Lp], [0.4*%Lp]
0, [-0.4*%Lp], [-0.4*%Lp]
#
# BOUNDARY CONDITIONS
*BC_MOTION
"left"
1
G, 123
V, X, 34, -1
*BC_MOTION
"right"
2
G, 234
V, X, 34
*FUNCTION
34
smooth_v(%disp, 0, %tend)
#
# CONTACT
*CONTACT
"general"
1
ALL, 0, ALL, 0
#
# PART SET
*SET_PART
12
1, 2
#
# GEOMETRIES
*GEOMETRY_BOX
123
[-%Lp-1.1*%hp], 0, 0, [-%Lp-0.9*%hp], 0, 0
*GEOMETRY_BOX
234
[%Lp+0.9*%hp], 0, 0, [%Lp+1.1*%hp], 0, 0
*END