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

Variable
Description
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:

$\displaystyle{ G(\alpha) = \frac{1}{2} ( \sigma_p \cdot \mathrm{cos} \alpha + \tau_p \cdot \mathrm{sin} \alpha ) \delta_{max} = G_I \cdot \mathrm{cos}^2 \alpha + G_{II} \cdot \mathrm{sin}^2 \alpha}$
Spring element representing adhesive between two surfaces
Spring element representing adhesive between two surfaces

Example

Glued aluminum sheets exposed to tensile loading

A complete model of a glued connection exposed to tensile loading.

*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" Rp = 0.02, "pipe radius" 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