#### MERGE_FAILURE_COHESIVE

###### Contact and tied interfaces
*MERGE_FAILURE_COHESIVE
mfid, $\sigma_{fail}$, $\tau_{fail}$, $G_{I}$, $G_{II}$, $\Delta_{ref}$
##### Parameter definition
VariableDescription
mfid Merge failure command ID
$\sigma_{fail}$ Tensile failure stress
$\tau_{fail}$ Shear failure stress
$G_{I}$ Modus I energy per unit area
$G_{II}$ Modus II energy per unit area
$\Delta_{ref}$ Element reference size
##### Description

Specifies failure of a merged interface MERGE. Failure is initiated when:

$\left( \frac{\xi \sigma}{\sigma_{fail}} \right)^2 + \left( \frac{\xi \tau}{\tau_{fail}} \right)^2 \geq 1$

where $\xi$ is a scale factor accounting the inability to resolve stress concentrations at coarse element grids:

$\xi = \mathrm{max} (1, \sqrt{\Delta/\Delta_{ref}})$

$\Delta$ is the local characteristic element size on the slave side of the merge interface. The stress unloading from failure is a linear function of the crack opening distance. It is defined such that the consumed energy per unit area of cracking $G$ is:

$G = \sqrt{\left( \frac{\sigma}{\sigma_{fail}} G_I \right)^2 + \left( \frac{\tau}{\tau_{fail}} G_{II} \right)^2}$