Linear Imperfect Interface

Description

This imperfect interface contact law assumes the normal and tangential tractions are linear and depend only on the normal and tangentatial displacement discontinuities, respectively:

      [math]\displaystyle{ T_n = D_n[u_n] }[/math]

      [math]\displaystyle{ T_t = D_t[u_t] }[/math]

where D_n and D_t are two interface parameters, which are infinite for a perfect interface (zero displacement discontinuity) and 0 for a debonded interface (zero traction). But this linear law would allow the two materials to interpenetrate, especially if D_n was low. To correct this issue, the traction law in the normal direction is allowed to be bilinear:

      [math]\displaystyle{ T_n = \left\{ \begin{array}{ll} D_{nt}[u_n] & {\rm \ if\ }[u_n]\gt 0 \\ D_{nc}[u_n] & {\rm \ otherwise} \end{array} \right. }[/math]

where D_nt and D_nc are separate interface parameters for the interface being in tension or compression.

Properties

The properties for this law are:

Property	Description	Units	Default
Dnt (or Dn)	Imperfect interface parameter for normal direction when in tension	pressure/length units	-1
Dnc	Imperfect interface parameter for normal direction when in compression. If Dnc is not specified, it set equal to Dnt.	pressure/length units	none
Dt	Imperfect interface parameter for tangential direction	pressure/length units	-1

In theory, very large interface parameters will result in a perfect interface, but they also make the numerical equations very "stiff" and therefore potentially unstable. To solve this issue, you can set any interface parameter to -1 to indicate an infinite interface parameter or a perfect interface. When a parameter is -1, the equations are handled different to avoid stability issues.