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 Dn and Dt 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 Dn 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 Dnt and Dnc are separate interface parameters for the interface being in tension or compression.