  An extension to the interface finite element with eMbedded Profile for Joint
Roughness (MPJR interface finite element) is herein proposed for solving the
frictional contact problem between a rigid indenter of any complex shape and an
elastic body under generic oblique load histories. The actual shape of the
indenter is accounted for as a correction of the gap function. A regularised
version of the Coulomb friction law is employed for modeling the tangential
contact response, while a penalty approach is introduced in the normal contact
direction. The development of the finite element (FE) formulation stemming from
its variational formalism is thoroughly derived and the model is validated in
relation to challenging scenarios for standard (alternative) finite element
procedures and analytical methods, such as the contact with multi-scale rough
profiles. The present framework enables the comprehensive investigation of the
system response due to the occurrence of tangential tractions, which are at the
origin of important phenomena such as wear and fretting fatigue, together with
the analysis of the effects of coupling between normal and tangential contact
tractions. This scenario is herein investigated in relation to challenging
physical problems involving arbitrary loading histories.
