  This article's main scope is the presentation of a computational method for
the simulation of contact problems within the finite element method involving
complex and rough surfaces. The approach relies on the MPJR (eMbedded Profile
for Joint Roughness) interface finite element proposed in [arXiv:1805.07207],
which is nominally flat but can embed at the nodal level any arbitrary height
to reconstruct the displacement field due to contact in the presence of
roughness. Here, the formulation is generalized to handle 3D surface height
fields and any arbitrary nonlinear interface constitutive relation, including
friction and adhesion. The methodology is herein validated with BEM solutions
for linear elastic contact problems. Then, a selection of nonlinear contact
problems prohibitive to be simulated by BEM and by standard contact algorithms
in FEM are detailed, to highlight the promising aspects of the proposed method
for tribology.
