  A new variational formulation is herein proposed for the solution of adhesive
contact problems for non-planar profiles of arbitrary shape indenting a
deformable half-plane. The method exploits the original idea of accounting for
the shape of roughness as a correction to the normal gap function, rather than
explicitly discretizing roughness with higher-order numerical interpolation
schemes. The resulting interface finite element with eMbedded Profile for Joint
Roughness (MPJR interface finite element) is derived and its implementation as
a user-defined element is comprehensively described. The method is validated
against Hertzian contact problems between a cylinder and a half-plane, also in
the presence of adhesion, showing a remarkable accuracy in spite of the
low-order interpolation used. The capability and efficiency of the method are
subsequently illustrated in relation to the challenging frictionless normal
contact problems between deformable substrates and rough profiles analytically
described by the Weierstrass-Mandelbrot function. This method opens new
perspectives for the solution of contact problems with roughness using the
finite element method that, so far, were strongly limited by the issue of
providing an accurate representation of roughness.

Soft Condensed Matter