  The contact of solids with rough surfaces plays a fundamental role in
physical phenomena such as friction, wear, sealing, and thermal transfer.
However, its simulation is a challenging problem due to surface asperities
covering a wide range of length-scales. In addition, non-linear local
processes, such as plasticity, are expected to occur even at the lightest
loads. In this context, robust and efficient computational approaches are
required. We therefore present a novel numerical method, based on integral
equations, capable of handling the large discretization requirements of real
rough surfaces as well as the non-linear plastic flow occurring below and at
the contacting asperities. This method is based on a new derivation of the
Mindlin fundamental solution in Fourier space, which leverages the
computational efficiency of the fast Fourier transform. The use of this Mindlin
solution allows a dramatic reduction of the memory imprint (as the Fourier
coefficients are computed on-the-fly), a reduction of the discretization error,
and the exploitation of the structure of the functions to speed up computation
of the integral operators. We validate our method against an elastic-plastic
FEM Hertz normal contact simulation and showcase its ability to simulate
contact of rough surfaces with plastic flow.
