Computational methods for contact problems with roughness

This chapter provides a self-consistent introduction to computational methods for the solution of contact problems between bodies separated by rough interfaces. Both frictional and frictionless contact problems are examined. The mathematical formulation of the boundary element method is presented first, with details on the possible algorithmic implementation strategies and their computational efficiency. In the second part of the chapter, the fundamentals of the finite element method for the solution of contact problems are presented, along with an overview on the different strategies available in the literature to accurately discretize the multiscale features of roughness. A synopsis of the major advantages and disadvantages provided by the computational methods based on the boundary element method or the finite element method concludes the chapter, illustrating also perspective research directions.