The aim of this project is to develop an efficient two-scale numerical scheme integrating implicit finite element computations at the macro-scale and the boundary element method at the micro-scale for the accurate solution of frictional contact problems with microscopic interface roughness. The whole range of sliding regimes, from the full stick to the full slip and also full sliding, will be handled, as well as any complex loading path. The problem of frictional contact is relevant in many research areas of engineering and physics. In mechanical engineering, it is important in configurations such as bolted joints, wheel-rail contact, bearings, brakes or wheel-asphalt contact. It is also of interest for the interaction between soil and pile foundations in civil and geotechnical engineering applications. In biomechanics, the relative motion in hip-joint prostheses leading to wear is also ruled by friction. In all of such fundamental problems, the interface between bodies in contact is not flat and its roughness presents multiscale features that influence the deformation and the stress states in the material. In this context, finite element (FE)-based computational methods are very promising for the solution of the frictional contact problem, due to their capability to deal with complex, realistic model geometries and with material and geometrical nonlinearities. Among the techniques available in the literature, the mortar method is considered as one of the most suitable ones for large relative sliding displacements, accommodating also different mesh discretizations of the two bodies in contact along their common interface. The present project aims at developing a new two-scale computational method to enrich the interface constitutive model of the basic mortar method, accounting for roughness. As a main difference from the existing approach where the contact interface is assumed to be nominally flat and the classical Coulomb friction law is postulated to govern the relative tangential motion, the proposed approach will allow the simulation of partial slip regimes ranging from full stick to full slip, and then followed by gross sliding, explicitly considering the effect of microscopical roughness. Previous attempts to include roughness in the finite element method (FEM) within node-to-surface contact algorithms have considered FE^2-type approaches where a nested finite element problem with roughness is solved at each integration point of the macroscopic flat interface. To accelerate computations, the use of look-up tables collecting contact results obtained from off-line finite element analyses has been proposed. As compared to these approaches, the proposed multi-scale method will use boundary element methods (BEM) instead of FEM at the microscale, to reduce the computational cost. Moreover, for the simulation of any arbitrary loading path, the micro-scale contact response will be determined by exploiting novel mathematical analogies to derive the solution from the history of the normal contact problem, with an expected significant speed-up of computations.    «

The aim of this project is to develop an efficient two-scale numerical scheme integrating implicit finite element computations at the macro-scale and the boundary element method at the micro-scale for the accurate solution of frictional contact problems with microscopic interface roughness. The whole range of sliding regimes, from the full stick to the full slip and also full sliding, will be handled, as well as any complex loading path. The problem of frictional contact is relevant in m...    »