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This note presents a modification of the integrated friction model structure proposed by Swevers et al., called the Leuven model. The Leuven model structure allows accurate modeling both in the presliding and the sliding regimes without the use of a switching function. The model incorporates a hysteresis function with nonlocal memory and arbitrary transition curves. This note presents two modifications of the Leuven model. A first modification overcomes a recently detected shortcoming of the original Leuven model: a discontinuity in the friction force which occurs during certain transitions in presliding. A second modification, using the general Maxwell slip model to implement the hysteresis force, eliminates the problem of stack overflow, which can occur with the implementation of the hysteresis force described in [10].

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This paper presents a theoretical model for (dry, low-velocity, wear-less) friction force dynamics based on asperity interaction considerations subject to the phenomenological mechanisms of creep/relaxation, adhesion and (elasto-plastic) deformation in their most generalized forms. The model simulates the interaction of a large population of idealised, randomly distributed asperities with arbitrarily chosen geometrical and elastic properties. Creep and adhesion are simulated by an expedient local coefficient of friction that increases with time of contact, while deformation effects are accounted for by rate-independent hysteresis losses occurring in the bulk of the material of an asperity that is breaking loose. An energy method is adopted to calculate the instantaneous, local friction force leading to better insight into the problem as well as higher numerical efficiency. The results obtained by this model show both qualitative and quantitative agreement with the known types and facets of friction force dynamic behaviour; in particular, pre-sliding quasi time-independent frictional hysteresis in the displacement, velocity weakening, slider ''lift-up'' effect and frictional lag, in addition to the influence of the various process parameters, all in a single formulation, such as no extant friction model could show before. Moreover, the model is still open for and capable of further refinement and elaboration so as to incorporate local inertia and viscous effects and thus to be extended to include velocity strengthening and lubricated rough contacts.