The prediction of both the tribological behaviour and mechanical analysis of the wear resistance are still of great research interest in order to improve the lifetime of material surfaces. This concerns both bulk and coated materials although coating processes have been often developed in order to protect substrates from tribological solicitations. The wear resistance of coated materials has been the subject of many studies which show that it is possible to protect and improve significantly the durability of substrates. A straightforward discretisation of the multi-scale problem of graded coatings on substrates exceed the memory and CPU capacity of current (and next generation) computers. The authors have proposed an efficient numerical model that can handle this multi-scale problem: using billion points and locally refined grids.

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