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Abstract
Abstract-This paper present a review of mathematical and physical approaches of homogenization, fractal and multifractal methods for the study of roughness effect in the bonded materials. In particular, attention is paid to the effects of roughness on materials joined through an adhesive. Firstly, considering the periodic roughness, the different homogenization methods are presented, including mathematical and physical approaches. Secondly, when the rough surface is no longer considered periodic and taking into account multi-scale of asperities, the article focuses on fractal methods. Lot of research has focused on the effect of roughness irregularities on surface contact, friction or wear, crack propagation using fractal theory. Multifractal analysis was introduced in the 80s and has overcome the limitations of fractal analysis. The multifractal analysis of fractal functions is performed using wavelets instead of boxes like in the classical multifractal formalism.
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Details
1 is associate researcher in Department of Mathematics of Bretagne Sud, Rue Andre Lwoff 56017 Vannes, France
2 is assistant professor in Department of Mathematics (modelisation mathematique et numerique), Conservatoire National des Arts et Metiers, 292 rue Saint Martin, 75141 Paris, FRANCE
3 is professor at Department of Mathematics of Bretagne Sud, Rue Andre Lwoff 56017 Vannes, France
4 is assistant professor at ENI de Tarbes, 47 avenue d'Azereix, 65016 Tarbes, France
5 is professor at ENI de Tarbes, 47 avenue d'Azereix, 65016 Tarbes, France