Abstract
In this paper, the influence of the resolution of fractal interfaces to the contact area is investigated by taking into account shear displacements. The paper is based on fractal approaches for the modeling of the multiscale self-affine topography of these interfaces where unilateral contact conditions are assumed to hold. More specifically for every value of the shear displacement a solution is taken in terms of normal forces and displacements at the interface, for different values of the resolution δ and for different values of normal forces. At each scale a classical Euclidean problem is solved. This procedure is applied for the simulation of a unilateral contact problem between two elastic bodies and between two bodies with elastoplastic behavior with hardening. In both cases the same fractal interface is adopted and the same multi-resolution analysis has been performed.
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References
Majumdar, Buhushan, B.: Role of fractal geometry in roughness characterization and contact mechanics of surfaces. Trans. ASME J. Tribology 112, 205–216 (1990)
Majumdar, Tien, C.L.: Fractal characterization and simulation of rough surfaces. Wear 136, 313–327 (1990)
Mandelbrot, B.: The Fractal Geometry of Nature. W.H. Freemann & Company, New York (1982)
Mandelbrot, B., Passoja, D., Paullay, A.: Fractal character of fractured surfaces of metals. Nature 308, 721–723 (1984)
Guang-Di Hu, E., Panagiotopoulos, P.D., Panagouli, O., Scherf, O., Wriggers, P.: Adaptive finite element analysis of fractal interfaces in contact problems. Comp. Methods Appl. Mech. Engrg. 182, 17–37 (2000)
Mistakidis, E.S., Panagouli, O.K.: Strength evalution of retrofit shear wall elements with interfaces of fractal geometry. Engineering Structures 24, 649–659 (2002)
Mistakidis, E.S., Panagouli, O.K.: Friction evolution as a result of roughness in fractal interfaces. Engineering Computations 20(1), 40–57 (2003)
Borodich, F.M., Onishchenko, D.A.: Similarity and fractality in the modelling of roughness by a multilevel profile with hierarchical structure. Solids and Structures 36(17), 2585–2612 (1999)
Xie, H.: Fractal nature on damage evolution of rock materials. In: 2nd International Symposium of Mining Technology and Science. CUMT Press (1991)
Falconer, K.J.: The Geometry of Fractal Sets. Cambridge University Press, Cambridge (1985)
Barnsley, M.: Fractals Everywhere. Academic Press, Boston- New York (1988)
Borri-Brunetto, M., Carpinteri, A., Chiaia, B.: Scaling phenomena due to fractal contact in concrete and rock fractures. Int. J. Fracture 95, 221–238 (1999)
Panagiotopoulos, P.D., Panagouli, O.K.: Fractal geometry in contact mechanics and numerical applications. In: Carpintieri, A., Mainardi, F. (eds.) CISM-Book on Scaling, Fractals and Fractional Calculus in Continum Mechanics, pp. 109–171. Springer
Panagiotopoulos, P.D.: Inequality Problems in Mechanics and Applications. Birkhäuser, Basel (1985)
Saouma, V.C.B., Gamaleldin, N.: Fractal characterization of fracture surfaces in concrete. Eng. Fract. Mech. 35, 47–53 (1990)
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Panagouli, O.K., Mistakidis, E.S. (2013). A Multi Resolution Study on the Behavior of Fractal Interfaces with Unilateral Contact Conditions. In: Stavroulakis, G. (eds) Recent Advances in Contact Mechanics. Lecture Notes in Applied and Computational Mechanics, vol 56. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33968-4_26
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DOI: https://doi.org/10.1007/978-3-642-33968-4_26
Publisher Name: Springer, Berlin, Heidelberg
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