Static and Dynamic Analysis of Deformable Fractal Surface in Contact With Rigid Flat

Introduction

Analysis of solid rough contact surface has immense importance in the present scenario because in MEMS and other micro-scale devices, the effect of the surface topography on the contact interactions becomes crucial (Dickrell et al., 2007; Rezvanian et al., 2007). To predict and control the solid surface interactions, clear understanding of the contact behavior is essential under static as well as under dynamic conditions. Fractal geometry first introduced by Mandelbrot (Mandelbrot, 1967; Mandelbrot & Blumen, 1989) is extensively utilized to characterize the realistic rough surface due to due to its scale-dependent, non-stationary, self-similar nature. Majumdar and Tien (1990), Majumdar and Bhushan (1990), and Ling (1990) formulated general methods to apply fractal geometry to model rough surface. Ausloos and Berman (1985) and Berry and Lewis (1980) furnished the applicability of the modified Weierstrass–Mandelbrot equation to represent rough fractal surface. The method to determine the value of the fractal dimension of physical rough surface was presented by Dubuc et al. (1989). Yan and Komvopolos (1998) investigated the elastic-plastic contact behavior between two approaching fractal rough surfaces through analytical approach. Several researchers carried out investigations on the normal contact stiffness of fractal rough surfaces under different conditions (Buczkowski et al., 2014; Pohrt & Popov, 2012; Xiao et al., 2019; Zhang et al., 2017). Since finite element analysis softwares have evolved as an extremely efficient tool for multiphysics analysis, it is also utilized to carry out contact analysis of fractal rough surfaces by several researchers (Chatterjee & Sahoo, 2013; Hyun et al., 2004; Pei et al., 2005; Sahoo & Ghosh, 2007).