An asperity-based statistical model for the adhesive friction of elastic nominally flat rough contact interfaces

Constitutive Behavior of Rocks During the Seismic Cycle

“…In the brittle field, the state evolution is fundamentally linked to changes in the real area of contact (Ben‐David & Fineberg, 2011; Ben‐David et al., 2010; Dieterich & Kilgore, 1994; Rubinstein et al., 2004; Selvadurai & Glaser, 2015, 2017) with the strength of contact modulated by chemical reactions near contact junctions and crack tips in aqueous solutions or atmospheric humidity (Bergsaker et al., 2016; Dieterich & Conrad, 1984; Frye & Marone, 2002; Renard et al., 2012; Rostom et al., 2013; Zeng et al., 2020). The physical basis of the model relies on quantifying the real area of contact, which varies instantaneously with shear and normal stress, but also evolves spontaneously over time (Dieterich & Kilgore, 1994, 1996; Maegawa et al., 2015; Mergel et al., 2019; Popov et al., 2021; Sahli et al., 2018; Weber et al., 2019; Xu et al., 2022). In this study, we consider a simple model whereby the area of contact is controlled by the effective normal stress and the local radius of curvature of micro‐asperities at contact junctions based on the roughness of natural surfaces with a fractal topography (Archard, 1957; Barbot, 2019b; Greenwood & Williamson, 1966) $$$\mathcal{A}=\frac{{c}_{0}+{\mu }_{0}\bar{\sigma }}{\chi }{\left(\frac{d}{{d}_{0}}\right)}^{\alpha },$$$ where $$\mathcal{A}$$ is the density of real area of contact, c 0 is a cohesion term, μ 0 is the reference friction coefficient, $$\bar{\sigma }$$ is the effective normal stress accounting for pore fluid pressure (Terzaghi, 1936), χ is the plowing hardness, d and d 0 are the effective and reference radii of curvature at contact junctions, and α is a power exponent.…”

“…In the brittle field, the state evolution is fundamentally linked to changes in the real area of contact (Ben-David & Fineberg, 2011;Ben-David et al, 2010;Dieterich & Kilgore, 1994;Rubinstein et al, 2004;Selvadurai & Glaser, 2015 with the strength of contact modulated by BARBOT 10.1029/2023AV000972 3 of 36 chemical reactions near contact junctions and crack tips in aqueous solutions or atmospheric humidity (Bergsaker et al, 2016;Dieterich & Conrad, 1984;Frye & Marone, 2002;Renard et al, 2012;Rostom et al, 2013;Zeng et al, 2020). The physical basis of the model relies on quantifying the real area of contact, which varies instantaneously with shear and normal stress, but also evolves spontaneously over time (Dieterich & Kilgore, 1994, 1996Maegawa et al, 2015;Mergel et al, 2019;Popov et al, 2021;Sahli et al, 2018;Weber et al, 2019;Xu et al, 2022). In this study, we consider a simple model whereby the area of contact is controlled by the effective normal stress and the local radius of curvature of micro-asperities at contact junctions based on the roughness of natural surfaces with a fractal topography (Archard, 1957;Barbot, 2019b;Greenwood & Williamson, 1966)…”

Literature review on engineering surface modeling

“…Nayak's seminal work[3], combined with the ideas proposed by Greenwood [2] , leads to analytical results via the so-called spectral moment method [ 47 , 48 ] for the summit height and curvature distributions of anisotropic Gaussian topography, which has propelled the development of asperity-based Gaussian rough surface contact analysis models including single-asperity [49] and multi-asperity [50] . That is, the spectral moments m 0 , m 2 and m 4 are defined as where mean() denotes the arithmetic mean and z denotes the section profile height vector in any direction along the surface.…”

“…Sabino analyzed the effect of non-Gaussianity on the statistical geometry of an isotropic self-affine rough surface [51] by comparing the summits height distribution, expected mean curvature and summits density of the rough surface under Weibull probability distribution with Nayak's Gaussian case theory. Regrettably, only the influencing factors and the corresponding trends are reported, and no quantitative analytical expressions are presented for the calculation of asperity-based statistical model [50] .…”

Equivalent characteristic model of a rough contact interface based on virtual material method

“…The method can push the simulation results closer to reality. In 2022, based on physically-rooted contact mechanics laws, Xu et al 16 used a statistical model to describe the contact between a smooth rigid flat surface and a nominally flat linear elastic rough surface, which considered the quasistatic tangential loading, up to full sliding. In 2022, Kang et al 17 put forward the non-Gaussian property to describe rough surfaces in the contact model of coated piston ring and honed cylinder liner.…”