Abstract
Contact mechanics models based on linearity assumptions, often using the viscoelastic half space theory and numerically implemented with the boundary element method, are known to provide accurate results for small mean square slope of the surface roughness. For large mean square slope, models accounting for finite deformations, often implemented with the non-linear finite element method, are more accurate but lead to a prohibitive computational cost. We propose a new hybrid multiscale approach able to account for the finite deformations arising due to large mean square slope, while keeping a computational cost similar to that associated to linear approaches. The basic strategy is a decomposition of the surface roughness power spectrum into a discrete number of waves, whose spectral range is partitioned into a high mean square slope range and a low mean square slope range. The contact mechanics in the former is accurately solved with the kinematically non-linear model and the results averaged out at the larger wavelength scale in terms of an effective interface interaction law. This law is then applied in the linear simulation involving the scales within the low mean square slope range. The proposed approach is a more accurate alternative to fully linear and a computationally faster alternative to fully non-linear contact mechanics approaches.
Highlights
The mechanics of contact taking place at the interface of rough soft solids is attracting a wide scientific interest due to its implications in a number of applications, ranging from biology and biomedical devices to machine elements (Persson, 2006)
In previous work (Scaraggi et al, 2016; Al-Qudsi, 2020) we have shown that the square slope of a given roughness wavelength strongly affects the numerically calculated contact area and hysteretic friction coefficient corresponding to that wavelength for given pressure and sliding velocity, and that the corresponding viscoelastic half-space (VHS)-based linear and kinematically non-linear predictions are quantitatively in agreement only up to roughness root mean square slopes less than a threshold ≈1
For sufficiently small values of m2, the contact mechanics models based on the linear VHS assumption can provide accurate results. This consideration is at the basis of the new approach for contact mechanics of real rough surfaces that we investigate in this paper
Summary
The mechanics of contact taking place at the interface of rough soft solids is attracting a wide scientific interest due to its implications in a number of applications, ranging from biology and biomedical devices to machine elements (Persson, 2006). The complexity in the prediction of rubber friction arises from the multiscale nature of the physical mechanisms taking place at the contact interface (Schallamach, 1953; Grosch, 1963; Persson, 2006). Rubbers typically exhibit non-linear mechanical behavior as well as wear-induced graded mechanical properties (Mokhtari and Schipper, 2016). This physical scenario determines a strong non-linear coupling between length and time scales
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