Hierarchical Spring-Block Model for Multiscale Friction Problems

Abstract

A primary issue in bio-materials science is to design materials with ad-hoc properties, depending on the specific application. Among these properties, friction is recognized as a fundamental aspect characterizing materials for many practical purposes. Recently, new and unexpected frictional properties have been obtained by exploiting hierarchical multiscale structures, inspired by those observed in many biological systems. In order to understand the emergent frictional behaviour of these materials at the macroscale, it is fundamental to investigate their hierarchical structure, spanning across different length scales. In this paper, we introduce a statistical multiscale approach, based on a one-dimensional formulation of the spring-block model, in which friction is modeled at each hierarchical scale through the classical Amontons-Coulomb force with statistical dispersion on the friction coefficients of the microscopic components. By means of numerical simulations, we deduce the global statistical distributions 1 of the elementary structure at micrometric scale, and use them as input distributions for the simulations at the next scale levels. We thus study the influence of microscopic artificial patterning on macroscopic friction coefficients. We show that is it possible to tune the friction properties of a hierarchical surface and provide some insight on the mechanisms involved at different length scales.

Tuning friction with composite hierarchical surfaces

“…In particular, if we extract the microscopic coefficients of the blocks from a single Gaussian distribution corresponding to the arithmetic mean, (µ s ) m3 = 0.75 (7) and (µ d ) m3 = 0.45 (3), we obtain (µ s ) M 3 = 0.592(3) and (µ d ) M 3 = 0.462(1), while the coefficients obtained with a pattern of rough and smooth zones are always smaller. These results are consistent with those obtained with a multiscale version of the model, whose implementation is conceptually different, but applied to the same structure [43].…”

Multi-Scale Surface Texturing in Tribology—Current Knowledge and Future Perspectives

“…Finally, Costagliola et al [234][235][236][237] proposed a spring-block modeling approach to investigate the fundamental mechanisms of dry friction between textured surfaces and how multi-scale surface textures influence static and dynamic friction. The model was used to show how the intricate surface geometry and local material properties on different length scales strongly affect the macroscopic friction force.…”

“…Finally, Costagliola et al [234][235][236][237] proposed a spring-block modeling approach to investigate the fundamental mechanisms of dry friction between textured surfaces and how multi-scale surface Figure 18. Overview of the multi-scale finite element method proposed by [233] to simulate hydrodynamic lubrication of large rough contact surfaces, which can be extended to deal with multi-scale textures.…”

A 2-D model for friction of complex anisotropic surfaces

“…In this study, we adopt a spring-block model based on the AC friction force and a statistical distribution on the friction coefficients [40]- [42]: while the block i is at rest, the friction force F n is the normal force on i. When this limit is exceeded, a constant dynamic friction force opposes the motion, i.e.…”