Static and dynamic friction of hierarchical surfaces

Abstract

Hierarchical structures are very common in nature, but only recently have they been systematically studied in materials science, in order to understand the specific effects they can have on the mechanical properties of various systems. Structural hierarchy provides a way to tune and optimize macroscopic mechanical properties starting from simple base constituents and new materials are nowadays designed exploiting this possibility. This can be true also in the field of tribology. In this paper we study the effect of hierarchical patterned surfaces on the static and dynamic friction coefficients of an elastic material. Our results are obtained by means of numerical simulations using a one-dimensional spring-block model, which has previously been used to investigate various aspects of friction. Despite the simplicity of the model, we highlight some possible mechanisms that explain how hierarchical structures can significantly modify the friction coefficients of a material, providing a means to achieve tunability.

A 2-D model for friction of complex anisotropic surfaces

“…One of the most widely used models is the one dimensional spring-block model, which was originally introduced to study earthquakes [29]- [31] and has also been used to investigate many aspects of dry friction of elastic materials [32]- [39]. In [40] we have extensively investigated the general behavior of the model and the effects of local patterning (regular and hierarchical) on the macroscopic friction coefficients, and in [41] we have extended the study to composite surfaces, i.e. surfaces with varying material stiffness and roughness; finally in [42] we have introduced the multiscale extension of the model to study the statistical effects of surface roughness across length scales.…”

“…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.…”

“…When calculating time averages, care must be taken in the order of the operations, if there is an inversion of the friction force (i.e. some blocks exceed the rest position, as in the analytical calculations of [40]) or a periodic motion takes place, switching the operations of norm and time average produces different results. In these cases, the calculation closer to the realistic experimental procedure must be adopted.…”

Emergence of the interplay between hierarchy and contact splitting in biological adhesion highlighted through a hierarchical shear lag model

“…To verify the mechanisms outlined in the previous Section, we develop a numerical procedure to simulate the complete detachment of hierarchical structures. The approach is similar to that adopted in the literature in models used to describe static and dynamic friction [37][38][39], although here we do not consider these aspects for simplicity. The system is discretized and modelled using a linear system of equations based on the Finite Element Method (FEM) in one dimension [40].…”

Nucleation and propagation of excitation fronts in self-excited systems

“…These propagating stick-slip states have been observed also by Costagliola at al. [20], who extended the interfacial spring-block chain to two dimensions [21,22].…”