A Caltech Library Service

Collective Behavior of Asperities as a Model for Friction and Adhesion


Hulikal Sampath Kumaran, Srivatsan (2015) Collective Behavior of Asperities as a Model for Friction and Adhesion. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/Z94M92HM.


Understanding friction and adhesion in static and sliding contact of surfaces is important in numerous physical phenomena and technological applications. Most surfaces are rough at the microscale, and thus the real area of contact is only a fraction of the nominal area. The macroscopic frictional and adhesive response is determined by the collective behavior of the population of evolving and interacting microscopic contacts. This collective behavior can be very different from the behavior of individual contacts. It is thus important to understand how the macroscopic response emerges from the microscopic one.

In this thesis, we develop a theoretical and computational framework to study the collective behavior. Our philosophy is to assume a simple behavior of a single asperity and study the collective response of an ensemble. Our work bridges the existing well-developed studies of single asperities with phenomenological laws that describe macroscopic rate-and-state behavior of frictional interfaces. We find that many aspects of the macroscopic behavior are robust with respect to the microscopic response. This explains why qualitatively similar frictional features are seen for a diverse range of materials.

We first show that the collective response of an ensemble of one-dimensional independent viscoelastic elements interacting through a mean field reproduces many qualitative features of static and sliding friction evolution. The resulting macroscopic behavior is different from the microscopic one: for example, even if each contact is velocity-strengthening, the macroscopic behavior can be velocity-weakening. The framework is then extended to incorporate three-dimensional rough surfaces, long- range elastic interactions between contacts, and time-dependent material behaviors such as viscoelasticity and viscoplasticity. Interestingly, the mean field behavior dominates and the elastic interactions, though important from a quantitative perspective, do not change the qualitative macroscopic response. Finally, we examine the effect of adhesion on the frictional response as well as develop a force threshold model for adhesion and mode I interfacial cracks.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Tribology, friction, adhesion, rate and state laws, collective behavior
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Mechanical Engineering
Awards:Demetriades-Tsafka-Kokkalis Prize in Seismoengineering, Prediction, and Protection, 2015
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Lapusta, Nadia (co-advisor)
  • Bhattacharya, Kaushik (co-advisor)
Thesis Committee:
  • Ravichandran, Guruswami (chair)
  • Andrade, Jose E.
  • Lapusta, Nadia
  • Bhattacharya, Kaushik
Defense Date:14 April 2015
Record Number:CaltechTHESIS:05172015-152006825
Persistent URL:
Related URLs:
URLURL TypeDescription adapted for ch. 2
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:8861
Deposited By: Srivatsan Hulikal Sampath Kumaran
Deposited On:26 May 2015 21:13
Last Modified:04 Oct 2019 00:07

Thesis Files

PDF - Final Version
See Usage Policy.


Repository Staff Only: item control page