Rate-and-state friction theory describes how friction evolves with slip. It has now been widely applied to explain frictional behaviors in both the lab and the tectonic scale. State variable is a key parameter in rate-and-state friction that describes how friction depends on the slip history. The underlying physics of the state variable, however, remains an active area of debate, because its current mathematical form was obtained by empirically fitting laboratory data.

In this project, we revisit the theory that explains the state variable as the real area of contact of the rough interfaces. The real area of contact Ar is usually way smaller than the apparent total contact area. The theory states that state dependence is due to creep or rejuvenation at the micro-contacts. We developed the existing theory, brought up a quantitative relation, and tested the relation with two published laboratory friction experiments: Dieterich and Kilgore (1994) and Svetlizky, Bayard, and Fineberg (2019). 

Our models explain the experimental data reasonably well, suggesting a valid constitutive relationship between the real area of contact and the size and age of micro-asperities at contact junctions. Our findings demonstrate a direct link between the state-variable and an observable quantity in the laboratory, providing new insights into the physical mechanisms underlying rate- and state-dependent friction laws.

Learn more in my paper, Wu & Barbot, 2025, PNAS: 

Last updated Nov-28-2025