Evolution of the contact between rough viscoelastic solids after decreasing loads: memory erasure and monotonic increase

The real area of contact governs, in part, the magnitude of the friction force, yet its time evolution in rough viscoelastic interfaces remains incompletely understood. In experiments of contact between polymethylmethacrylate blocks under decreasing normal loads, Dillavou and Rubinstein have shown that the true contact area exhibits, after unloading, a decreasing phase and long-term memory of the contact state prior to unloading. It is however unclear what modeling ingredients are necessary to reproduce these two features. Here, we investigate these effects using fractional viscoelastic rough contact models. By adapting existing contact theories and numerical simulation methods to fractional viscoelasticity, which induces a wide relaxation spectrum, we reproduce logarithmic aging under constant load, but show that memory of the contact state is erased upon unloading. Indeed, the contact area behaves as if it had always experienced the reduced load, even on short time-scales, contrasting with the response of a standard linear solid. Moreover, none of our results show a decreasing regime of the contact area after unload: we ultimately prove that this is the case for all linear viscoelastic models – despite capturing logarithmic aging – leading to the conclusion that additional local internal variables are required to explain both long-term contact memory and contact area reduction after unloading.

💡 Research Summary

**
The paper investigates the time evolution of the true contact area between rough viscoelastic solids when the normal load is reduced, a situation that has been experimentally shown to produce a transient decrease in contact area followed by a long‑term memory of the pre‑unload state (Dillavou & Rubinstein, 2020). The authors aim to determine which modeling ingredients are required to reproduce both the logarithmic aging observed under constant load and the non‑monotonic behavior after unloading.

To this end, they employ two complementary approaches. First, an analytical framework based on the Lee‑Radok‑Ting method is adapted to rough contacts using Persson’s theory for the small‑contact regime. In this formulation the normalized contact area A(t) is expressed as a convolution of the loading history with the material’s creep function J(t) during the loading phase, and with the relaxation function G(t) during the unloading phase. Second, they develop a numerical simulation scheme that can handle fractional viscoelasticity. The fractional Zener model (a Scott‑Blair element in series with a spring, in parallel with another spring) is chosen because its single fractional order ν∈