Nonlinear model of ice surface softening during friction

TL;DR

This paper models ice surface softening during friction as a nonlinear process driven by external heating, using coupled equations that reveal a first-order transition mechanism influenced by shear modulus and heating rate.

Contribution

It introduces a nonlinear model combining viscoelastic and thermodynamic equations to explain ice softening as a first-order phase transition during friction.

Findings

Softening occurs via a first-order transition mechanism.

Critical heating rate depends on shear modulus and temperature.

Model equations coincide with the Lorenz system, revealing synergetic behavior.

Abstract

The ice surface softening during friction is shown as a result of spontaneous appearance of shear strain caused by external supercritical heating. This transformation is described by the Kelvin-Voigt equation for viscoelastic medium, by the relaxation equations of Landau-Khalatnikov-type and for heat conductivity. The study reveals that the above-named equations formally coincide with the synergetic Lorenz system, where the order parameter is reduced to shear strain, stress acts as the conjugate field, and temperature plays the role of a control parameter. Using the adiabatic approximation, the stationary values of these quantities are derived. The examination of dependence of the relaxed shear modulus on strain explains the ice surface softening according to the first-order transition mechanism. The critical heating rate is proportional to the relaxed value of the ice shear modulus and inversely proportional to its typical value.