An elastic–inelastic model for dry friction with a smooth transition

Abstract A model for dry friction is developed based on a model of a shearing layer with a smooth elastic–inelastic transition. The resulting model for friction has a single history-dependent variable that characterizes elastic shear strain in the layer and is determined by integrating an evolution equation for its rate. The model uses an experimentally determined functional form for the coefficient of friction which decreases with increased shearing rate. The shear stress applied to the shearing layer is proportional to the normal compressive stress for transient response and the proportionality function becomes the coefficient of friction for steady-state response. The model also predicts the observed result that the transitional total shear strain for a jump in total shearing rate remains in a specified range for a large range of applied shear rate and is independent of the applied normal stress.