Analytical solutions to the shear-induced anisotropic area reduction in frictional elastomer contact

Shear-induced contact area reduction is a common phenomenon across scales. The corresponding contact morphology controls almost all the macroscopic features of the interface, including adhesion, wear, viscoelastic properties, stiffness, and even electric resistance. It is a long-standing challenge to predict the contact morphology of nonlinear soft elastomer contact since there has been no available analytical solution. The work presented in this paper aims to fill the blank. Here, we first establish a new framework for contact morphology, which involves two evolution equations of the contact boundary. The framework decouples nonlinear contact kinematics and contact forces to formulate the corresponding initial-value problem in a modular approach. Based on this, we present analytical solutions to the shear-induced anisotropic area reduction in elastomer contact by using the method of undetermined coefficient and Boussinesq type models. We theoretically demonstrate that the shear-induced normal deformation (originated from Poynting’s effect), but not tangential deformation, governs the anisotropic area reduction. Also, the power laws of the reduction parameters for both contact area and size are provided. The results show quantitative agreement with recent simulations and experiments. Our approaches to the contact morphology of frictional contact involving soft materials may shed some light on the theoretical modeling of large deformation contact mechanics.