Modeling tangential response of rough interfaces: A multi-scale analysis with shoulder-shoulder elasto-plastic contact

The tangential contact of rough interfaces critically influences the dynamics and stability of mechanical systems. Existing models often oversimplify contact behavior and lack a physical basis for the tangential response. This study presents a novel multi-scale analytical model for predicting the tangential response of rough interfaces, incorporating shoulder-shoulder elasto-plastic contact. At the asperity scale, the normal contact is coupled with a tangential Jenkins element, based on the normal-tangential integration oriented from the shoulder-shoulder geometry. At the rough-surface scale, an improved IWAN model is proposed with a physics-based critical slip displacement distribution derived from multi-scale normal contact. This model enables the prediction of tangential contact stiffness and energy dissipation, and its accuracy is validated against experiments and reported models. The analysis further examines the influences of interface topography, material properties, and the largest length scale on the tangential response, demonstrating that the shoulder-shoulder geometry enhances tangential stiffness, while smoother surfaces, higher elastic modulus, lower hardness, and a larger largest length scale increase energy dissipation, suppress slip progression, and strengthen nonlinear stiffness behavior.