Analytical and numerical of contact edges under mixed-mode (Peel and Shear)

In most analyses of edge stresses, in-plane shear is prioritized, yet peel stresses at bonded edges frequently determine failure in structural adhesive joints. This work explicitly incorporates out-of-plane (Mode I) peel in mixed-mode loading of adhesive contacts into an Adhesive contact model based on asymptotic wedge-corner analysis. By connecting Mode I and Mode II contributions through the wedge eigenvalues and geometry, we provide an asymptotic description for the interfacial peel traction in a two-dimensional wedge and relate the resulting intensity to the contact area and applied loads. Finite-element simulations (COMSOL Multiphysics) of single-lap-like joints subjected to combined peel and shear with a bending moment are used to evaluate the analytical predictions. The local edge geometry is systematically varied sharp corner (2\alpha = 270), intermediate (2\alpha = 202.5), smoothed (2\alpha = 180), and a manufacturable U-notch. Reducing the internal angle or adding a U-notch suppresses edge singularities and lowers peak peel, shear, and von Mises stresses in all cases, according to both analysis and simulation. The 180 transition produces the largest reductions, and the U-notch provides a useful compromise between stress reduction and manufacturability. The mixed-mode Adhesive contact model provides a concise, geometry-based view of adhesive-joint edge shaping. We discuss implications for durability and fatigue and suggest directions for experimental confirmation.