On force–displacement relations at contact between elastic–plastic adhesive bodies

The loading–unloading of dissimilar adhesive elastic–plastic bodies is studied both analytically and numerically, including elastic–ideal plastic and deformation hardening behavior. The contacting bodies are assumed to be spherical in the region of contact and consequently the presented model is partly based on results pertinent to Brinell indentation. The problem of adhesive unloading is solved in two steps; first the unloading in the absence of adhesion is studied and then an adhesive pressure term is added. The analytical model is derived using fracture mechanics arguments and is based on one parameter, the fracture energy. The model is finally verified with finite element simulations by introducing a cohesive behavior between the modeled spheres. The analytical model shows very good agreement with the FE-simulations both during loading and unloading and also concerning the case of force and displacement at separation.