Contact between spheres and general surfaces

This work presents a mathematical model to establish the weak form and tangent operator contributions due to contact between spherical surfaces and general surfaces. Normal and friction components are included, such as dissipative actions. The main concern herein is the proper consideration of the kinematics of the spherical surface and its influence on contact forces, including the appropriate description of the spherical motion by gap functions in normal and tangential directions. This leads to the possibility of dealing with complex kinematics of rolling or alternating rolling/sliding of the spherical surface, mapping its motion on another general surface. To achieve that, the model is based on rotational and translational degrees of freedom used to map the motion of contacting surfaces. One may employ such strategy for interactions between spheres and rigid or flexible bodies, modeled using finite element meshes. As examples, parameterizations of rigid and flexible surfaces are proposed and used. Practical applications are shown, with usage of beam and shell finite elements, experiencing contact interactions.