A scaled boundary-finite cell method for simulating planar frictionless contact dynamics of large deformation bodies with complex interfaces

Contact problems involving flexible bodies with large deformation and complex interfaces are particularly challenging because they require robust mesh handling and reliable treatment of complex contact interactions. To efficiently overcome the difficulties brought by these challenges, a scaled boundary-finite cell method (SB-FCM) is proposed. A quadtree-based decomposition algorithm is employed to automatically generate Cartesian meshes. The interior domain is described by scaled boundary polygon elements (SBPEs), while the boundary domain in contact with complex shapes is modeled by the finite cell method (FCM). The SBPEs allow for local mesh refinement by increasing the number of internal sections without generating hanging nodes. Lagrangian segments are used to reconstruct contact interfaces within boundary cells, enabling precise contact detection and consistent enforcement of contact conditions. Using the proposed method, the classic complex boundary-conforming mesh process can be avoided, which significantly reduces the system’s degrees of freedom. Finally, several static and dynamic examples are presented to validate the accuracy and efficiency of the proposed method.