The global-local mechanical behaviors of multilayered structure and applications to superconducting coils

Differently from the continuum medium, multilayered structures are discontinuous systems, which consist of a series of plates or shells stacked on each other. The global kinematic feature of the multilayered structure is determined by the local kinematics of its monolayers and the interfacial movement between them. At the interface, contact pressure works in the normal direction, and friction works in the tangential direction, which remarkably impacts the mechanical responses of multilayered structures. The multilayered structures have the following kinematic characteristics: interfacial slip is kinematically permissible and the contact gap can be negligible during deformation. Based on these features, the midplane displacements of each shell layer can be constructed as a continuous field. Layer-to-layer interactions are treated as internal forces, and the Coulomb friction law is incorporated as a material constitutive relationship. In kinematics, interfacial slip is taken into account in the global strain–displacement relationship, which leads to a correction term in the governing equation according to the dual relationship. In dynamics, the principle of minimum potential energy is utilized to derive the governing equation, with friction being accounted for through the mechanism of energy dissipation. Then, a continuum theory for multilayered structures is proposed in this paper and validated by comparisons with the discrete contact model and experiments. The proposed model is further extended to the mechanical study of high-temperature superconducting (HTS) magnets. The complexity of HTS magnets stems from the large number of contacts and the corresponding contact nonlinearity, which gives rise to computational inefficiencies and convergence problems. The proposed model could address these challenges and facilitate the mechanical analysis of HTS magnets.