Hybrid Carrera Unified Formulation Plate Elements for Nearly Incompressible Hyperelastic Plates

Abstract

Incompressible hyperelastic plates are widely used as fundamental structures in soft robotics and flexible devices, yet their nonlinear analysis remains challenging due to volumetric and shear locking. This work develops a family of locking-free hybrid carrera unified formulation (CUF) plate elements based on a mixed u–p variational setting. By exploiting the features of CUF, various structural theories with different displacement–pressure approximate orders are constructed to balance computational accuracy and efficiency, and the mixed interpolation of tensorial components (MITC) technique is incorporated to ensure locking-free performance for low-order in-plane discretizations in the thin-plate limit. Several benchmark and representative numerical examples, covering different through-the-thickness descriptions of the primary unknowns and mesh densities, demonstrate that the proposed hybrid CUF elements eliminate locking and accurately capture pressure variations with significantly fewer degrees of freedom than conventional three-dimensional solid models.