A variationally consistent reduced-order peridynamic formulation for shell structures

A variationally consistent reduced-order peridynamic formulation is developed for medium-thick shell structures undergoing finite deformation, large rotation, elastoplastic response, and brittle fracture. The formulation is designed as a general mid-surface framework that retains the efficiency of shell models while preserving the three-dimensional kinematic and energetic information required for standard stress–strain constitutive updates. A director-based shell kinematics is combined with a tangent-space surface correspondence operator to reconstruct the three-dimensional deformation and velocity gradients at through-thickness integration points. The director is updated by an exponential map to accommodate large rotations. Elastic and co-rotational J 2 plastic constitutive updates are then performed under a plane-stress constraint. In the framework of peridynamic theory, the nonlocal translational and rotational balance equations are derived by reducing the three-dimensional internal virtual power through the shell thickness, leading to energy-conjugate membrane-force, bending-moment, and transverse-director states. Within the same work-conjugate structure, an energy-consistent stabilization is introduced to suppress correspondence zero energy modes, and a bond-level viscous dissipation term is incorporated for explicit dynamic calculations. Meanwhile, a bond-energy brittle-fracture criterion is derived for through-thickness brittle cracking. The proposed formulation is implemented within a GPU-parallel computational framework. Numerical examples involving elastic response, thickness dependence, curved-shell deformation, large rotations, elastoplastic loading, and brittle fracture demonstrate the accuracy and extensibility of the proposed formulation.