Ordinary state-based peridynamics for geometrically nonlinear analysis of plates

This study presents a novel ordinary state-based peridynamic model for geometrically nonlinear analysis of plates. The nonlinear strain energy density and nonlinear equations of motion for a plate in peridynamics are obtained based on the principle of virtual displacements by using Total Lagrange formulation. The numerical procedure for geometrically nonlinear analysis of a plate is also provided. The accuracy of the proposed nonlinear peridynamic model is validated by considering large deformations of a plate subjected to bending and a plate subjected to transverse shear forces. To further demonstrate the capabilities of the proposed nonlinear model, damages on a plate with a single crack subjected to stretching and tearing, a plate with two parallel cracks subjected to tearing, and a plate subjected to torsional loading are predicted.