Impact dynamics of graded cellular projectiles on clamped circular plates: A coupling analysis theory and verification

Abstract

Graded cellular projectiles (GCPs) have emerged as promising blast-loading simulators due to their controllable impact loads, offering potential for rapid evaluation of anti-blast performance of structures. The coupling relations between velocity and pressure at the projectile–plate interface play a critical role in determining the impact loads. However, for prevalent plate structures, the coupling process between projectiles and plates remains unclear, which limits the density design of GCPs and their application in testing the blast resistance of plates. In this work, the dynamic response process of linear GCPs impacting clamped circular plates is studied through theoretical, numerical, and experimental methods. A projectile–plate coupling (PPC) analysis theory is established by integrating the shock wave model of projectiles, the moving plastic hinge model of plates, and the velocity consistency condition at the projectile–plate interface. A membrane factor method (MFM) is employed to simplify the governing equations of plates under large deflection without compromising the prediction accuracy. Theoretical predictions demonstrate that, under equivalent momentum and kinetic energy, cellular projectiles with negative density gradients or high matrix material strength exhibit higher kinetic energy transfer efficiency and induce greater permanent deformation of plates compared to the projectiles with uniform/positive density gradients or low matrix material strength. Dimensionless analysis indicates that the areal mass ratio of the projectile to the plate is the dominant parameter governing the projectile–plate coupling effect. Increasing the areal mass ratio enhances the coupling effect and amplifies the influence of density gradients on the impact process. Finite element simulations utilizing the 3D Voronoi technique, combined with experimental impact tests on 3D-printed GCPs, demonstrate the predictive accuracy of the theory with high reliability. The proposed theory elucidates the coupling mechanism between projectiles and deformable plates, which lays a solid foundation for the density design of GCPs applied in anti-blast evaluation.