A novel technique for low-velocity impact of shallow arches

In the current study, an analytical model to analyze the low-velocity impact (LVI) response of metamaterial shallow arches subjected to rigid body impact is presented. The presented nonlinear model considers transverse deformation of the cross-section and geometric nonlinearity based on the higher-order shear theory and von Kármán nonlinearity. The research delves into three key aspects. The first is concerned with the establishment of a contact model to capture the contact characteristics between the impactor and the arch. The second aspect deals with the design of the member with Negative Poisson’s Ratio (NPR). The third aspect is concerned with the asymptotic solution of dynamic equations by using a two-perturbation technique. The proposed model is used to analyze the effects of auxetic, initial deformation, and foundation on the impact response and post-impact vibration of the arch. The results show that the contact area between the sphere impactor and the arch is elliptical. It is also noted that the contact force and indentation are highly dependent on the laminated configuration and auxetic properties. The study reveals that the presented model is a valid technique to evaluate the impact characteristics of metamaterial arches along with optimal design impact resistance of arches.