In the past few decades polymer composites have been utilized more in structures where high strength and light weight are major concerns. It is well known that they are susceptible to damage resulting from lateral impact by foreign objects, such as dropped tools, hail and debris thrown up from the runway. Although commercial software is capable of analyzing such impact processes, it often requires extensive expertise and rigorous training for design and analysis. Analytical models are useful as they can provide a foundation for validating the numerical results from large-scale commercial software. Therefore, it is necessary to develop analytical or semi-analytical models to better understand the behaviors of composite structures under impact and their associated failure process.
In this study, several analytical models are proposed in order to analyze the impact response of composite laminated plates. Based on Meyer’s Power Law, a semi-analytical model is obtained for small mass impact response of infinite composite laminates by the method of asymptotic expansion. The original nonlinear second-order ordinary differential equation is transformed into two linear ordinary differential equations. As a result, the semi-analytical solution of the overall impact response can be applied to contact laws with varying coefficients. Then an analytical model accounting for permanent deformation based on an elasto-plastic contact law is proposed to obtain the closed-form solutions of the wave-controlled impact responses of composite laminates.The analytical model is also used to predict the threshold velocity for delamination onset by combining with an existing quasi-static delamination criterion. The predictions are compared with experimental data and explicit finite element LS-DYNA simulation. The comparisons show reasonable agreement.
Furthermore, an analytical model is developed to evaluate the combined effects of prestresses and permanent deformation based on the linearized elasto-plastic contact law and the Laplace Transform technique. It is demonstrated that prestresses do not have noticeable effects on the time history of contact force and strains, but they have significant consequences on the plate central displacement. The combined analytical and numerical investigations provide validated models for elastic and elasto-plastic impact analysis of composite structures and shed light on the design of impact-resistant composite systems.