Transient nonlinear responses of a sandwich plate with micro-cellular auxetic core based on modified strain gradient theory under impact loads

This study investigates the nonlinear dynamic response of an auxetic sandwich structure under impact load. The core is made of a micro-cellular auxetic structure. The main point of interest is studying the micro-cellular core properties’ effects on the structure’s nonlinear dynamic response. First, the mechanical properties of the micro-cellular auxetic core are introduced based on modified strain gradient theory (MSGT), followed by experimental and numerical validation. Then, Hamilton’s principle is applied to derive the sandwich structure’s nonlinear governing partial differential equations. Lastly, Galerkin’s method paved the way to achieving the final solution. So as to perform frequency-response analysis, the four-dimensional averaged equations are obtained using the perturbation method. In order to carry out experimental validation, a nanosecond laser system is used for micro-cellular auxetic sample fabrication, and the tensile tests are carried out per ISO 6892 standard. The comparison between the experimental and the theoretical results indicates an excellent agreement among the results. It can be concluded that MSGT plays a significant role in the mechanical properties and the nonlinear dynamic response of the micro-cellular auxetic structures. The present study is applicable in the field of protective panels, sensors, and energy harvesters.