Crashworthiness design of graded cellular materials: An asymptotic solution considering loading rate sensitivity. (September 2020) - Chang, Baixue; Zheng, Zhijun; Zhang, Yongliang; Zhao, Kai; He, Siyuan; Yu, Jilin
Highlights: Using well-designed graded cellular materials can improve the crashworthiness of structures. A design strategy based on a shock model considering the loading rate sensitivity is developed. An asymptotic solution of the relative density distribution for the design strategy is derived. The second-order approximate solution of the asymptotic solution is suitable for application. The validity of crashworthiness design is verified with the cell-based finite element method. Abstract: Introducing graded cellular materials into energy absorber may improve the crashworthiness of protective structures. In order to meet the crashworthiness requirement that the impact force does not exceed the value that the protected object can afford, a backward strategy guiding the design of relative density distribution of cellular material is improved by considering the loading rate sensitivity in a shock model. Asymptotic solutions of the relative density distribution are obtained for the cases with or without considering the loading rate sensitivity, when a constant impact force is required. It is found that the second-order approximate solutions of the relative density distribution are good enough to approximate the exact solutions calculated by the fourth-order Runge-Kutta scheme. The validity of the design method is further verified by the cell-based finite element method, and the results indicate that the deformation localization at the proximal end is caused by both the density gradient and inertial effect. It is shown that the average impact force from the design without considering loading rate sensitivity exceeds the affordable value of the protected object, but that considering loading rate sensitivity can well meet the crashworthiness requirement. Therefore, the asymptotic solution of the relative density distribution from the design strategy considering loading rate sensitivity is suitable and convenient to guide the crashworthiness design in practical engineering.