梯度多胞材料耐撞性设计的简化模型和渐近解

A simplified model and its asymptotic solution for the crashworthiness design of graded cellular material

多胞材料具有很强的吸能特性,并被广泛应用于结构耐撞性设计领域,其力学响应与密度分布息息相关.因此可以通过对多胞材料密度分布的设计达到对材料的宏观力学响应的有效控制,以满足实际应用中的耐撞性要求.基于非线性塑性冲击波模型可以实现对密度梯度的反向设计,但其求解较为困难.本文利用级数法获得了耐撞性反向设计理论的渐近解,针对常冲击力的耐撞性要求给出了一个具有足够精度的近似解.利用二维随机Voronoi技术构建了细观有限元模型,并运用有限元软件ABAQUS/Explicit进行了数值验证,结果表明密度分布的反向设计理论的渐近解对于指导梯度多胞材料的耐撞性设计是有效的,且二阶渐近解已提供足够的设计精度.基于冲击波模型的反向设计方法为主动设计梯度多胞材料提供了重要依据.

Cellular materials have strong energy absorption capacity and have been extensively used in crashworthiness design of structures. The mechanical responses of cellular materials are related to their relative density. Introducing a density gradient to cellular materials may further improve their crashworthiness. A backward design method based on a nonlinear plastic shock model was developed to meet the crashworthiness requirement of protecting a mass when impinging a graded cellular rod. For the case of constant impact force, an asymptotic solution to the density distribution of graded cellular rod is obtained in this paper. The density distributions between the explicit asymptotic solution and the exact solution numerically obtained with a fourth-order Runge-Kutta scheme have been compared. The first-order approximate solution is a linear approximation, and the second-order approximate prediction is basically consistent with the numerical solution. For the impact force history, the first-order approximate prediction has a large deviation, and the second-order approximate prediction has a slight deviation. For practical application the second-order approximate solution seems to be accurate enough. Cell-based finite element models are employed to verify the asymptotic solution. The finite element models have been constructed and computed via ABAQUS/Explicit code. Samples of graded cellular rods designed from the asymptotic solution are tested numerically. The predictions using the second-order approximate solution of density distribution is very close to the finite element results. The design using the first-order approximate solution is not accurate enough, but in fact it is not so bad. Compared the uniform density distribution, the second-order approximate prediction is good for the crashworthiness optimization. The design of density distribution for a specific impact scenario is found to be inappropriate for much high velocity impact. In summary, a case study shows that the second-order approximate solution is very close to the exact solution and it is good enough for the design. The backward design method and the asymptotic solution of density distribution are helpful to guide the crashworthiness design of graded cellular materials.