Double shock mode in graded cellular rod under impact

Abstract

This paper presents an analytical study of the effect of the gradient in quasi-static plateau stress on the dynamic behavior of graded cellular rods under impact loading. Finite element (FE) simulations of graded hexagonal and circular cells’ chains under uniaxial impact loading are first carried out by using ABAQUS/EXPLICIT to observe their dynamic deformation modes. To build an analytical model, a graded cellular rod, whose quasi-static plateau stress varies along the axial direction, is supposed to be impinged by a rigid mass G with initial velocity V0. Only one shock front appears when the gradient is positive, while two shock fronts appear in the rod with negative gradient. Analytical expressions of the dynamic response parameters for the graded cellular rod are theoretically derived by using the one-dimensional shock theory originally proposed by Reid and Peng (1997). Closed form solution is found for the single shock (SS) mode, while finite difference method is employed to obtain solutions for the double shock (DS) mode. Densification velocity, at which the graded rod is just fully crushed at the end of its dynamic response, is determined; and accordingly, the maximum energy-absorbing capacity of the graded cellular rod is determined. The weakest part of the graded rod is suggested to be placed at the impact end to achieve higher energy absorption. The theoretical models are then extended to the second scenario in which the graded cellular rod together with attached mass G impinges onto a rigid target. Similar to Scenario I, the gradient significantly influences the capacity of the graded cellular rod when the ratio of mass G to the mass of the rod is relatively small. The comparison between the FE simulation results and analytical predictions shows good agreement, which validates the theoretical model.