Two-dimensional granular-thin plate interface for shock mitigation

摘要

The efficacy for shock mitigation of an interface between a hexagonally-packed ordered granular medium and an elastic solid - referred to as the "granular-solid interface", is studied. The granular medium is composed of three columns of granules (with the intermediate column composed of "intruders", i.e., of lighter granules compared to their neighbors) which are closely packed but without any initial precompression. The granular medium is in contact with a thin plate (the elastic solid) in plane stress so that only planar motions are considered. This yields a strongly nonlinear, hybrid, i.e., discrete-continuum 2D acoustical problem. A half-sine distributed shock is applied to the left granular column, and the aim is to mitigate as much as possible the shock energy transmitted to the thin plate. The discrete element (DE) method is adopted to model the granular responses which incorporate not only Hertzian (normal) contact interactions, but also frictional effects due to granule rotations. A computational algorithm based on interpolations and iterations is employed to accurately simulate the contact forces at the interface between the granular medium and the thin plate, modeled using finite element, and the numerical stability is checked at each successive (variable) time step to ensure unconditional convergence of the numerical results. It is shown that the granular medium can be designed to absorb a major portion of the applied impulsive energy. To this end a study of the energy partition in the granular interface is performed by changing the sizes and material properties of the column of intruders, and investigating the amount of impulsive energy that is eventually transmitted to the thin plate. When lighter polytetrafluoroethylene (PTFE) intruders are combined with heavier steel granules, it is shown that the impulsive energy is mostly localized in the first column of the granular medium and negligible energy reaches the thin plate. The reason for this effective shock mitigation is the disparity in the time scales between the responses of the steel granules and the PTFE intruders, which, in turn, leads to an effective impedance mismatch that confines the impulsive energy, preventing it from propagating through the interface. Moreover, being nonlinear, the shock mitigation effectiveness of the granular-solid interface is tunable with energy, with enhanced effectiveness for weaker shocks. The methods and results reported in this work pave the way for predictively designing hybrid interfaces for drastically enhanced shock mitigation, with broad engineering applications.