The impact response of clamped sandwich beams with ordinary and hierarchical cellular cores

Abstract

The response of clamped sandwich beams subjected to impact loading is analyzed based on the works of Fleck & Deshpande (2004) [9] and Reid et al. (2010) [14]. This study differentiates itself from that of Fleck & Deshpande in that the “conservation of momentum” method instead of the “energy balance” method is adopted to model the “compaction stage” of the core upon impact loading. Finite element method (FEM) is used to validate the developed analytical model and good agreement between the analytical method and FEM results is observed. Obtained results also show that, compared to the Fleck & Deshpande model, the present model gives improved predictions of the maximum lateral deflection of the front face and the boundary of the two regions where the cellular core is totally compacted and partly compacted. The developed model is then applied to study the effects of core relative density and core thickness on the maximum impulsive momentum that the sandwich beam can sustain (impact resistance), and near-optimum design is identified for a regular hexagonal core sandwich beam with given mass. In addition, based on the present model, the performance of sandwich beams with self-similar hierarchical hexagonal honeycomb cores under impact loading is studied. It is shown that, for given relative density, the strength of the self-similar hierarchical hexagonal honeycomb decreases with the hierarchical order increasing. Therefore, both the energy absorbed per unit mass of the core during the compaction stage and the impact resistance of the sandwich beam decrease as the hierarchical order increases.