In-plane crushing of a hierarchical honeycomb

Properly introduced hierarchy in cellular materials has the potential to further improve their energy absorption capacity. The in-plane uniaxial collapse response of a second order hierarchical honeycomb (i.e., a regular hexagonal honeycomb with its cell walls consisting of an equilateral triangular honeycomb) is investigated. Its failure modes for quasi-static crushing and dynamic impact in two directions are systematically explored by finite element simulations. A two-scale method is proposed and analytical expressions for the quasi-static collapse stresses of the hierarchical honeycomb in the two directions are obtained. In conjunction with the conservation of momentum, the analytical quasi-static collapse stress models are extended to dynamic crushing. The obtained theoretical collapse stresses are validated by finite element simulations for a wide range of impact velocity and relative density. Both numerical and analytical results show that the hierarchical honeycomb has an improved collapse stress over traditional hexagonal and triangular honeycombs. The improvement is found to be more pronounced for low velocity impact than for high velocity impact.