Mechanical properties of hierarchical cellular materials. Part I: Analysis

Two-dimensional (2D) hierarchical cellular materials made up of sandwich walls are predicted to have superior mechanical properties compared with solid-wall cellular materials. Equations of the stiffness, the buckling strength, the plastic collapse strength, the brittle failure strength and the fracture toughness were deduced. The enhancement of the mechanical properties of 2nd order hierarchical honeycombs is substantial (even an order of magnitude). The hierarchical honeycomb is much more damage tolerant and insensitive to wavy imperfections of the cell wall. Sandwich struts also enhance the buckling strength of the stretching-dominated 2nd order lattice grid material. Made up of sandwich struts, the hierarchical honeycomb has comparable mechanical properties with the stretching-dominated lattice grid material.