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The crushing behaviour and energy absorption of honeycombs made of a linear elastic-perfectly plastic material with constant and functionally graded density were studied up to large crushing strains using finite element simulation. Our numerical simulations showed three distinct crushing modes for honeycombs with a constant relative density: quasi-static, transition and dynamic. Moreover, irregular cellular structures showed to have energy absorption similar to their counterpart regular honeycombs of same relative density and mass. To study the dynamic crushing of functionally graded cellular structures, a relative density gradient in the direction of crushing was introduced in the computational models by a gradual change of the cell wall thickness. Decreasing the relative density in the direction of crushing was shown to enhance the energy absorption of honeycombs at early stages of crushing. We also developed detailed finite element models of a three-dimensional closed-cell rhombic dodecahedron structure subjected to dynamic crushing. We specifically quantified the distribution of plastic strain and energy absorption of the cellular structure and provided a comparison with the results obtained in analysis of 2-D cellular structures. The results provide new insight into the behavior of engineered and biological cellular materials, and could be used in development of a new class of energy absorbent cellular structures

Mechanical properties and energy absorption of heterogeneous and functionally graded cellular structures