Regular, irregular, functionally graded, and hierarchical cellular structures

From the structural point of view, cellular structures have properties that are much superior compared to the properties of the material that they are made of, including high strength to weight ratio and energy absorption. One of the key applications of the cellular structures is the design of structural components with superior energy absorption and impact resistance. Nowadays, the application of cellular structures has been extended in various fields of engineering. In this perspective, it is vital to develop a detailed understanding of the relationship between mechanical properties and microstructure of cellular materials.;We investigate the in-plane dynamic crushing of two-dimensional cellular structures using finite element methods. Both regular and randomly-distributed cellular structures, as well as functionally graded cellular structures are considered and their response is modeled up to large crushing strains. We have also studied the energy absorption of hierarchical honeycombs where every three-edge vertex of a regular hexagonal lattice is replaced with a smaller hexagon.;Our numerical simulations of in-plane dynamic crushing of cellular structures show three distinct deformation shapes of regular hexagonal cellular materials: quasi-static, moderate-rate dynamic mode and high-rate dynamic mode. Special attention was made towards quantifying the energy absorbent characteristics of the cellular structure as a function of cellular structure relative density and impact velocity, as well as the density gradient for functionally graded structures, where 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. Our results also showed that hierarchical honeycombs of first and second order can be up to 2.0 and 3.5 times stiffer than regular honeycomb at the same mass (i.e., same overall average density) and they have advanced energy absorption capacity compared to regular honeycomb with the same mass. 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.