Relation between topology and mechanical properties of cellular materials

The periodic structure and mechanical behavior of typical two-dimensional and three-dimensional cellular materials were analyzed to relate the mechanical behavior to the topologies of the cellular materials. The strengths and stiffnesses of various stretching and bending dominated materials were compared along with the relative densities of these materials. The stretching dominated materials were much stronger and stiffer than the bending dominated materials, with the basic topological characteristics of stretching dominated materials determined based on the non-singularity of the stiffness matrix of the equivalent continuous media using the Deshpande topology criterion. The results show that not less than three stacks of continuous struts with different directions are needed for 2-D stretching dominated cellular materials, with not less than six stacks needed for 3-D materials.