Elastic in–plane properties of cellular materials: Discrete approach

Elastic properties of two–dimensional cellular lattice materials are studied using a discrete model. The model is based on a representation of the lattice as a set of interacting nodes. A potential of interaction between the nodes is calibrated such that to simulate elastic linking. The analytical homogenization based on Cauchy–Born rule allowed determining the elastic properties of the effective continuum corresponding to the specific lattice. On the other hand, the same properties were found from the numerical simulations based on particle dynamics. It is shown that both ways lead to the same values of elastic constants. This approach allows using particle–based numerical simulations to design various applications of lattice materials.