Prestress-mediated damage strength of lattice metamaterials and its optimization

Abstract

Lattice metamaterials have been attracting wide research interests due to their excellent mechanical properties. Most of meta-properties have been implemented by proper geometric designs of microstructures. In this study, we examine another way to obtain outstanding properties, which has been relatively less explored. That is, we aim to adjust the loading bearing capability of lattices by periodically introducing prestress into particular lattice segments. Based on existing related works, we focus on the following two problems deserving further investigations. First, results have been provided based on a single cell with/without taking into account the interactions between each two of neighboring individual cells. Second, it is interesting to search for the optimal distribution of prestress in lattices subjected to a specific load. For the former, we propose a set of constraint equations for implementing periodic boundary conditions (PBC) on a periodic unit cell and confirm its correctness. The significance of PBC related to rotational degrees of freedom is emphasized. We then use the proposed method to calculate the initial damage surface of four kinds of prestressed lattice unit cells under PBC. For the latter, we build a new optimization algorithm with the help of the so-called Symbiotic-Organisms-Search technique (SOS), to calculate the optimal prestress setting corresponding to the requested properties. As an example, the optimal prestress setting is found to almost double the critical load to failure of the lattice in a special direction. This work may be helpful to design lattice metamaterials with programmable strengths.