Evolutionary topology optimization for mechanical metamaterials with auxetic property

Mechanical metamaterials with auxetic property have attracted a lot of attention in both the computational intelligence and engineering applications. However, the works relate to the efficient Bi-directional evolutionary structural optimization (BESO) method is infrequent due to the discrete nature of design variables. This paper obtains the orthotropic materials with auxetic property by imposing two numerical strategies on the sensitivity calculation and variable updating, which are used to stabilize the evolutionary process and easy to be implemented. In addition, this paper develops a robust objective function while taking into account of the mechanical properties in all directions of the material microstructure, and the explicit sensitivity information of the objective function with respect to design variables is derived, then the powerful OC-type algorithm is adopted to solve this problem. The macroscopic equivalent elastic behavior is evaluated by the comprehensible energy-based homogenization method (EBHM). Several numerical examples are tested to demonstrate the feasibility and effectiveness of the proposed algorithm for the design of orthotropic materials with auxetic properties. Finally, two experiments are arranged to further illustrate the effect of negative Poisson's ratio of the designed material microstructures.