Over the past decade, there has been an increase in the intentional design of meso-structured materials that are optimized to target desired material properties. This paper reviews and critically compares common numerical methodologies and optimization techniques used to design these meso-structures by analyzing the methods themselves and published applications and results. Most of the reviewed research targets mechanical material properties, including effective stiffness and crushing energy absorption. The numerical methodologies reviewed include topology and size/shape optimization methods such as homogenization, Solid Isotropic Material with Penalization, and level sets. The optimization techniques reviewed include genetic algorithms (GAs), particle swarm optimization (PSO), gradient based, and exhaustive search methods. The research reviewed shows notable patterns. The literature reveals a push to apply topology optimization in an ever-growing number of 3-dimensional applications. Additionally, researchers are beginning to apply topology optimization and size/shape optimization to multiphysics problems. The research also shows notable gaps. Although PSOs are comparable evolutionary algorithms to GAs, the use of GAs dominates over PSOs. These patterns and gaps, along with others, are discussed in terms of possible future research in the design of meso-structured materials.

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