Efficient biscale design of semiregular porous structures with desired deformation behavior

Porous materials/structures are observed in many natural objects, exhibit exceptional properties, and have wide industrial applications. The rapid advance in additive manufacturing has also facilitated the process to fabricate such complex porous structures with fine accuracy control. However, the design of optimal porous structures with the desired deformation behavior is still very challenging because of its high computational complexity. In this study, a novel and efficient approach was developed to solve this problem by designing a semiregular porous structure with a hole within each mesh element of a given quad/hex-mesh layout of the design domain. The proposed approach ultimately analytically expresses the displacement of the design model as a function of the design variables, and consequently solves the optimization problem of porous structure design efficiently. The novelty was mainly achieved by representing a compact design space, building approximate analytical structure-property relation, and estimating the displacement variations of material property. The good property was achieved using the advanced numerical techniques: model reduction, homogenization theory, metamodeling, and the combined approximations. Various numerical examples were also tested to demonstrate the performance of the approach.