Distributed Design of Two-Scale Structures With Unit Cells

The use of unit cell structures in mechanical design has seen a steady increase due to their abilities to achieve a wide range of material properties and accommodate multi-functional requirements with a single base material. We propose a novel material property envelope (MPE) that encapsulates the attainable effective material properties of a given family of unit cell structures. The MPE interfaces the coarse and fine scales by constraining the combinations of the competing material properties (e.g., volume fraction, Young’s modulus, and Poisson’s ratio of isotropic materials) during the design of coarse scale material properties. In this paper, a sampling and reconstruction approach is proposed to represent the MPE of a given family of unit cell structures with the method of moving least squares. The proposed approach enables the analytical derivatives of the MPE, which allows the problem to be solved more accurately and efficiently during the design optimization of the coarse scale effective material property field. The effectiveness of the proposed approach is demonstrated through a two-scale structure design with octet trusses that have cubically symmetric effective stiffness tensors.