Well-chosen cellular microstructures can be used to efficiently design multi-scale structures that offer strong mechanical performance and are easy to fabricate via additive manufacturing. In this paper, we consider a special class of cellular single-scale microstructures originally discovered by Vigdergauz (1994, 1999). We present a conceptually simple method for calculating and interpolating those microstructures in the three regular tessellations (square, triangular, and hexagonal). We use that method to investigate the potential of Vigdergauz microstructures for applications in multi-scale optimization and additive manufacturing. In particular, we show that Vigdergauz microstructures allow one to design functionally graded material with competitive performance in terms of stiffness, local stress concentration, buckling, and geometric compatibility between adjacent cells. The application of such microstructures to multi-scale structural design is detailed and illustrated on some examples.
