Dehomogenization for Multiscale Topology Optimization via Triangular Lattice Structures

Abstract Dehomogenization is a post-processing step for generating physically realizable structures from homogenized designs. Typically employed in conjunction with homogenization-based topology optimization (HBTO), dehomogenization is used to derive a binary representation of the initially homogenized (gray) design. Currently, most dehomogenization approaches rely on an implicit representation of microscale topologies using periodic functions, which limits their applicability to specific parameterized microstructures, such as rectangular voids. This work introduces a novel dehomogenization approach that allows the projection of a homogenized mechanical property field onto a discrete lattice structure of arbitrary shape. This results in a well-connected, functionally graded lattice structure featuring control over the length scale, orientation, and complexity of the final design. The proposed approach incorporates an optimization algorithm to find the lattice thickness distribution that minimizes the difference between a local target homogenized property and a corresponding lattice homogenized stiffness tensor. The definition of a signed distance function between connected nodes yields tapered beam designs with smoothly varying thicknesses. The effectiveness of the approach is demonstrated on a half MBB beam, a clamped beam, and an L-bracket. The compatibility of the resulting non-periodic structures indicates that the performance of the dehomogenized design is maintained or improved compared to the homogenized design.