Topology Optimization of Three-Dimensional Woven Materials Using a Ground Structure Design Variable Representation

Abstract

Three-dimensional (3D) weaving has recently arisen as viable means for manufacturing metallic, architected microlattices. Herein, we describe a topology optimization approach for designing the architecture of such 3D woven lattices. A ground structure design variable representation is combined with linear manufacturing constraints and a projection mapping to realize lattices that satisfy the rather restrictive topological constraints associated with 3D weaving. The approach is demonstrated in the context of inverse homogenization to design lattices with maximized fluid permeability. Stokes flow equations with no-slip conditions governing unit cell flow fields are interpolated using the Darcy–Stokes finite element model, leveraging existing work in the topology optimization of fluids. The combined algorithm is demonstrated to design manufacturable lattices with maximized permeability whose properties have been experimentally measured in other published work.