Stress‐Aligned Hexahedral Lattice Structures

Abstract Maintaining the maximum stiffness of components with as little material as possible is an overarching objective in computational design and engineering. It is well‐established that in stiffness‐optimal designs, material is aligned with orthogonal principal stress directions. In the limit of material volume, this alignment forms micro‐structures resembling quads or hexahedra. Achieving a globally consistent layout of such orthogonal micro‐structures presents a significant challenge, particularly in three‐dimensional settings. In this paper, we propose a novel geometric algorithm for compiling stress‐aligned hexahedral lattice structures. Our method involves deforming an input mesh under load to align the resulting stress field along an orthogonal basis. The deformed object is filled with a hexahedral grid, and the deformation is reverted to recover the original shape. The resulting stress‐aligned mesh is used as basis for a final hollowing procedure, generating a volume‐reduced stiff infill composed of hexahedral micro‐structures. We perform quantitative comparisons with structural optimization and hexahedral meshing approaches and demonstrate the superior mechanical performance of our designs with finite element simulation experiments.