Differentiable Voronoi diagram towards a new design method for the additive manufacturing of 3D disordered cellular structure

The rise of additive manufacturing (AM), or 3D printing, has unlocked the potential to fabricate complex cellular architectures. However, the design of these intricate, tessellating structures poses a major obstacle, which constrains exploration to a limited repertoire of simple truss-based or periodic geometries. In this paper, a differentiable Voronoi diagram has been presented to design 3D open-cell cellular structures, with key improvements in randomness regulation and controllable design efficiency. Specifically, by manipulating the density field, the proposed method achieves high spatial randomness of cellular structures while enabling precise control over cell shape, overcoming the trade-off between randomness and controllability in traditional methods. Furthermore, a distorted strut has been achieved in 3D cellular by offering a novel pseudo points concept for the Voronoi diagram. Experimentally, the Voronoi C-clip has a 16.94% higher maximum load than the original structure, and a bridge sample demonstrates over 300% higher specific energy absorption (SEA) than the uniform Voronoi cells. Eventually, the proposed method provides an implicit modeling methodology for the design of disordered cellular, with promising applications in energy absorption and lightweight scenarios.