Explicit Topology Optimization of Conforming Voronoi Foams

TL;DR

This paper introduces a novel topology optimization method for conforming Voronoi foams using seed positions and radii as design variables, enabling explicit control, improved accuracy, and better performance in low volume fractions.

Contribution

The paper presents a new Voronoi-based topology optimization approach that allows free topology changes, explicit geometric control, and enhanced simulation accuracy for porous foams.

Findings

Voronoi foam outperforms classical methods in mechanical properties.

The approach effectively handles low volume fraction targets.

The method provides explicit control over foam granularity.

Abstract

Topology optimization is able to maximally leverage the high DOFs and mechanical potentiality of porous foams but faces three fundamental challenges: conforming to free-form outer shapes, maintaining geometric connectivity between adjacent cells, and achieving high simulation accuracy. To resolve the issues, borrowing the concept from Voronoi tessellation, we propose to use the site (or seed) positions and radii of the beams as the DOFs for open-cell foam design. Such DOFs cover extensive design space and have clear geometrical meaning, which makes it easy to provide explicit controls (e.g. granularity). During the gradient-based optimization, the foam topology can change freely, and some seeds may even be pushed out of the shape, which greatly alleviates the challenges of prescribing a fixed underlying grid. The mechanical property of our foam is computed from its highly heterogeneous density field counterpart discretized on a background mesh, with a much improved accuracy via a new material-aware numerical coarsening method. We also explore the differentiability of the open-cell Voronoi foams w.r.t. its seed locations, and propose a local finite difference method to estimate the derivatives efficiently. We do not only show the improved foam performance of our Voronoi foam in comparison with classical topology optimization approaches, but also demonstrate its advantages in various settings, especially when the target volume fraction is extremely low.