Simple single-scale microstructures based on optimal rank-3 laminates

TL;DR

This paper introduces a method for designing simple, manufacturable single-scale microstructures based on optimal rank-3 laminates, achieving near-optimal elastic performance across various loading conditions.

Contribution

It proposes a novel approach to approximate rank-3 laminates on a single scale and demonstrates their effectiveness as starting guesses for inverse homogenization, improving convergence to near-optimal designs.

Findings

Microstructures perform within 5-8% of theoretical energy bounds.

Using rank-3 laminate approximations improves convergence in inverse homogenization.

Microstructures are simple and manufacturable, suitable for multiple load cases.

Abstract

With the goal of identifying optimal elastic single-scale microstructures for multiple loading situations, the paper shows that qualified starting guesses, based on knowledge of optimal rank-3 laminates, significantly improves chances of convergence to near optimal designs. Rank-3 laminates, optimal for a given set of anisotropic loading conditions, are approximated on a single scale using a simple mapping approach. We demonstrate that these mapped microstructures perform relatively close to theoretical energy bounds. Microstructures with performance even closer to the bounds can be obtained by using the approximated rank-3 structures in a further step as starting guesses for inverse homogenization problems. Due to the non-convex nature of inverse homogenization problems, the starting guesses based on rank-3 laminates outperform classical starting guesses with homogeneous or random material distributions. Furthermore, the obtained single-scale microstructures are relatively simple, which enhances manufacturability. Results, obtained for a wide range of loading cases, indicate that microstructures with performance within 5-8% of the theoretical optima can be guarantied, as long as feature sizes are not limited by minimium size constraints.