Design Optimization for Uniform Stress Distribution in Mechanical Metamaterials Using a Maximum Material Utilization Metric

Abstract Mechanical metamaterials have garnered considerable interest for their enhanced properties, such as high strength-to-weight ratios, remarkable resilience, and superior energy absorption capabilities. Despite their advantages, localized stress concentrations in additively manufactured metamaterial geometries remain a challenge. In this article, we propose a bioinspired design optimization framework to achieve metamaterials with uniformly distributed stresses. The framework uses the maximum material utilization (MMU) metric to quantify and uniformly distribute stresses in metamaterial geometries. Optimization begins with the selection of an initial conceptual design from a qualitative library of planar metamaterials previously developed by the authors. Once we have a conceptual design, we optimize it using the MMU metric for both size and shape. We assessed our optimization methods on two planar auxetic metamaterials: negative Poisson’s ratio microstructures with low shear (NPLS) and negative Poisson’s ratio microstructures with high shear (NPHS). The optimized designs achieved a uniform stress distribution across the entire topology, at both the microstructural and material levels. We highlight the efficacy of our design methodology by using numerical simulations and experiments. In addition, we demonstrate the utility of stress-optimized metamaterials by conducting numerical dynamic impact tests on optimized and unoptimized NPLS lattices. The optimized lattice absorbed more energy than its unoptimized counterpart. This study paves the way for computationally inexpensive, insightful, and stress-based design optimization of metamaterials.