DESIGN OPTIMIZATION FRAMEWORK FOR UNIFORM STRESS DISTRIBUTION OF MECHANICAL METAMATERIALS

Mechanical metamaterials have gained considerable interest because of their enhanced mechanical properties, such as being lightweight, having high energy absorption, and having high resistance to fracture and indentation. The macroscopic elastic properties of mechanical materials are governed by their microstructural geometry. Despite their advantages, attaining microstructures with evenly distributed stresses for improved load-bearing ability remains a challenge. Furthermore, employing stress constraints in tandem with numerical homogenization in structural optimization schemes has been time-intensive and complex. This paper presents a design optimization framework for metamaterial designs with uniformly distributed stresses using a bioinspired maximum material utilization (MMU) metric. The material microstructures can be size optimized by maximizing the MMU metric to attain designs with uniform stress distributions. The proposed design optimization involves two sequential steps. The first step involves the conceptual design, using a load flow technique and insights from the strain energy-based homogenization method to design material microstructures. Once we obtain a conceptual solution, we perform size optimization on the material microstructures to maximize the MMU metric. We test our optimization method on two planar auxetic metamaterials - (a) negative Poisson's ratio microstructures with low shear (NPLS) and (b) negative Poisson's ratio microstructures with high shear (NPHS). The optimized designs attained uniformly distributed stress levels throughout their topology at the microstructural and material levels. We showcase the efficacy of the proposed design methodology with numerical simulations and experiments. This study paves the way for computationally inexpensive, insightful, stress-based design optimization of metamaterials.