On the design of three-dimensional mechanical metamaterials using load flow visualization

Mechanical metamaterials have generated considerable interest due to their unique attributes such as light weight, high strength, enhanced energy absorption, high impact, and fracture resistance. However, most of the design methodologies in literature are predominantly computational and provide limited user-insight (especially for three-dimensional designs). This paper presents an alternative two-phase design methodology for the conceptual synthesis of three-dimensional tunable mechanical metamaterials. In the first phase, we obtain a kinematically feasible conceptual topology using a building block-based design approach. In the second phase, the conceptual topology is refined using shape/size optimization to meet specific elastic properties and conform to manufacturing requirements. The building block-based approach uses a unique visualization formulation that represents the deformation behavior as 'load flow' in the constituent members. An immersive virtual reality tool is developed to mitigate the visual difficulty in the design of three-dimensional microstructures. Furthermore, the load flow formulation is used to propose a qualitative classification scheme for negative Poisson's ratio elastic metamaterials based on relative values of shear moduli and bi-axial elastic stiffnesses. The efficacy of the framework is illustrated through the design of microstructures with negative Poisson's ratios in spatial directions and the ability to achieve isotropic microstructures from a qualitative understanding of the conceptual designs. Such a framework can lead to the design of synthetic materials that have potential applications in multifunctional structures, shape morphing structures, and soft robotics.