From structure to properties (and back) in truss-based architected materials

Architected materials, also known as mechanical metamaterials, derive their macroscopic properties from a carefully engineered small-scale cellular architecture consisting of trusses, plates, or shells. Being a playground for experimentalists and modelers alike, such multiscale architectures make the interface between materials and structures dissolve, while offering a tremendous design space for enhanced material functionality. Here, we focus on truss-based architectures and address the link between microscale architecture and macroscopic properties. We highlight homogenization approaches for the efficient prediction of the effective mechanical behavior of periodic and spatially graded networks. We demonstrate where classical homogenization breaks down (e.g., when investigating fracture) and quasicontinuum approaches gain importance. Finally, we also mention the inverse homogenization problem (how do we find structures that have target properties?), which is addressed by topology optimization or data-driven approaches. The goal is to provide an overview of state-of-the-art theoretical/computational approaches for the exploration of periodic structural networks and their effective properties.