  Materials that are lightweight yet exhibit superior mechanical properties are
of compelling importance for several technological applications that range from
aircrafts to household appliances. Lightweight materials allow energy saving
and reduce the amount of resources required for manufacturing. Researchers have
expended significant efforts in the quest for such materials, which require new
concepts in both tailoring material microstructure as well as structural
design. Architectured materials, which take advantage of new engineering
paradigms, have recently emerged as an exciting avenue to create bespoke
combinations of desired macroscopic material responses. In some instances,
rather unique structures have emerged from advanced geometrical concepts (e.g.
gyroids, menger cubes, or origami/kirigami-based structures), while in others
innovation has emerged from mimicking nature in bio-inspired materials (e.g.
honeycomb structures, nacre, fish scales etc.). Beyond design, additive
manufacturing has enabled the facile fabrication of complex geometrical and
bio-inspired architectures, using computer aided design models. The combination
of simulations and experiments on these structures has led to an enhancement of
mechanical properties, including strength, stiffness and toughness. In this
review, we provide a perspective on topologically engineered architectured
materials that exhibit optimal mechanical behaviour and can be readily printed
using additive manufacturing.
