A Mechanical Metamaterial with Extreme Stiffness and Strength

J. Berger
Nama Development LLC,
United States

Keywords: mechanical metamaterials, cellular materials, high stiffness materials, high strength materials


The significant performance of modern aerospace vehicles, deep-sea submersibles, high fuel efficiency automobiles, sports equipment, space telescopes, and a wide variety of other lightweighting applications, require that shape control be maintained under significant stress while mass is minimized. Recent advances in additive manufacturing and automated assembly techniques now allow complex material geometries to be fabricated on scales from a few nanometers to meters, with relatively low (and declining) cost. These new routes to fabrication are giving rise to metamaterials with novel properties and the potential for extremal performance, limited primarily by available designs. We have used finite element modeling, validated by micromechanical analysis methods, to discover an internal metamaterial geometry that, for the first time, achieves the theoretical bounds for isotropic elastic stiffness. This geometry can store a maximum amount of strain energy independent of the loading direction. The relatively simple design that has been discovered can be manufactured through origami-like sheet folding and bonding methods, providing access to many constituent material systems. In identifying this material, we examine the structural efficiency, and the manner in which strain energy distributes under macroscopic loads, in stiff cellular materials. Some of the lightest, stiffest and strongest materials available are honeycombs with, for example, square, triangular or hexagonal cross-sections, composed of high performance alloys, composites and ceramics. These honeycombs are, however, anisotropic by nature, with relatively poor in plane properties, limiting their use when multiaxial loads must be tolerated. In contrast, we have identified a material geometry with stiffness comparable to the transverse (maximum) properties of honeycombs, but whose properties are isotropic. This geometry stores strain energy more efficiently than any other known geometry, facilitating extremely high strengths as well. This unique design is composed of two highly anisotropic subgeometries, whose relative contribution can be systematically chosen to produce functionally graded and highly optimized designs and even smart structures. In contrast to lattice materials, this geometry shows little influence from edge effects, avoiding a size constraint and limitation commonly associated with cellular materials, facilitating designs of arbitrary periodicity. Compression experiments on unit-cell test specimens agree very well with finite element predictions for stiffness and strength. In this work, we explore the opportunity to fill unoccupied regions of property space with novel material systems, and explore some of the available routes to fabrication for this particular material geometry.