4 Lattices and Architected Materials

Lattices, cellular materials, periodic structures, and architected materials — these are as diverse as the assortment of names used to describe them. Fundamentally, they are hybrids of solid material and empty space (or gas) with the precise arrangement dictating the effective mechanical properties. The amount of material is, of course, important as well and is referred to as relative density: the mass of the lattice divided by the mass of a solid block of its parent material.

Some typical suspects in the cellular world include honeycombs, foams, lattices, and shell-like continuous structures such as gyroids, each having their own pros and cons. These can be employed in a variety of ways: uniformly as shown in Figure 5, as an infill of a shelled part, conformally over a surface, or spatially varying within a complex domain.

  • Honeycombs are hard to beat in stiffness-to-weight ratio in their extruded direction but are much softer in the other two orthogonal directions (by around an order of magnitude).

  • Octet lattices are stiff in all three principal directions but more difficult to manufacture.

  • Stochastic foams are much more compliant but the easiest to finely tailor to a design's functional requirements through cell size and relative density.

  • Auxetic honeycombs can be designed to exhibit special properties like a negative Poisson's ratio (contracts inwards when compressed, instead of barreling outwards).

  • The gyroid and broader family of triply periodic structures inherently have two sides or fluid domains to them, making them natural candidates for heat-exchanger applications. They can be easily tailored or biased in different directions to alter stiffness or flow properties as needed.

Cellular materials are perhaps most applicable to engineering in the form of sandwich structures. These are prevalent throughout all levels of the lightweighting value spectrum, from cardboard packaging to commercial aircraft to interplanetary spacecraft. The effect is all the same: separate two thin sheets of material (the bread) by a lightweight core (the filling, available in the flavors shown above), and you can attain tremendous strength and stiffness increases for a minor increase in mass. Turn this around by keeping strength and stiffness constant, and you have significant lightweighting potential.

5 Topology Optimization

Figure 6. A titanium spacecraft bracket, lightweighted with topology optimization and built with electron beam melting (EBM). (Image Credit: nTopology)

Last stop: topology optimization (Figure 6). Some refer to this as generative design but we'll stick to the engineering term here. Several methods and algorithms exist but the general idea is to apply loads and restraints to a design region and then whittle away material from this region until some constraints and objectives are met. At the bare-bones level, this is usually minimizing compliance (or maximizing stiffness) subject to a volume target. Many cases require additional constraints like maximum stress or displacement, or some restriction on manufacturing technique. The result is usually something exotic and organic-looking, which perhaps adds to its allure.

While seemingly hands-off, this approach is far from it. Some steps of it deserve automation, like reconstructing native geometry from the resultant density field or mesh. But users must take extra care in setting up their problems appropriately and understand the assumptions behind the algorithms that they wield. One common oversight is that many simple codes neglect buckling. Consider the very long, thin, slender ligaments seen in many generative design examples and how these would behave when they run over a bump on the road — likely suboptimally.

What if those loads are applied off-angle? Uncertainty quantification and design for robustness techniques are being developed for this now. This is less specific to topology optimization methods but relevant to lightweight design in general: as you get closer and closer to the optimum, the result is only as appropriate as the design assumptions.


Hopefully, these examples have you thinking about where you can cut weight from your parts through one or several of the approaches described above: care in material selection, consolidating parts by their functions to eliminate fasteners and redundancy, conformal ribbing for stiffening, multifunctional design with lattices and architected materials, or topology optimization to make it lightweight and look great simultaneously. The value of a pound here and there can add up significantly — the thousands of dollars per pound for spacecraft applications makes the combination of all of these methods often justifiable.

Lightweighting is clearly an important strategy across multiple industries. Whatever the goals of a particular design engineering team or OEM, the compounding effects that the methodologies described here can have on one another are motivating engineers to take their light-weighting efforts to new creative heights.

This article was written by Jonathan Harris, Ph.D., Lead Application Engineer at nTopology, New York, NY. For more information, visit here .