When engineers design things like buildings, airplanes, bridges and electronic devices, they perform calculations to ensure these structures can withstand mechanical forces without breaking or deforming too much.
The classical elasticity theory works well for predicting the behavior of most ordinary materials, including steel, aluminum and concrete. But for some materials, this theory is too limiting.
Roderic Lakes
A Wisconsin Distinguished Professor of nuclear engineering and engineering physics and materials science and engineering at the University of Wisconsin-Madison, Roderic Lakes and graduate student Zachariah Rueger have recently made new materials that behave in an unusual way that defies the standard theory of elasticity.
It’s an advance that could open the door to designing novel materials for applications that require high toughness.
Lakes and Rueger used 3D printing to make their new polymer lattice materials. Their lattice design—in other words, the regular pattern in which the materials’ polymer strips are arranged—is a repeating crisscross structure. And when it’s twisted or bent, a bar of this polymer lattice is about 30 times stiffer than would be expected based on classical elasticity theory.
The researchers described their new lattice materials in the journal Physical Review Letters on Feb. 8, 2018.
Performing measurements in the lab, Lakes determined that the materials’ behavior was consistent with Cosserat elasticity, a more descriptive theory of elasticity that takes into consideration the size of the underlying structure in a material.
“When you have a material with substructure in it, such as some foams, lattices and fiber-reinforced materials, there’s more freedom in it than classical elasticity theory can handle,” Lakes says. “So we’re studying the freedom of materials to behave in ways not anticipated by the standard theory.”
This increased freedom offers a potential path to creating novel materials that are immune to stress concentration; in other words, materials with improved toughness. Such materials would be useful for a variety of applications—for example, airplane wings that are more fracture resistant.
If a crack forms in an airplane wing, stress is concentrated around the crack, making the wing weaker. “You need a certain amount of stress to break something, but if there’s a crack in it, you can break it with less stress,” Lakes says.
Using the Cosserat theory of elasticity to inform materials design will yield tougher materials in which stresses are distributed throughout the materials differently, according to Lakes.
These same effects are present in materials such as bone and certain types of foams. However, when engineers make foam for a seat cushion, for example, they don’t have much control over the foam’s substructure—the tiny bubbles that form and make up the cells inside the foam. As a result, they have limited ability to tailor the Cosserat effects.
In contrast to foam, the UW-Madison researchers can tune the Cosserat effects and make them very strong. “We developed a material in which we have exceptionally detailed control over the fine structure of our lattice, and that enabled us to achieve very strong effects when bending and twisting the material,” Lakes says.
This work was supported by the National Science Foundation (grant No. CMMI-1361832.)