Cut open a bone and you'll see a subtly disordered structure. Tiny beams, called trabeculae, connect to one another in irregular patterns, distributing stress and lending bones an impressive toughness. What if human-made materials could exhibit similar properties?
In a new paper in Proceedings of the National Academy of Sciences Nexus , researchers at Penn Engineering, Penn Arts & Sciences and Aarhus University found that adding just the right amount of disorder to the structure of certain materials can make them more than twice as resistant to cracking.
The finding opens the door to more widespread use of so-called "mechanical metamaterials," a class of materials whose internal structures — often produced via digital manufacturing techniques such as 3D printing and laser cutting — give them unique properties, including enhanced strength or stiffness per weight.
Until this point, one of the greatest challenges posed by mechanical metamaterials has been their fragility. "Toughness is a limiting factor in not all, but many 3D-printed mechanical metamaterials," says Kevin Turner , Professor and John Henry Towne Department Chair of Mechanical Engineering and Applied Mechanics (MEAM) at Penn Engineering and the paper's senior author.
This new result promises to address this issue and at relatively low cost. "Without changing the material at all, just simply by altering the internal geometry," says Turner, "you can increase the toughness by 2.6 times."
Inspired by Nature
Natural materials commonly exhibit disorder at small scales. In addition to human bone, the researchers point to nacre, the iridescent material inside seashells, and the threads mussels use for attaching to surfaces. Rather than regular repeating structures, these materials contain minute, seemingly random variations in the space between their structural components.
For decades, engineers have taken inspiration from nature, but often by replicating easy-to-manufacture structures like a honeycomb pattern, which reduces a material's weight while maintaining its strength. Honeycomb structures can be found in some cardboard packaging and the metal reinforcements inside airplane wings. "That's a very regular pattern," Turner points out.
In contrast, the metamaterials tested in the paper exhibited a wide range of patterns, from regular to highly disordered. "The samples that performed the best, in which it was most difficult for a crack to grow, did not consist of regular repeating patterns," says Sage Fulco , a postdoctoral researcher in MEAM and the paper's lead author. "They had different geometry in different areas."
Testing the Limits of Disorder
To test whether disorder makes mechanical metamaterials tougher, the researchers performed thousands of computational mechanics simulations of numerous different patterns, all based on a triangular lattice, called a truss. In some, the triangles were arranged in perfect symmetry, while in others, the pattern had been perturbed by moving the nodes where the triangles meet.
The team subjected the patterns to rounds of computer simulations and created physical versions of a representative set of geometries, including both ordered geometries and those with varying levels of disorder.
When they attempted to break the materials — in the lab and in the simulations — a clear trend emerged. "There was a specific level of disorder, so that the patterns we cut into the material looked somewhat regular but not exactly symmetrical, where we were able to achieve the highest level of performance," says Fulco.
Striking the Right Balance
The perfect level of disorder — not too little, or too much — retained most of the material's strength and stiffness while enhancing its toughness, but took substantially more effort to design than a repeating structure. "Disordered systems aren't often used in engineering because the design is much more complex," Turner points out.
Fulco worked with Michael Budzik , Associate Professor in Mechanical and Production Engineering at Aarhus University, to fine-tune the fabrication process, traveling to Denmark to use an extremely precise laser cutter in Budzik's lab to carve the patterns. "I had to completely rebuild our experimental setup to make use of their fabrication equipment," says Fulco. "But that allowed the experiments to actually succeed."
Visualizing the Strength of Disorder
To understand how the disordered structures increased toughness, the team ran an experiment conceived in collaboration with Douglas Durian , Mary Amanda Wood Professor in Physics and Astronomy at Penn Arts & Sciences, and Hongyi Xiao , then a postdoctoral fellow in Durian's lab. (The four were researchers in Penn's Materials Research Science and Engineering Center , or MRSEC).
When certain materials — including the polymer into which Fulco cut the patterns — are stretched, their birefringence, a property that causes light to split into two different paths, changes. Viewed through the right setup, the material's appearance shifts with different levels of mechanical stress.
By taking images of samples with different patterns — some with a regular pattern and others with varying levels of disorder — while loading them to failure, the researchers were able to visualize exactly what happened as cracks propagated through the materials.
In short, the disorder prevented cracks from traveling in straight lines. "For the crack to grow through a disordered material, damage has to occur over a much larger area," says Fulco. In images captured by the team, fracture events appear closer together in a straight line in the symmetrical sample, but are scattered about in the optimally disordered one.
Going Beyond the Lab
Moving forward, the researchers hope their findings will encourage a broader exploration of disordered patterns in mechanical metamaterials and mechanical design. "We used triangles, but this work is very fundamental," says Fulco. "Other groups can apply it to many different geometries."
The success of the nature-inspired design also suggests that engineers may have significantly more to learn from the design of natural materials. "Combining different types of materials and adding different geometries at different scales are very exciting opportunities," says Fulco. "That's what we see when we look at the highest performing natural materials."
Ultimately, the team envisions these advances leading to the development of improved materials and structures with applications in industries like aerospace, where resisting crack growth and tolerating damage are critical. "We're enabling broader use of mechanical metamaterials in structural applications by identifying a geometric route to increase toughness," says Turner.
This study was conducted at Penn Engineering, the University of Pennsylvania School of Arts & Sciences and Aarhus University and supported by the National Science Foundation (NSF) MRSEC program (awards DMR-1720530 and DMR-2309043), the National Defense Science & Engineering Graduate (NDSEG) Fellowship Program, and the Villum Foundations under the Villum Experiment programme (VIL50302).
