AMS Spring 2023

LLNL Uses 3D Printing to Predict and Test Failure Modes in Miniature Lattice Structures

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There’s a good reason why you see so many 3D printed Eiffel Towers. It’s not just because the building is beautiful and iconic, though that’s certainly part of it. It’s also a great showcase for a 3D printer’s capabilities, particularly in terms of resolution – which is why so many 3D printer manufacturers feature printed models of the French monument so prominently in their advertising. The Eiffel Tower is possibly the most famous lattice structure in the world, and lattice structures are a prime example of what 3D printing can do that other forms of manufacturing cannot.

Lattice structures have been used in construction for hundreds of years. They’re lightweight and low-density yet extremely strong and stiff, and 3D printing has proven itself to be capable of taking the typically large-scale structures down to a minuscule scale. Researchers at Lawrence Livermore National Laboratory (LLNL) have been working with 3D printed lattices a great deal, testing them for strength, creating super-strong microscopic structures, and even translating the structures into graphene aerogels. Now LLNL has published two new research papers that delve further into the miniaturization of lattice structures.

The big question for Mark Messner and Holly Carlton was whether the models used to predict failure behavior in large-scale lattice structure would apply to smaller-scale lattices. Messner, who is now with Argonne National Laboratory, published his work in an article entitled “Optimal lattice-structured materials,” and used a new equivalent continuum model to predict failure behavior in truss structures. When applied to typical larger-scale structures, the model predicts either a yield-dominated or a buckling-dominated failure mode at critical relative density. That critical relative density, however, Messner argues, depends on the manufacturing process.

“Previous work demonstrates that lattice materials have excellent stiffness- and strength-to-weight scaling, outperforming natural materials. However, there are currently no methods for producing optimal mesostructures that consider the full space of possible 3D lattice topologies,” Messner states. “The inverse homogenization approach for optimizing the periodic structure of lattice materials requires a parameterized, homogenized material model describing the response of an arbitrary structure.

This work develops such a model, starting with a method for describing the long-wavelength, macroscale deformation of an arbitrary lattice. The work combines the homogenized model with a parameterized description of the total design space to generate a parameterized model. Finally, the work describes an optimization method capable of producing optimal mesostructures. Several examples demonstrate the optimization method. One of these examples produces an elastically isotropic, maximally stiff structure, here called the isotruss, that arguably outperforms the anisotropic octet truss topology.”

Carlton, whose work is documented in a paper entitled “Mapping local deformation behavior in single cell metal lattice structures,” conducted quasi-static compression tests paired with in situ tomography at Lawrence Berkeley National Laboratory’s Advanced Light Source. The tests, which were performed on miniature 3D printed structures, showed real-time deformation in unit cell lattice structures, particularly showing a transition in failure mode from catastrophic buckling to yielding at a low relative density (between 10 to 20 percent of bulk density), validating Messner’s predictions.

“Two types of structures, known to show different stress-strain responses, were evaluated using synchrotron radiation micro-tomography while performing in-situ uniaxial compression tests to capture the local micro-strain deformation,” Carlton’s paper explains. “These structures included the octet-truss, a stretch-dominated lattice, and the rhombic-dodecahedron, a bend-dominated lattice. The tomographic analysis showed that the stretch- and bend-dominated lattices exhibit different failure mechanisms and that the defects built into the structure cause a heterogeneous localized deformation response.”

Additional authors on Carlton’s paper include Messner, Jonathan Lind, Nickolai A. Volkoff-Shoemaker, Harold S. Barnard, Nathan R. Barton, and Mukul Kumar.

These studies are the first in which theoretical models were used to predict failure in miniaturized lattice structures and then tested to see if the predictions held up. The structures may have been small, but the results aren’t; they could have large implications for how other structures are designed and fabricated in the future. Discuss in the LLNL forum at


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