Abstract: We introduce a general theory of the microbuckling field for modelling microbuckling and other material instabilities in cellular solids such as foams, lattices, and mechanical metamaterials. The model's main novelty lies in the assignment of a scalar-valued microbuckling field indicating the degree to which a material point is locally microbuckled. Two independent strain energies are prescribed: one for locally unbuckled and another for locally microbuckled material points. The former energy corresponds to linear elasticity of the underlying cells, while the latter to their microbuckling and eventual densification. These energies are constructed using standard Gibson-Ashby formulae for effective cellular solid constitutive parameters in terms of the microstructural topology and composition. The microbuckling field unifies the pair of strain energies into a single overall energy via a first-order regularization of the microbuckling field. Unlike existing continuum models for material instabilities, none of the strain energies need violate polyconvexity. In this manner, localized material behavior is described not by the absence of convexity but instead by the extended kinematic setting. The length scales conferred by the first-order regularization are precisely those relevant to the localized material behavior. We demonstrate that the model is amenable to both analytical and computational treatments and recovers phenomena distinctive of cellular solids such as localized compression bands and global softening mechanisms.
About the speaker: Ryan McAvoy is a PhD Candidate in the Department of Mechanical Engineering at UC Berkeley. He received his BS in Engineering Physics and BA in Applied Mathematics from University of California, Berkeley in 2022, his MS in Mechanical Engineering from the same institution in 2023, and his MS in Aeronautics and Astronautics from Stanford University in 2025. His research interests span theoretical and computational mechanics with a particular focus on the development and analysis of models for materials with microstructure. Ryan is a recipient of the NSF Graduate Research Fellowship and is co-advised by Professors David Steigmann and Oliver O'Reilly.