A discrete-to-continuum model of weakly interacting incommensurate two- dimensional lattices: The hexagonal case

MI Espanol and D Golovaty and JP Wilber, JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS, 173, 105229 (2023).

DOI: 10.1016/j.jmps.2023.105229

In this paper, we extend the discrete-to-continuum procedure we developed in Espanol et al. (2018) to derive a continuum variational model for a hexagonal twisted bilayer material in which one layer is fixed. We use a discrete energy containing elastic terms and a weak interac-tion term that could utilize either a Lennard-Jones potential or a Kolmogorov-Crespi potential. To validate our modeling, we perform numerical simulations to compare the predictions of the original discrete model and the proposed continuum model, which also show an agreement with experimental findings for, e.g., twisted bilayer graphene.

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