The synthesis of graphene, a one-atom thick two-dimensional (2D) graphitic sheet, was a revolution in materials physics. Since then a host of other 2D materials have been discovered that can be stacked and manipulated to create layered heterostructures with remarkable properties (including the recent discovery of superconductivity in twisted graphene bilayers). Such properties are related to structural reconstructions that occur in 2D heterostructures starting from an initial moiré pattern that is created when mismatched layers are stacked. Taking graphene bilayers as an example, I will describe the mechanics and physics of these fascinating materials and show how they can be modeled using a combination of nonlinear continuum finite elements and high-fidelity machine learning interatomic potentials. These simulations predict an interesting scaling behavior in the reconstruction that is related to the initial imposed twist and
leads to qualitative change in electron diffraction patterns, which was subsequently verified experimentally. New results for “strain engineering” the electronic properties of graphene bilayers will also be discussed.