Continuum atomic relaxation models for twisted bilayer graphene involve minimization of the sum of intralayer elastic energy and interlayer adhesion energy. The elastic energy favors a rigid twist, i.e., no distortion in the twisted honeycomb lattices, while the adhesion energy favors Bernal stacking and breaking the relaxation into triangular AB- and BA-stacked domains. We compare the results of two relaxation models with the published Bragg interferometry data, finding good agreement with one of the models. We then provide a method for finding a highly accurate approximation to the solution of this model which holds above the twist angle of $\approx 0.7^{\circ }$ and thus covers the first magic angle. We find closed-form expressions in the absence as well as in the presence of external heterostrain. These expressions are not written as a Taylor series in the ratio of adhesion and elastic energy because, as we show, the radius of convergence of such a series is too small to access the first magic angle.

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• Electronic structure
• Flat bands
• Strain
• Twist deformation
• Bilayer graphene
• Graphene
• Twisted bilayer graphene