Unlike conventional two-dimensional (2D) semiconductor superlattices, moiré patterns in 2D materials are flexible and their electronic, magnetic, optical, and mechanical properties depend on their topography. Within a $\text{continuous}+\text{atomistic}$ theory treating 2D materials as crystalline elastic membranes, we abandon the flat-membrane scenario usually assumed for these materials and address out-of-plane deformations. We confront our predictions to experimental analyses on model systems, epitaxial graphene, and ${\mathrm{MoS}}_2$ on metals and reveal that compression/expansion and bending energies stored in the membrane can compete with adhesion energy, leading to a subtle moiré wavelength selection and the formation of wrinkles.

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• Adhesion
• Bending
• Disclinations & dislocations
• Elastic deformation
• Epitaxial strain
• Intercalation
• Surface reconstruction
• 2-dimensional systems
• Graphene
• Surfaces
• Materials modeling
• Scanning tunneling microscopy