We discuss novel mathematical models for the analysis and computational prediction of mechanical relaxation of two-dimensional layered atomic crystals in the presence of large-scale moiré patterns. The concept of configuration space or hull, previously introduced for the study of transport properties in aperiodic materials by Bellissard et al., is shown to allow for a unified description of continuum as well as atomistic models of elastic relaxation for a wide range of materials in the truly incommensurate (aperiodic) regime.

In the case of twisted bilayers with identical materials, we will present some preliminary analysis and numerical results in the asymptotic regime of small twist angle (inducing a large-scale moiré pattern) and small interlayer Van der Waals forces, in particular the well-known case of graphene/graphene but also MoS2/MoS2.