  In this paper we propose a continuum variational model for a two-dimensional
deformable lattice of atoms interacting with a two-dimensional rigid lattice.
The two lattices have slightly different lattice parameters and there is a
small relative rotation between them. This is a prototypical example of a
three-dimensional system consisting of a graphene sheet suspended over a
substrate. The continuum model recovers both qualitatively and quantitatively
the behavior observed in the corresponding discrete model. The continuum model
predicts that the deformable lattice develops a network of domain walls
characterized by large shearing, stretching, and bending deformation that
accommodate the misalignment and/or mismatch between the deformable and rigid
lattices. Two integer-valued parameters that can be identified with the
components of a Burgers vector, describe the mismatch between the lattices and
determine the geometry and the detail of deformation associated with the domain
walls.
