  We develop a continuum dislocation description of twist and stretch moire
superlattices in 2D material bilayers. The continuum formulation is based on
the topological constraints introduced by the periodic dislocation network
associated with the moire structure. The approach is based on solving
analytically for the structural distortion and displacement fields that satisfy
the topological constraints, and which minimize the total energy. The total
energy is described by both the strain energy of each individual distorted
layer, and a Peierls-Nabarro like interfacial contribution arising from
stacking disregistry. The dislocation core emerges naturally within the
formalism as a result of the competition between the two contributions. The
approach presented here captures the structure and energetics of twist and
stretch moire superlattices of dislocations with arbitrary direction and
character, without assuming an analytical solution a priori, with no adjustable
parameters, while accounting naturally for dislocation-dislocation image
interactions. In comparisons to atomistic simulations using classical
potentials, the maximum structure deviation is 6%, while the maximum line
energy deviation is 0.019 eV/Angstrom. Several applications of our model are
shown, including predicting the variation of structure with twist angle, and
describing dislocation line tension and junction energies.
