  Strain-induced lattice mismatch leads to moir\'{e} patterns in homobilayer
transition metal dichalcogenides (TMDs). We investigate the structural and
electronic properties of such strained moir\'{e} patterns in TMD homobilayers.
The moir\'{e} patterns in strained TMDs consist of several stacking domains
which are separated by tensile solitons. Relaxation of these systems
distributes the strain unevenly in the moir\'{e} superlattice, with the maximum
strain energy concentrating at the highest energy stackings. The order
parameter distribution shows the formation of aster topological defects at the
same sites. In contrast, twisted TMDs host shear solitons at the domain walls,
and the order parameter distribution in these systems shows the formation of
vortex defects. The strained moir\'{e} systems also show the emergence of
several well-separated flat bands at both the valence and conduction band
edges, and we observe a significant reduction in the band gap. The flat bands
in these strained moir\'{e} superlattices provide platforms for studying the
Hubbard model on a triangular lattice as well as the ionic Hubbard model on a
honeycomb lattice. Furthermore, we study the localization of the wave functions
corresponding to these flat bands. The wave functions localize at different
stackings compared to twisted TMDs, and our results are in excellent agreement
with recent spectroscopic experiments [1].
