  Strain, both naturally occurring and deliberately engineered, can have a
considerable effect on the structural and electronic properties of 2D and
layered materials. Uniaxial or biaxial heterostrain modifies the stacking
arrangement of bilayer graphene (BLG) which subsequently influences the
electronic structure of the bilayer. Here, we use Density Functional Theory
(DFT) calculations to investigate the interplay between an external applied
heterostrain and the resulting stacking in BLG. We determine how a strain
applied to one layer is transferred to a second, 'free' layer and at what
critical strain the ground-state AB-stacking is disrupted. To overcome
limitations introduced by periodic boundary conditions, we consider an
approximate system consisting of an infinite graphene sheet and an armchair
graphene nanoribbon (AGNR). We find that above a critical strain of ~1%, it is
energetically favourable for the free layer to be unstrained, indicating a
transition between uniform AB-stacking and non-uniform mixed stacking. This is
in agreement with a simple model estimate based on the individual energy
contributions of strain and stacking effects. Our findings suggest that small
levels of strain provide a platform to reversibly engineer stacking order and
Moir\'e features in bilayers, providing a viable alternative to twistronics to
engineer topological and exotic physical phenomena in such systems.
