Due to atomically thin structure, graphene/hexagonal boron nitride (G/hBN) heterostructures are intensively sensitive to the external mechanical forces and deformations being applied to their lattice structure. In particular, strain can lead to the modification of the electronic properties of G/hBN. Furthermore, moire structures driven by misalignment of graphene and hBN layers introduce new features to the electronic behavior of G/hBN. Utilizing {it ab initio} calculation, we study the strain-induced modification of the electronic properties of diverse stacking faults of G/hBN when applying in-plane strain on both layers, simultaneously. We observe that the interplay of few percent magnitude in-plane strain and moire pattern in the experimentally applicable systems leads to considerable valley drifts, band gap modulation and enhancement of the substrate-induced Fermi velocity renormalization. Furthermore, we find that regardless of the strain alignment, the zigzag direction becomes more efficient for electronic transport, when applying in-plane non-equibiaxial strains.
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