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We explore the effect of mechanical strain on the electronic spectrum ofpatterned graphene based heterostructures. We focus on the competition ofKekul\'e-O type distortion favoring a trivial phase and commensurate Kane-Meletype spin-orbit coupling generating a topological phase. We derive a simplelow-energy Dirac Hamiltonian incorporating the two gap promoting mechanisms andinclude terms corresponding to uniaxial strain. The derived effective modelexplains previous ab initio results through a simple physical picture. We showthat while the trivial gap is sensitive to mechanical distortions, thetopological gap stays resilient.

Competition of trivial and topological phases in patterned graphene based heterostructures