  Graphene subject to high levels of shear strain leads to strong
pseudo-magnetic fields resulting in the emergence of Landau levels. Here we
show that, with modest levels of strain, graphene can also sustain a classical
valley hall effect (VHE) that can be detected in nonlocal transport
measurements. We provide a theory of the strain-induced VHE starting from the
quantum Boltzmann equation. This allows us to show that, averaging over
short-range impurity configurations destroys quantum coherence between valleys,
leaving the elastic scattering time and inter-valley scattering rate as the
only parameters characterizing the transport theory. Using the theory, we
compute the nonlocal resistance of a Hall bar device in the diffusive regime.
Our theory is also relevant for the study of moderate strain effects in the
(nonlocal) transport properties of other two-dimensional materials and van der
Walls heterostructures.
