With molecular dynamics simulations,we systematically uncover a new kind of intrinsic thermal resistance that exists in two-dimensional materials under uneven external perturbation,by using partly encased graphene as a typical example.Combining with lattice dynamics analysis,we demonstrate that this intrinsic thermal resistance originates from the softening of flexural phonons partly in graphene induced by inhomogeneous external potential field or substrates which serve as perturbation.At the interface between graphene sections with and without external potential field,in-plane phonon modes can transmit well,whereas,low frequency flexural phonon modes are reflected,leading to this nontrivial intrinsic thermal resistance in the individual single-layer graphene.This intrinsic thermal resistance closely depends on coupling strength between graphene and substrates,and could be significant when the coupling is strong.Nevertheless,it is suppressed at high temperature.It is also found that this intrinsic thermal resistance depends on the size of the system to some extent,and a length independent value is extrapolated.Moreover,we demonstrate that thermal rectification can be realized by including the uneven external perturbation.Our study provides new insight to better understand thermal transport in two-dimensional materials.