A phenomenological cohesive term is proposed and added to an existing cohesive constitutive law (by Roy and Dodds) to model the crack tip high inertia region proposed by Gao. The new term is attributed to fracture mechanisms that result in high energy dissipation around the crack tip and is assumed to be a function of external energy per volume input into the system. Finite element analysis is performed on PMMA with constant velocity boundary conditions and mesh discretization based on the work of Xu and Needleman. The cohesive model with the proposed dissipative term is only applied in the high inertia zone i.e., to cohesive elements very close to the crack tip and the traditional Roy and Dodds model is applied on cohesive elements in the rest of the domain. It was observed that crack propagated in three phases with a speed of 0.35cR before branching, which are in good agreement with experimental observations. Thus, modeling of high inertia zone is one of the key aspects to understanding brittle fracture.