A damage evolution law is proposed to consider the frictional behavior within an Eulerian material after full damage as a Lagrangian material, where the mesh explicitly describes the newly born interface interactions. This approach is prominent for simulating severe plastic deformation (SPD) processes during which material separation can occur. Among these, orthogonal cutting represents the simplest process for comparison with the simulation because it offers accessibility for measuring physical quantities in situ in the vicinity of the tool. Therefore, a numerical model based on a coupled Eulerian-Lagrangian formulation to simulate segmented chip formation mechanisms during orthogonal cutting was developed. A simple damage initiation criterion was used, and the damage evolution criterion was coded in the ABAQUS subroutine VUSDFLD. The model can simulate both segmented and continuous chip formation, depending on the experimental configuration, while satisfactorily predicting chip morphology and physical quantities such as temperature, primary shear band and cutting forces. Additionally, a non-negligible material side flow observed experimentally was successfully predicted by simulation. The model accuracy in predicting the material plastic behavior is auspicious for its subsequent extension to the three-dimensional model of SPD processes (i.e., milling, friction stir welding, etc.).