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Hard, brittle and wear-resistant materials like ceramics pose a problem when being machined using conventional machining processes. Machining ceramics even with a diamond cutting tool is very difficult and costly. Near net-shape processes, like laser evaporation, produce micro-cracks that require extra finishing. Thus it is anticipated that ceramic machining will have to continue to be explored with new-sprung techniques before ceramic materials become commonplace. This numerical investigation results from the numerical simulations of the thermal and mechanical modeling of simultaneous material removal from hard-to-machine materials using both laser ablation and conventional tool cutting utilizing the finite element method. The model is formulated using a two dimensional, planar, computational domain. The process simulation acronymed, LAHM (Laser Ablation Hybrid Machining), uses laser energy for two purposes. The first purpose is to remove the material by ablation. The second purpose is to heat the unremoved material that lies below the ablated material in order to ``soften'' it. The softened material is then simultaneously removed by conventional machining processes. The complete solution determines the temperature distribution and stress contours within the material and tracks the moving boundary that occurs due to material ablation. The temperature distribution is used to determine the distance below the phase change surface where sufficient ``softening'' has occurred, so that a cutting tool may be used to remove additional material. The model incorporated for tracking the ablative surface does not assume an isothermal melt phase (e.g. Stefan problem) for laser ablation. Both surface absorption and volume absorption of laser energy as function of depth have been considered in the models. LAHM, from the thermal and mechanical point of view is a complex machining process involving large deformations at high strain rates, thermal effects of the laser, removal of 2b1af7f3a8