This article provides an overview of the smooth particle hydrodynamics (SPH) approach and its mathematical modeling. SPH is a numerical technique based on a mesh-free Lagrangian scheme for evaluating the continuum mechanics problems. This method is suitable in the case of continuum objects undergoing large deformation, as conventional finite element methods are unreliable due to mesh failure and convergence issues. It is a widely used approach in the field of astrophysics, fluid mechanics, structural mechanics, soil mechanics, automobiles, and so on. A numerical example is also considered in this research paper to demonstrate the applicability of the method. The simulation process was achieved using LS-Dyna explicit solver software, and plots related to cutting and thrust forces, von Mises stress, plastic strain, temperature distribution, and so on, were obtained. Also, the effect of Time-Scaling Factor (TSSFAC) on SPH simulations was observed in this research.

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