Modelling of cutting force on a viscoelastic body for surgical simulation

This paper presents the development of a closed form solution of stress distribution in a linear viscoelastic half-space subjected to distributive surface forces. The purpose is to analyze the cutting efficiency based on stress fields under different cutting parameters, such as cutting angle or blade sharpness, and to provide a guideline for practical applications. In developing the model, the body is assumed as a linear viscoelastic, isotropic and homogenous half-space. The interaction between the blade and the body is modeled as distributive forces acting on a rectangular area on the free surface of the half-space. To model the linear viscoelasticity, Burgers model is used to describe the stress relaxation behaviors. A trapezoidal force profile is applied in the intersection of the blade. The solution is developed in two steps: First, by applying the elastic-viscoelastic correspondence principle, we obtain the viscoelastic solution with a point load from the elastic case. Second, a surface-integration of the solution over the contacting area is performed to obtain the stress distribution under distributive forces. The result serves as a mathematical model to simulate the stress distribution during biomaterial cutting and can be used in many practices such as surgical simulations and trainings.