A fracture mechanics approach to haptic synthesis of tissue cutting with scissors

An analytical model for cutting of a plate of material with a pair of scissors is presented in terms of concepts of contact and fracture mechanics. The forces of contact between the blade of the scissors and the plate are expressed by a nonlinear function of deflection at the crack front multiplied by the length of the contact region between the blade and the plate. The cutting model captures the combined effect of multiple fracture modes. The level of deflection that causes fracture is obtained using an energy approach. The cutting model predicts that, during fracture, force and torque responses of the scissors depend on the toughness and geometry of the plate, but do not depend on the stiffness of the plate. The model is used for haptic synthesis of interaction between a pair of scissors and a virtual plate. An implementation of the model is presented for the case of surgical scissors in contact with skin. The simulation results are compared to previous experimental data, demonstrating the realism of the cutting model behavior. This haptic rendering technique is computationally efficient and can be applied to real-time simulation.