We present a method for the real-time, interactive simulation of tissue tearing during laparoscopic surgery. The method is designed to work at haptic feedback rates (i.e., around 1kHz). Tissue tearing is simulated under the general framework of continuum damage mechanics. The problem is stated as a general, multidimensional parametric problem, which is solved by means of Proper Generalized Decomposition (PGD) methods. One of the main novelties is the reduction of history-dependent problems, such as damage mechanics, by resorting to an approach in which a reduced-order field of initial damage values is considered as a parameter of the formulation. We focus on the laparoscopic cholecystectomy procedure as a general example of the performance of the method
