Haptic Rendering of Cutting: A Fracture Mechanics Approach

Cutting a deformable body may be viewed as an interchange between three forms of energy: the elastic energy stored in the deformed body, the work done by a sharp tool as it moves against it, and the irreversible work spent in creating a fracture. Other dissipative phenomena such as friction can optionally also be considered. The force applied can be found by evaluating the work done by a tool which is sufficiently sharp to cause local deformation only. To evaluate this work, we propose a computational model that reduces cutting to the existence of three modes of interaction: deformation, rupture, and cutting, each of which considers the exchange between two forms of energy. During deformation, the work done by a tool is recoverable. During rupture, this work is zero. During cutting, it is equal to the irreversible work spent by fracture formation. The work spent in separating the sample is a function of its fracture toughness and of the area of a crack extension. It is in principle necessary to compute the deformation caused by a sharp tool in order to recover the force. This is in general an unsolved problem. However, for the case of a sharp interaction, measurements from tests performed on samples used in conjunction with analytical approximations to the contact problem, make it possible to propose a model which is applicable to haptic rendering. The technique is then compared to experimental results which confirms the model hypotheses. An implementation of the model that yields realistic results is also described.