Haptic Rendering of Cutting: A Fracture Mechanics Approach

Abstract

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. The work dissipated by 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. The paper also describes a model implementation that yields realistic results.