Abstract
We introduce here a novel approach for the numerical simulation of nonlinear, hyperelastic soft tissues at kilohertz feedback rates necessary for haptic rendering. This approach is based upon the use of proper generalized decomposition techniques, a generalization of PODs. Proper generalized decomposition techniques can be considered as a means of a priori model order reduction and provides a physics-based meta-model without the need for prior computer experiments. The suggested strategy is thus composed of an offline phase, in which a general meta-model is computed, and an online evaluation phase in which the results are obtained at real time. Results are provided that show the potential of the proposed technique, together with some benchmark test that shows the accuracy of the method.
Highlights
Real-time simulation is one of the most challenging scenarios for simulation-based engineering sciences
Haptic surgery simulators compute the response of biological soft tissues and give it back to the peripherals at, at least, 25 Hz of feedback rate if visual realism is needed and, notably, 500 Hz–1 kHz if haptic response is desired [1, 2]
We present a novel technique for the simulation of biological soft tissues under hyperelasticity assumptions at haptic feedback rates
Summary
Real-time simulation is one of the most challenging scenarios for simulation-based engineering sciences. The resulting PGD solution to the problem is expressed as a finite sum of separable functions that provides a meta-model for the problem, for which no prior computer experiment ( known as snapshots in the model order reduction community) is necessary This meta-model can be successfully applied in real time to obtain the response of the system at kilohertz rates, as will be demonstrated in subsequent sections of this paper. We present a novel technique for the simulation of biological soft tissues under hyperelasticity assumptions at haptic feedback rates It is based on the use of the aforementioned PGD approach and an explicit linearization of the weak form generated by nonlinear strain measures. It is shown how the PGD approach to the problem of real-time simulation of soft tissue deformation opens new insights on how the problem can be attacked
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