Accounting for Geometric Non-Linearities in Real-Time Simulation of Soft Tissues by Model Reduction Techniques
Résumé
Model reduction techniques have shown to constitute a valuable tool for real-time simulation in surgical environments and other fields. However, some limitations, imposed by real-time constraints, have not yet been overcome. One of such limitations is the severe limitation in time (established in 500 Hz of frequency for the resolution) that precludes the employ of Newton-like schemes. Thus, reduced models in real-time environments are actually linear, although the best set of basis functions, in statistical sense, is employed. In this work we present a technique able to deal with geometrically non-linear models, based on the employ of model reduction techniques, together with an Asymptotic Numerical Method (ANM) to expand the solution in the neighbourhood of the last equilibrium point. Examples of the performance of the technique over academic as well as surgical examples will be given.
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