Model Reduction for Complex Continua – At the Example of Modeling Soft Tissue in the Nasal Area

Numerical simulation plays an important role in research fields with increasing complexity. Among these are e. g. extended continua, biomechanics, production technology, medical technology and many more. Modern simulation tools often provide both, realistic results and a close link to the physics of the problem. However, increased accuracy is paid by very high computational effort which makes realtime simulation impossible. Nevertheless the latter is urgently needed in important application fields. A good example are surgery training and on-line support during minimally invasive real surgeries. Here, a numerical model can be well used to give otherwise unaccessible information about the stress and strain state in the biological material. The development of such a real-time computation method requires to extend existing model reduction concepts to non-linear solid mechanics based on complex continua. This paper discusses the effectiveness of two singular value decomposition based model reduction methods in this context. Currently, the modal basis reduction method as well as the proper orthogonal decomposition method are widely used for solving linear problems. We will extend these approaches to nonlinear elasticity including large deformations. The performance of the extended concepts is first investigated for the simple geometry of a cantilever beam and then for the very complex system of a human nose. Comparing the results puts us into the position to discuss the suitability of the two model reduction methods for non-linear solid mechanics, especially from the point of view of biomechanics.