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Model order reduction of dynamic skeletal muscle models
Author(s) -
Mordhorst Mylena,
Wirtz Daniel,
Röhrle Oliver
Publication year - 2016
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201610414
Subject(s) - proper orthogonal decomposition , nonlinear system , finite element method , reduction (mathematics) , model order reduction , mathematics , partial differential equation , elasticity (physics) , interpolation (computer graphics) , compressibility , mathematical optimization , computer science , point of delivery , mathematical analysis , algorithm , mechanics , physics , structural engineering , engineering , geometry , thermodynamics , animation , projection (relational algebra) , computer graphics (images) , quantum mechanics , agronomy , biology
Forward‐dynamics simulations of three‐dimensional continuum‐mechanical skeletal muscle models are a complex and computationally expensive problem. Considering a fully dynamic modelling framework based on the theory of finite elasticity is challenging as the muscles' mechanical behaviour requires to consider a highly nonlinear, viscoelastic and incompressible material behaviour. The governing equations yield a nonlinear second‐order differential algebraic equation (DAE), which represents a challenge to model order reduction (MOR) techniques. This contribution shows the results of the offline phase that could be obtained so far by applying a combination of the proper orthogonal decomposition (POD) and the discrete empirical interpolation method (DEIM). (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)