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Authors: Mordhorst, Mylena
Title: Towards a fast and stable dynamic skeletal muscle model
Issue Date: 2020
Publisher: Stuttgart : Institute for Modelling and Simulation of Biomechanical Systems, Chair of Continuum Biomechanics and Mechanobiology, University of Stuttgart Dissertation vi, 165
Series/Report no.: CBM;5
ISBN: 978-3-946412-04-5
Abstract: This thesis investigates the possibility to reduce the computational effort of a dynamic skeletal muscle model making use of model order reduction methods. For that purpose, a three-dimensional, nonlinear, dynamic skeletal muscle model based on the theory of incompressible finite hyperelasticity is introduced. After discretisation in space and time, using the mixed Taylor-Hood finite elements and the implicit Euler scheme, respectively, the obtained complex and high-dimensional differential algebraic equation system describing the three fields position, velocity and pressure, is investigated from a theoretical as well as computational point of view. Furthermore, the stability issues, encountered with a reduced-order model, built by projecting each field of the high-dimensional model onto a reduced subspace, are demonstrated. The reason for these problems is additionally investigated and confirmed from the theoretical perspective. In order to propose a suitable approach for obtaining a stable reduced order skeletal muscle model, the well-established technique of combining the reduced basis approximation with the proper orthogonal decomposition needs to be customised. The performance with respect to stability, effciency and accuracy of different reduced-order models, built from various combinations and sizes of subspaces, each of them again constructed from differently calculated POD bases, with and without enrichment by approximate supremizer solutions, is compared.
Appears in Collections:02 Fakultät Bau- und Umweltingenieurwissenschaften

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