Please use this identifier to cite or link to this item: doi:10.22028/D291-28321
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Title: Identifying Elastic and Viscoelastic Material Parameters by Means of a Tikhonov Regularization
Author(s): Diebels, Stefan
Scheffer, Tobias
Schuster, Thomas
Wewior, Aaron
Language: English
Title: Mathematical problems in engineering : theories, methods and applications
Volume: 2018
Publisher/Platform: Hindawi
Year of Publication: 2018
Publikation type: Journal Article
Abstract: For studying the interaction of displacements, stresses, and acting forces for elastic and viscoelastic materials, it is of utmost importance to have a decent mathematical model available. Usually such a model consists of a coupled set of nonlinear differential equations together with appropriate boundary conditions. However, since the different material classes vary significantly with respect to their physical and mechanical behavior, the parameters which appear in these equations are unknown and therefore have to be determined before the equations can be used for further investigations or simulations. It is this very step which is addressed in this article where we consider elastic as well as viscoelastic material behavior. The idea is to compute the parameters as solutions of a minimization problem for Tikhonov functionals. Tikhonov regularization is a well-established solution technique for tackling inverse problems. On the one hand, it assures a computation that is stable with respect to noisy input data, and on the other hand, it involves desired a priori information on the solution. In this article we develop problem adapted Tikhonov functionals and prove that a Tikhonov regularization improves the accuracy especially when the underlying system is ill-conditioned.
DOI of the first publication: 10.1155/2018/1895208
URL of the first publication: https://www.hindawi.com/journals/mpe/2018/1895208/
Link to this record: hdl:20.500.11880/27599
http://dx.doi.org/10.22028/D291-28321
ISSN: 1563-5147
1024-123X
Date of registration: 3-Aug-2019
Faculty: MI - Fakultät für Mathematik und Informatik
Department: MI - Mathematik
Professorship: MI - Prof. Dr. Thomas Schuster
Collections:Die Universitätsbibliographie

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