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Numerical analysis of a relaxed variational model of hysteresis in two-phase solids
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Carstensen, Carsten and Plechac, Petr (2001) Numerical analysis of a relaxed variational model of hysteresis in two-phase solids. ESAIM: Mathematical Modelling and Numerical Analysis, Vol.35 (No.5). pp. 865-878. doi:10.1051/m2an:2001139 ISSN 0764-583X.
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Official URL: http://dx.doi.org/10.1051/m2an:2001139
Abstract
This paper presents the numerical analysis for a variational formulation of rate-independent phase transformations in elastic solids due to Mielke et al. The new model itself suggests an implicit time-discretization which is combined with the finite element method in space. A priori error estimates are established for the quasioptimal spatial approximation of the stress field within one time-step. A posteriori error estimates motivate an adaptive mesh-refining algorithm for efficient discretization. The proposed scheme enables numerical simulations which show that the model allows for hysteresis.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics Q Science > QC Physics |
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Elastic solids -- Mathematical models, Phase transformations (Statistical physics), Hysteresis | ||||
Journal or Publication Title: | ESAIM: Mathematical Modelling and Numerical Analysis | ||||
Publisher: | EDP Sciences | ||||
ISSN: | 0764-583X | ||||
Official Date: | 2001 | ||||
Dates: |
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Volume: | Vol.35 | ||||
Number: | No.5 | ||||
Page Range: | pp. 865-878 | ||||
DOI: | 10.1051/m2an:2001139 | ||||
Status: | Peer Reviewed | ||||
Access rights to Published version: | Open Access (Creative Commons) | ||||
Funder: | Max-Planck-Gesellschaft zur Förderung der Wissenschaften [Max Planck Society for the Advancement of Science], Deutsche Forschungsgemeinschaft (DFG), University of Delaware Research Foundation | ||||
Grant number: | UDRF-19990115 (Delaware) |
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