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Kalorik in ferroelektrischen Werkstoffen – von der Variationsformulierung zur Modellierung und Simulation
Abstract
Ferroelectric materials are nowadays used in many areas due to their special electro-mechanical properties. Since their material properties are partly strongly dependent on temperature and the temperature can have a decisive influence on the reliability and life time of ferroelectric components, caloric aspects have increasingly been investigated in recent years, not least because the electrocaloric effect is suitable for solid-state refrigeration. The thesis deals with the modeling and simulation of nonlinear thermo-ferroelectric material behavior. The focus is particularly on the modeling of temperature changes due to domain wall motion in the material and its numerical implementation. To establish a corresponding numerical discretization scheme, a weak form has to be derived, which conatins the constitutive and balance equations of dissipative thermo-electro-magneto-mechanical multi-field problems. The method of weighted residuals is usually used for this purpose, since a classical functional of caloric and electrodynamic problems, as a prerequisite for a cariational approach, is not known. Deficiencies lie in the different units, which, in contrast to mechanical stress, electric displacement and magnetic field, intrinsically involve time rates in the fluxes of heat and electrical current. By combining classical variational principles, i.e. Hamilton’s and Jourdain’s principles, and introducing a heat and a charge flux potential, a modified variational principle is introduced and referred to as the principle of Hamilton-Jourdain. Based on the weak formulation, an algebraic system of equations is finally set up and implemented together with the thermo-electro-mechanical constitutive model into a commercial finite element software, which is finally used to numerically solve various boundary value problems.
Additional Information
Zugleich: Dissertation, Universität Kassel, 2021Druckausgabe
Link zu kassel university press
Citation
@book{doi:10.17170/kobra-202112145254,
author={Wingen, Marius},
title={Kalorik in ferroelektrischen Werkstoffen – von der Variationsformulierung zur Modellierung und Simulation},
publisher={kassel university press},
year={2021}
}
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5550 {{Thermodynamik}}
5550 {{Ferroelektrikum}}
5550 {{Werkstoff}}
5550 {{Stoffeigenschaft}}
5550 {{Leistungsbilanz}}
5550 {{Mehrfeldproblem}}
5550 {{Modellierung}}
5550 {{Simulation}}
7136 ##0##http://hdl.handle.net/123456789/13517
<resource xsi:schemaLocation="http://datacite.org/schema/kernel-2.2 http://schema.datacite.org/meta/kernel-2.2/metadata.xsd"> 2022-01-14T07:38:33Z 2022-01-14T07:38:33Z 2021 doi:10.17170/kobra-202112145254 http://hdl.handle.net/123456789/13517 Zugleich: Dissertation, Universität Kassel, 2021 ger kassel university press Namensnennung 4.0 International http://creativecommons.org/licenses/by/4.0/ Ferroelektrika Kalorik Thermo-ferroelektrisches Materialverhalten Variationsformulierung Mehrfeldprobleme Modellierung und Simulation Leistungsbilanz 600 Kalorik in ferroelektrischen Werkstoffen – von der Variationsformulierung zur Modellierung und Simulation Buch Ferroelectric materials are nowadays used in many areas due to their special electro-mechanical properties. Since their material properties are partly strongly dependent on temperature and the temperature can have a decisive influence on the reliability and life time of ferroelectric components, caloric aspects have increasingly been investigated in recent years, not least because the electrocaloric effect is suitable for solid-state refrigeration. The thesis deals with the modeling and simulation of nonlinear thermo-ferroelectric material behavior. The focus is particularly on the modeling of temperature changes due to domain wall motion in the material and its numerical implementation. To establish a corresponding numerical discretization scheme, a weak form has to be derived, which conatins the constitutive and balance equations of dissipative thermo-electro-magneto-mechanical multi-field problems. The method of weighted residuals is usually used for this purpose, since a classical functional of caloric and electrodynamic problems, as a prerequisite for a cariational approach, is not known. Deficiencies lie in the different units, which, in contrast to mechanical stress, electric displacement and magnetic field, intrinsically involve time rates in the fluxes of heat and electrical current. By combining classical variational principles, i.e. Hamilton’s and Jourdain’s principles, and introducing a heat and a charge flux potential, a modified variational principle is introduced and referred to as the principle of Hamilton-Jourdain. Based on the weak formulation, an algebraic system of equations is finally set up and implemented together with the thermo-electro-mechanical constitutive model into a commercial finite element software, which is finally used to numerically solve various boundary value problems. open access Wingen, Marius 2021-05-2021 xvi, A5 Kassel, Universität Kassel, Fachbereich Maschinenbau Ricoeur, Andreas (Prof. Dr.) Kästner, Markus (Prof. Dr.) Kassel 978-3-7376-1006-3 Thermodynamik Ferroelektrikum Werkstoff Stoffeigenschaft Leistungsbilanz Mehrfeldproblem Modellierung Simulation publishedVersion Berichte des Instituts für Mechanik Bericht 4/2021 true 39,00 Berichte des Instituts für Mechanik Naturwissenschaft, Technik, Informatik, Medizin Dissertation FB 15 / Maschinenbau Softcover DIN A5 true </resource>
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