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|Title:||A higher gradient theory of mixtures for multi-component materials with numerical examples for binary alloys|
|Authors:||Böhme, Thomas; Dreyer, Wolfgang; Duderstadt, Frank; Müller, Wolfgang H.|
|Published in:||Preprint / Weierstraß-Institut für Angewandte Analysis und Stochastik , Volume 1286, ISSN 0946-8633|
|Publisher:||Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik|
|Abstract:||A theory of mixture for multi-component materials is presented based on a novel, straightforward method for the exploitation of the Second Law of thermodynamics. In particular the constitutive equations for entropy, heat and diffusion flux as well as the stress tensor are formulated as a consequence of the non-negative entropy production. Furthermore we derive the established Gibbs equation as well as the Gibbs Duhem relation which also follow from the formalism. Moreover, it is illustrated, how local mechanical strains due to eigenstrains or external loadings, modify the free energy and, consequently, change the chemical potentials of the components. All consecutive steps are illustrated, first, for simple mixtures and, second, for a system containing two different phases. So-called higher gradients of the concentrations are considered, which take the nonuniform composition into account. It will also become apparent that more/other variables of modified/different physical pr oblems beyond the illustrated ones can be easily treated within the presented framework. This work ends with the specification to binary alloys and with the presentation of various numerical simulations.|
|Keywords:||Thermodynamics; structured surfaces and interfaces; coexistent phases; Analysis of microstructure; Transformations involving diffusion|
|License:||This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.|
Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.
|Appears in Collections:||Mathematik|
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