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Identifier |
000368491 |
Title |
Computational Methods on Atomistic and Quasi-Continuum Models |
Alternative Title |
Υπολογιστικές μέθοδοι σε ατομιστικά και κατά προσέγγιση-συνεχή μοντέλα σε κρυσταλικά υλικά |
Author
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Κιλικιάν, Ειρήνη-Βιργινία Παναγιώτης
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Thesis advisor
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Μακριδάκης, Χαράλαμπος
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Abstract |
Continuum models are in most cases conditional approximations of atomistic models. Although the atomistic
models are considered to capture in a more accurate way the true nature of significant applications,
it is extremely difficult to base computational models on them, because of the vast number of unknowns
due to the scale of the formulation. A kind of such atomistic models that is of interest are the crystal
lattices models, which appear in modern material science. In a more macroscopic perspective, discrete
models can be replaced by continuum ones described by PDEs, where difference operators are replaced
by derivatives. However, it is already known that in many cases the continuum models fail to describe
properly the behaviour of discrete equations. To tackle this fundamental issue, new methods are proposed
: methods that picture the phenomena in a quasi-continuum way : in areas where the solution is expected
to be relatively smooth, far from discontinuities and large gradients, the discrete lattice is replaced by a
continuum material described by finite elements theory, while the initial discrete (atomistic) form is maintained
in areas of non-smooth or large gradient solutions. The aim of this work is the study and analysis
of methods with quasi-continuum approach in 1D.
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Language |
English |
Subject |
Coarse-graining |
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Coupling |
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Crystal deformation |
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Finite elements |
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Quasicontinuum method |
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Stresses |
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Δυνάμεις τάσης |
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Εκτράχυνση μοντέλων |
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Παραμόρφωση κρυστάλλων |
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Πεπερασμένα στοιχεία |
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Σχεδόν-συνεχής μέθοδος |
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Σύζευξη μοντέλων |
Issue date |
2011-07-15 |
Collection
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School/Department--School of Sciences and Engineering--Department of Mathematics--Post-graduate theses
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Type of Work--Post-graduate theses
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Permanent Link |
https://elocus.lib.uoc.gr//dlib/2/b/d/metadata-dlib-772e0fdc23fd0dfc32ef7fc65c241c56_1314682779.tkl
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Views |
349 |