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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

Κιλικιάν, Ειρήνη-Βιργινία Παναγιώτης

Thesis advisor

Μακριδάκης, Χαράλαμπος

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.

Language

English

Subject

Coarse-graining

Coupling

Crystal deformation

Finite elements

Quasicontinuum method

Stresses

Δυνάμεις τάσης

Εκτράχυνση μοντέλων

Παραμόρφωση κρυστάλλων