Forces on dislocations and the limits of classical elasticity in 2D
Autor(a) principal: | |
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Data de Publicação: | 2023 |
Tipo de documento: | Tese |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UFPE |
Texto Completo: | https://repositorio.ufpe.br/handle/123456789/54076 |
Resumo: | This thesis investigates some limits of the classical theory of elasticity in 2D, especially concerning forces on topological defects called dislocations. Initially, the thesis comments each approximating step used in deriving Classical Elasticity. Novel discussions are made about the continuum assumption and the limits of the sum-to- integral approximation. Moreover, an alternative mathematical formalism to deformations in 2D is introduced in order to obtain simpler equations and physical inferences. Thereafter, the notion of the core force is studied. This is a correction to the classical force on dislocation, called Peach-Koehler force, and which appears when in the presence of strain gradients. It has been predicted by different approaches but never observed, until a work which is presented in this thesis. A simulation model to investigate such force and its results are shown. By comparing with the previous theoretical approaches, it is verified that none of them is capable of providing a way to quantitatively predict the core force. Furthermore, it is shown that, for some systems, results from the core force can be used to predict a definite value for the core energy of the dislocation. |
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PEREIRA, Paulo César do Nascimentohttp://lattes.cnpq.br/2084709462294618http://lattes.cnpq.br/1975993976921900APOLINÁRIO, Sérgio Wlademir da Silva2023-12-13T13:21:29Z2023-12-13T13:21:29Z2023-03-21PEREIRA, Paulo César do Nascimento. Forces on dislocations and the limits of classical elasticity in 2D. 2023. Tese (Doutorado em Física) – Universidade Federal de Pernambuco, Recife, 2023.https://repositorio.ufpe.br/handle/123456789/54076This thesis investigates some limits of the classical theory of elasticity in 2D, especially concerning forces on topological defects called dislocations. Initially, the thesis comments each approximating step used in deriving Classical Elasticity. Novel discussions are made about the continuum assumption and the limits of the sum-to- integral approximation. Moreover, an alternative mathematical formalism to deformations in 2D is introduced in order to obtain simpler equations and physical inferences. Thereafter, the notion of the core force is studied. This is a correction to the classical force on dislocation, called Peach-Koehler force, and which appears when in the presence of strain gradients. It has been predicted by different approaches but never observed, until a work which is presented in this thesis. A simulation model to investigate such force and its results are shown. By comparing with the previous theoretical approaches, it is verified that none of them is capable of providing a way to quantitatively predict the core force. Furthermore, it is shown that, for some systems, results from the core force can be used to predict a definite value for the core energy of the dislocation.CAPESCNPqEsta tese investiga alguns limites da teoria clássica da eslasticidade em 2D, especialmente no que concerne a forças em defeitos topológicos chamados dislocations. Inicialmente, a tese comenta cada passo de aproximação usado ao se derivar a Elasticidade Clássica. Novas discussões são feitas sobre a suposição do contínuo e sobre os limites de sua aproximação soma-para-integral. Adicionalmente, um formalismo matemático alternativo para deformações em 2D é introduzido a fim de obter equações e inferências física mais simples. Após isso, a noção de força do “core” é estudada. Esta é uma correção à força clássica cobre um dislocation, chamada força de Peach-Koehler, e que apareça quando na presença de gradientes de deformação. Ela tinha sido prevista por diferentes abordagens, mas nunca observada, até um trabalho que é apresentado nesta tese. Um modelo de simulação para investigar esta força e seus resultados são mostrados. Ao comparar com as abordagens teóricas anteriores, verifica-se que nenhuma delas é capaz de fornecer uma forma de prever quantitativamente a força do “core”. Além disso, é mostrado que, para alguns sistemas, resultados desta força podem ser usados para prever um valor definido para a chamada energia do “core” de um dislocation.engUniversidade Federal de PernambucoPrograma de Pos Graduacao em FisicaUFPEBrasilAttribution-NonCommercial-NoDerivs 3.0 Brazilhttp://creativecommons.org/licenses/by-nc-nd/3.0/br/info:eu-repo/semantics/openAccessFísica teórica e computacionalFísica do estado sólidoCristais bidimensionaisTeoria da elasticidadePlasticidadeDislocationsForces on dislocations and the limits of classical elasticity in 2Dinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/doctoralThesisdoutoradoreponame:Repositório Institucional da UFPEinstname:Universidade Federal de Pernambuco (UFPE)instacron:UFPEORIGINALTESE Paulo César do Nascimento Pereira.pdfTESE Paulo César do Nascimento Pereira.pdfapplication/pdf3952128https://repositorio.ufpe.br/bitstream/123456789/54076/1/TESE%20Paulo%20C%c3%a9sar%20do%20Nascimento%20Pereira.pdf2e6434d6e0e8ba587c6a4f3804660183MD51LICENSElicense.txtlicense.txttext/plain; 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dc.title.pt_BR.fl_str_mv |
Forces on dislocations and the limits of classical elasticity in 2D |
title |
Forces on dislocations and the limits of classical elasticity in 2D |
spellingShingle |
Forces on dislocations and the limits of classical elasticity in 2D PEREIRA, Paulo César do Nascimento Física teórica e computacional Física do estado sólido Cristais bidimensionais Teoria da elasticidade Plasticidade Dislocations |
title_short |
Forces on dislocations and the limits of classical elasticity in 2D |
title_full |
Forces on dislocations and the limits of classical elasticity in 2D |
title_fullStr |
Forces on dislocations and the limits of classical elasticity in 2D |
title_full_unstemmed |
Forces on dislocations and the limits of classical elasticity in 2D |
title_sort |
Forces on dislocations and the limits of classical elasticity in 2D |
author |
PEREIRA, Paulo César do Nascimento |
author_facet |
PEREIRA, Paulo César do Nascimento |
author_role |
author |
dc.contributor.authorLattes.pt_BR.fl_str_mv |
http://lattes.cnpq.br/2084709462294618 |
dc.contributor.advisorLattes.pt_BR.fl_str_mv |
http://lattes.cnpq.br/1975993976921900 |
dc.contributor.author.fl_str_mv |
PEREIRA, Paulo César do Nascimento |
dc.contributor.advisor1.fl_str_mv |
APOLINÁRIO, Sérgio Wlademir da Silva |
contributor_str_mv |
APOLINÁRIO, Sérgio Wlademir da Silva |
dc.subject.por.fl_str_mv |
Física teórica e computacional Física do estado sólido Cristais bidimensionais Teoria da elasticidade Plasticidade Dislocations |
topic |
Física teórica e computacional Física do estado sólido Cristais bidimensionais Teoria da elasticidade Plasticidade Dislocations |
description |
This thesis investigates some limits of the classical theory of elasticity in 2D, especially concerning forces on topological defects called dislocations. Initially, the thesis comments each approximating step used in deriving Classical Elasticity. Novel discussions are made about the continuum assumption and the limits of the sum-to- integral approximation. Moreover, an alternative mathematical formalism to deformations in 2D is introduced in order to obtain simpler equations and physical inferences. Thereafter, the notion of the core force is studied. This is a correction to the classical force on dislocation, called Peach-Koehler force, and which appears when in the presence of strain gradients. It has been predicted by different approaches but never observed, until a work which is presented in this thesis. A simulation model to investigate such force and its results are shown. By comparing with the previous theoretical approaches, it is verified that none of them is capable of providing a way to quantitatively predict the core force. Furthermore, it is shown that, for some systems, results from the core force can be used to predict a definite value for the core energy of the dislocation. |
publishDate |
2023 |
dc.date.accessioned.fl_str_mv |
2023-12-13T13:21:29Z |
dc.date.available.fl_str_mv |
2023-12-13T13:21:29Z |
dc.date.issued.fl_str_mv |
2023-03-21 |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/doctoralThesis |
format |
doctoralThesis |
status_str |
publishedVersion |
dc.identifier.citation.fl_str_mv |
PEREIRA, Paulo César do Nascimento. Forces on dislocations and the limits of classical elasticity in 2D. 2023. Tese (Doutorado em Física) – Universidade Federal de Pernambuco, Recife, 2023. |
dc.identifier.uri.fl_str_mv |
https://repositorio.ufpe.br/handle/123456789/54076 |
identifier_str_mv |
PEREIRA, Paulo César do Nascimento. Forces on dislocations and the limits of classical elasticity in 2D. 2023. Tese (Doutorado em Física) – Universidade Federal de Pernambuco, Recife, 2023. |
url |
https://repositorio.ufpe.br/handle/123456789/54076 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.rights.driver.fl_str_mv |
Attribution-NonCommercial-NoDerivs 3.0 Brazil http://creativecommons.org/licenses/by-nc-nd/3.0/br/ info:eu-repo/semantics/openAccess |
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Attribution-NonCommercial-NoDerivs 3.0 Brazil http://creativecommons.org/licenses/by-nc-nd/3.0/br/ |
eu_rights_str_mv |
openAccess |
dc.publisher.none.fl_str_mv |
Universidade Federal de Pernambuco |
dc.publisher.program.fl_str_mv |
Programa de Pos Graduacao em Fisica |
dc.publisher.initials.fl_str_mv |
UFPE |
dc.publisher.country.fl_str_mv |
Brasil |
publisher.none.fl_str_mv |
Universidade Federal de Pernambuco |
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reponame:Repositório Institucional da UFPE instname:Universidade Federal de Pernambuco (UFPE) instacron:UFPE |
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UFPE |
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