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A Computational Multi-scale Approach to the Micro-discrete to Macro-continuum Transition / KIM HOANG

Swansea University Author: KIM HOANG

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DOI (Published version): 10.23889/SUthesis.58879

Abstract

The purpose of this work is the development and application of an RVE-based multiscale modelling framework for the transition from micro-discrete to macro- continuum by means of the Method of Multi-scale Virtual Power (MMVP). In con- tinua, the homogenisation operators (micro-to-macro) are successfu...

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Published: Swansea 2021
Institution: Swansea University
Degree level: Doctoral
Degree name: Ph.D
Supervisor: de Souza Neto, Eduardo A. ; Prof. Dettmer, Wulf G.
URI: https://cronfa.swan.ac.uk/Record/cronfa58879
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computational 1
elements 1
fem 1
homogenisation 1
macro-scale 1
micro-scale 1
modelling 1
multi-scale 1
power 1
representative 1
virtual 1
volume 1
first_indexed 2021-12-02T17:35:55Z
last_indexed 2021-12-03T04:19:48Z
id cronfa58879
recordtype RisThesis
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spelling 2021-12-02T18:21:46.7383300 v2 58879 2021-12-02 A Computational Multi-scale Approach to the Micro-discrete to Macro-continuum Transition d6c9b8d5fa5d60f28b50d5c2f6cceae1 KIM HOANG KIM HOANG true false 2021-12-02 The purpose of this work is the development and application of an RVE-based multiscale modelling framework for the transition from micro-discrete to macro- continuum by means of the Method of Multi-scale Virtual Power (MMVP). In con- tinua, the homogenisation operators (micro-to-macro) are successfully developed and implemented purely within the context of applied and computational solid mechanics. In order to predict mechanical properties and design new composite materials with complex microscopic structures, it is essential to use the discrete microscopic models based on Representative Volume Elements (RVE).In the first part of this thesis, a methodology is developed for the micro-discrete to macro-continuum transition by means of the MMVP. A discrete model of atomic structure is proposed which incorporates interatomic potential energies using well- known potential functions and molecular force field constants. At the micro-scale level, a Finite Element-type procedure is used to describe interatomic forces and a Newton-Raphson/arc-length method is used to solve the corresponding equilibriumproblem.The second part of this work investigates the macroscopic continuum elastic prop- erties and strength of atomic lattices. Macroscopic strength is determined as the onset of material instability at the macroscale. This is predicted by means of the analysis of the acoustic tensor associated with the homogenised constitutive tangent operators that results from the proposed micro-to-macro transition procedure.Numerical examples are presented including the modelling of two common atomic structures: graphene and boron nitride. In addition, the atomic RVE models are considered as a single layer and multiple layers, with and without defects. The ob- tained results are in good agreement with numerical and experimental data reported in the literature. The results demonstrate the capability of the proposed framework to predict the behaviour of macro-continuum with discrete structure at microscalelevel. E-Thesis Swansea Computational homogenisation, Multi-scale Modelling, Microdiscrete,Atomic structure, Representative Volume Element (RVE), Atomistic-tocontinuummodelling, Strain localisation, Acoustic tensor, Graphene, Boron-Nitride. 2 12 2021 2021-12-02 10.23889/SUthesis.58879 Kim-Quang Hoang. ORCiD identifier: https://orcid.org/0000-0002-4357-777X COLLEGE NANME COLLEGE CODE Swansea University de Souza Neto, Eduardo A. ; Prof. Dettmer, Wulf G. Doctoral Ph.D 2021-12-02T18:21:46.7383300 2021-12-02T17:25:57.7393955 Faculty of Science and Engineering School of Engineering and Applied Sciences - Uncategorised KIM HOANG 1 Under embargo Under embargo 2021-12-02T18:10:20.1219074 Output 4775529 application/pdf E-Thesis – open access true 2023-10-18T00:00:00.0000000 Copyright: The Author. true eng
title A Computational Multi-scale Approach to the Micro-discrete to Macro-continuum Transition
spellingShingle A Computational Multi-scale Approach to the Micro-discrete to Macro-continuum Transition
KIM HOANG
title_short A Computational Multi-scale Approach to the Micro-discrete to Macro-continuum Transition
title_full A Computational Multi-scale Approach to the Micro-discrete to Macro-continuum Transition
title_fullStr A Computational Multi-scale Approach to the Micro-discrete to Macro-continuum Transition
title_full_unstemmed A Computational Multi-scale Approach to the Micro-discrete to Macro-continuum Transition
title_sort A Computational Multi-scale Approach to the Micro-discrete to Macro-continuum Transition
author_id_str_mv d6c9b8d5fa5d60f28b50d5c2f6cceae1
author_id_fullname_str_mv d6c9b8d5fa5d60f28b50d5c2f6cceae1_***_KIM HOANG
author KIM HOANG
author2 KIM HOANG
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publishDate 2021
institution Swansea University
doi_str_mv 10.23889/SUthesis.58879
college_str Faculty of Science and Engineering
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hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Engineering and Applied Sciences - Uncategorised{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Engineering and Applied Sciences - Uncategorised
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description The purpose of this work is the development and application of an RVE-based multiscale modelling framework for the transition from micro-discrete to macro- continuum by means of the Method of Multi-scale Virtual Power (MMVP). In con- tinua, the homogenisation operators (micro-to-macro) are successfully developed and implemented purely within the context of applied and computational solid mechanics. In order to predict mechanical properties and design new composite materials with complex microscopic structures, it is essential to use the discrete microscopic models based on Representative Volume Elements (RVE).In the first part of this thesis, a methodology is developed for the micro-discrete to macro-continuum transition by means of the MMVP. A discrete model of atomic structure is proposed which incorporates interatomic potential energies using well- known potential functions and molecular force field constants. At the micro-scale level, a Finite Element-type procedure is used to describe interatomic forces and a Newton-Raphson/arc-length method is used to solve the corresponding equilibriumproblem.The second part of this work investigates the macroscopic continuum elastic prop- erties and strength of atomic lattices. Macroscopic strength is determined as the onset of material instability at the macroscale. This is predicted by means of the analysis of the acoustic tensor associated with the homogenised constitutive tangent operators that results from the proposed micro-to-macro transition procedure.Numerical examples are presented including the modelling of two common atomic structures: graphene and boron nitride. In addition, the atomic RVE models are considered as a single layer and multiple layers, with and without defects. The ob- tained results are in good agreement with numerical and experimental data reported in the literature. The results demonstrate the capability of the proposed framework to predict the behaviour of macro-continuum with discrete structure at microscalelevel.
published_date 2021-12-02T04:15:45Z
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score 11.012678

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