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Variational Foundations and Generalized Unified Theory of RVE-Based Multiscale Models

Pablo J. Blanco, Pablo J. Sánchez, Eduardo De Souza Neto Orcid Logo, Raúl A. Feijóo

Archives of Computational Methods in Engineering, Volume: 23, Issue: 2, Pages: 191 - 253

Swansea University Author: Eduardo De Souza Neto Orcid Logo

Abstract

A unified variational theory is proposed for a general class of multiscale models based on the concept of Representative Volume Element. The entire theory lies on three fundamental principles: (1) kinematical admissibility, whereby the macro- and micro-scale kinematics are defined and linked in a ph...

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Published in: Archives of Computational Methods in Engineering
ISSN: 1134-3060 1886-1784
Published: 2016
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URI: https://cronfa.swan.ac.uk/Record/cronfa22546
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spelling 2017-06-30T15:07:29.7873580 v2 22546 2015-07-20 Variational Foundations and Generalized Unified Theory of RVE-Based Multiscale Models 91568dee6643b7d350f0d5e8edb7b46a 0000-0002-9378-4590 Eduardo De Souza Neto Eduardo De Souza Neto true false 2015-07-20 CIVL A unified variational theory is proposed for a general class of multiscale models based on the concept of Representative Volume Element. The entire theory lies on three fundamental principles: (1) kinematical admissibility, whereby the macro- and micro-scale kinematics are defined and linked in a physically meaningful way; (2) duality, through which the natures of the force- and stress-like quantities are uniquely identified as the duals (power-conjugates) of the adopted kinematical variables; and (3) the Principle of Multiscale Virtual Power, a generalization of the well-known Hill-Mandel Principle of Macrohomogeneity, from which equilibrium equations and homogenization relations for the force- and stress-like quantities are unequivocally obtained by straightforward variational arguments. The proposed theory provides a clear, logically-structured framework within which existing formulations can be rationally justified and new, more general multiscale models can be rigorously derived in well-defined steps. Its generality allows the treatment of problems involving phenomena as diverse as dynamics, higher order strain effects, material failure with kinematical discontinuities, fluid mechanics and coupled multi-physics. This is illustrated in a number of examples where a range of models is systematically derived by following the same steps. Due to the variational basis of the theory, the format in which derived models are presented is naturally well suited for discretization by finite element-based or related methods of numerical approximation. Numerical examples illustrate the use of resulting models, including a non-conventional failure-oriented model with discontinuous kinematics, in practical computations. Journal Article Archives of Computational Methods in Engineering 23 2 191 253 1134-3060 1886-1784 30 6 2016 2016-06-30 10.1007/s11831-014-9137-5 COLLEGE NANME Civil Engineering COLLEGE CODE CIVL Swansea University 2017-06-30T15:07:29.7873580 2015-07-20T13:57:53.1355742 Faculty of Science and Engineering School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Civil Engineering Pablo J. Blanco 1 Pablo J. Sánchez 2 Eduardo De Souza Neto 0000-0002-9378-4590 3 Raúl A. Feijóo 4 0022546-27022017200629.pdf PaperDualityMultiscale-v45_ARCME_FEIJOO-et-al.pdf 2017-02-27T20:06:29.5200000 Output 3257085 application/pdf Accepted Manuscript true 2017-02-27T00:00:00.0000000 false eng
title Variational Foundations and Generalized Unified Theory of RVE-Based Multiscale Models
spellingShingle Variational Foundations and Generalized Unified Theory of RVE-Based Multiscale Models
Eduardo De Souza Neto
title_short Variational Foundations and Generalized Unified Theory of RVE-Based Multiscale Models
title_full Variational Foundations and Generalized Unified Theory of RVE-Based Multiscale Models
title_fullStr Variational Foundations and Generalized Unified Theory of RVE-Based Multiscale Models
title_full_unstemmed Variational Foundations and Generalized Unified Theory of RVE-Based Multiscale Models
title_sort Variational Foundations and Generalized Unified Theory of RVE-Based Multiscale Models
author_id_str_mv 91568dee6643b7d350f0d5e8edb7b46a
author_id_fullname_str_mv 91568dee6643b7d350f0d5e8edb7b46a_***_Eduardo De Souza Neto
author Eduardo De Souza Neto
author2 Pablo J. Blanco
Pablo J. Sánchez
Eduardo De Souza Neto
Raúl A. Feijóo
format Journal article
container_title Archives of Computational Methods in Engineering
container_volume 23
container_issue 2
container_start_page 191
publishDate 2016
institution Swansea University
issn 1134-3060
1886-1784
doi_str_mv 10.1007/s11831-014-9137-5
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 Aerospace, Civil, Electrical, General and Mechanical Engineering - Civil Engineering{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Civil Engineering
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description A unified variational theory is proposed for a general class of multiscale models based on the concept of Representative Volume Element. The entire theory lies on three fundamental principles: (1) kinematical admissibility, whereby the macro- and micro-scale kinematics are defined and linked in a physically meaningful way; (2) duality, through which the natures of the force- and stress-like quantities are uniquely identified as the duals (power-conjugates) of the adopted kinematical variables; and (3) the Principle of Multiscale Virtual Power, a generalization of the well-known Hill-Mandel Principle of Macrohomogeneity, from which equilibrium equations and homogenization relations for the force- and stress-like quantities are unequivocally obtained by straightforward variational arguments. The proposed theory provides a clear, logically-structured framework within which existing formulations can be rationally justified and new, more general multiscale models can be rigorously derived in well-defined steps. Its generality allows the treatment of problems involving phenomena as diverse as dynamics, higher order strain effects, material failure with kinematical discontinuities, fluid mechanics and coupled multi-physics. This is illustrated in a number of examples where a range of models is systematically derived by following the same steps. Due to the variational basis of the theory, the format in which derived models are presented is naturally well suited for discretization by finite element-based or related methods of numerical approximation. Numerical examples illustrate the use of resulting models, including a non-conventional failure-oriented model with discontinuous kinematics, in practical computations.
published_date 2016-06-30T03:27:19Z
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