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Novel multiscale models in a multicontinuum approach to divide and conquer strategies

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

Computational and Applied Mathematics, Volume: 42, Issue: 4

Swansea University Author: Eduardo De Souza Neto Orcid Logo

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DOI (Published version): 10.1007/s40314-023-02288-9

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This contribution presents a comprehensive, in-depth analysis of the solution of the mechanical equilibrium problem for a generic solid with microstructure. The exact solution to this problem, referred to here as the reference solution, corresponds to the full-scale model of the problem that takes i...

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Published in: Computational and Applied Mathematics
ISSN: 2238-3603 1807-0302
Published: Springer Science and Business Media LLC 2023
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URI: https://cronfa.swan.ac.uk/Record/cronfa63228
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spelling v2 63228 2023-04-24 Novel multiscale models in a multicontinuum approach to divide and conquer strategies 91568dee6643b7d350f0d5e8edb7b46a 0000-0002-9378-4590 Eduardo De Souza Neto Eduardo De Souza Neto true false 2023-04-24 CIVL This contribution presents a comprehensive, in-depth analysis of the solution of the mechanical equilibrium problem for a generic solid with microstructure. The exact solution to this problem, referred to here as the reference solution, corresponds to the full-scale model of the problem that takes into account the kinematics and constitutive behavior of its entire microstructure. The analysis is carried out based on the Principle of Multiscale Virtual Power (PMVP) previously proposed by the authors. The PMVP provides a robust theoretical setting whereby the strong links between the reference solution and solutions of the mechanical equilibrium obtained using coarser scale models are brought to light. In this context, some fundamental properties of coarser scale solutions are identified by means of variational arguments. These findings unveil a new homogenization landscape for Representative Volume Element (RVE) multiscale theories, leading to the construction of new Minimal Kinematical Restriction (MKR)-based models where either displacements or tractions may be prescribed on the RVE boundary. A careful observation of the aforementioned landscape leads naturally to the proposal of a new, multicontinuum strategy (a generalized continuum counterpart of multigrid strategies) to approximate the reference solution at low computational cost. In the proposed strategy, the mechanical interactions among neighboring microcells are accounted for in an iterative fashion by means of suitably chosen boundary conditions enforced alternately on the new MKR-based models. The proposed developments are presented assuming a classical continuum at all scales, but the results are equally valid when different kinematical and constitutive assumptions are made at different scales. Journal Article Computational and Applied Mathematics 42 4 Springer Science and Business Media LLC 2238-3603 1807-0302 Multiscale modeling, Virtual power, Boundary conditions, Multigrid approach, Direct Numerical Solution 1 6 2023 2023-06-01 10.1007/s40314-023-02288-9 http://dx.doi.org/10.1007/s40314-023-02288-9 COLLEGE NANME Civil Engineering COLLEGE CODE CIVL Swansea University PJB and RAF acknowledge the support of the Brazilian agencies CNPq (grant numbers 301224/2016-1, 407751/2018-1, and 301636/2019-2), and FAPESP (grant numbers 2014/50889-7 and 2018/14221-2). PJS acknowledges the financial support from CONICET and ANPCyT (grant PICT-2020-SERIEA-02793). 2023-05-24T12:20:00.8070652 2023-04-24T09:36:21.5285954 Faculty of Science and Engineering School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Civil Engineering Raúl A. Feijóo 1 Pablo J. Blanco 0000-0003-3527-619x 2 Eduardo De Souza Neto 0000-0002-9378-4590 3 Pablo J. Sánchez 4 Under embargo Under embargo 2023-05-03T09:08:07.3360286 Output 719530 application/pdf Accepted Manuscript true 2024-04-06T00:00:00.0000000 true eng
title Novel multiscale models in a multicontinuum approach to divide and conquer strategies
spellingShingle Novel multiscale models in a multicontinuum approach to divide and conquer strategies
Eduardo De Souza Neto
title_short Novel multiscale models in a multicontinuum approach to divide and conquer strategies
title_full Novel multiscale models in a multicontinuum approach to divide and conquer strategies
title_fullStr Novel multiscale models in a multicontinuum approach to divide and conquer strategies
title_full_unstemmed Novel multiscale models in a multicontinuum approach to divide and conquer strategies
title_sort Novel multiscale models in a multicontinuum approach to divide and conquer strategies
author_id_str_mv 91568dee6643b7d350f0d5e8edb7b46a
author_id_fullname_str_mv 91568dee6643b7d350f0d5e8edb7b46a_***_Eduardo De Souza Neto
author Eduardo De Souza Neto
author2 Raúl A. Feijóo
Pablo J. Blanco
Eduardo De Souza Neto
Pablo J. Sánchez
format Journal article
container_title Computational and Applied Mathematics
container_volume 42
container_issue 4
publishDate 2023
institution Swansea University
issn 2238-3603
1807-0302
doi_str_mv 10.1007/s40314-023-02288-9
publisher Springer Science and Business Media LLC
college_str Faculty of Science and Engineering
hierarchytype
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
url http://dx.doi.org/10.1007/s40314-023-02288-9
document_store_str 0
active_str 0
description This contribution presents a comprehensive, in-depth analysis of the solution of the mechanical equilibrium problem for a generic solid with microstructure. The exact solution to this problem, referred to here as the reference solution, corresponds to the full-scale model of the problem that takes into account the kinematics and constitutive behavior of its entire microstructure. The analysis is carried out based on the Principle of Multiscale Virtual Power (PMVP) previously proposed by the authors. The PMVP provides a robust theoretical setting whereby the strong links between the reference solution and solutions of the mechanical equilibrium obtained using coarser scale models are brought to light. In this context, some fundamental properties of coarser scale solutions are identified by means of variational arguments. These findings unveil a new homogenization landscape for Representative Volume Element (RVE) multiscale theories, leading to the construction of new Minimal Kinematical Restriction (MKR)-based models where either displacements or tractions may be prescribed on the RVE boundary. A careful observation of the aforementioned landscape leads naturally to the proposal of a new, multicontinuum strategy (a generalized continuum counterpart of multigrid strategies) to approximate the reference solution at low computational cost. In the proposed strategy, the mechanical interactions among neighboring microcells are accounted for in an iterative fashion by means of suitably chosen boundary conditions enforced alternately on the new MKR-based models. The proposed developments are presented assuming a classical continuum at all scales, but the results are equally valid when different kinematical and constitutive assumptions are made at different scales.
published_date 2023-06-01T12:19:59Z
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score 11.016235

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