A computational multiscale homogenization framework accounting for inertial effects: application to acoustic metamaterials modelling

A framework, based on an extended Hill–Mandel principle accounting for inertial effects (Multiscale Virtual Work principle), is developed for application to acoustic problems in the context of metamaterials modelling. The classical restrictions in the mean values of the micro-displacement fluctuatio...

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Authors: Roca Cazorla, David|||0000-0001-6336-6024, Lloberas Valls, Oriol|||0000-0001-8405-8725, Cante Terán, Juan Carlos|||0000-0002-9887-4448, Oliver Olivella, Xavier|||0000-0001-8717-1483
Format: article
Publication Date:2017
Country:España
Institution:Universitat Politècnica de Catalunya (UPC)
Repository:UPCommons. Portal del coneixement obert de la UPC
Language:English
OAI Identifier:oai:upcommons.upc.edu:2117/111284
Online Access:https://hdl.handle.net/2117/111284
https://dx.doi.org/10.1016/j.cma.2017.10.025
Access Level:Open access
Keyword:Metamaterials--Acoustic properties
Multiscale modelling Computational homogenization Inertial problems Acoustic metamaterials Local resonance phenomena COMP-DES-MAT Project COMPDESMAT Project
Metamaterials
Acústica
Àrees temàtiques de la UPC::Física::Acústica
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network_acronym_str ES
network_name_str España
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spelling A computational multiscale homogenization framework accounting for inertial effects: application to acoustic metamaterials modellingRoca Cazorla, David|||0000-0001-6336-6024Lloberas Valls, Oriol|||0000-0001-8405-8725Cante Terán, Juan Carlos|||0000-0002-9887-4448Oliver Olivella, Xavier|||0000-0001-8717-1483Metamaterials--Acoustic propertiesMultiscale modelling Computational homogenization Inertial problems Acoustic metamaterials Local resonance phenomena COMP-DES-MAT Project COMPDESMAT ProjectMetamaterialsAcústicaÀrees temàtiques de la UPC::Física::AcústicaA framework, based on an extended Hill–Mandel principle accounting for inertial effects (Multiscale Virtual Work principle), is developed for application to acoustic problems in the context of metamaterials modelling. The classical restrictions in the mean values of the micro-displacement fluctuations and their gradients are then accounted for in a saddle-point formulation of that variational principle in terms of Lagrange functionals. A physical interpretation of the involved Lagrange multipliers can then be readily obtained. The framework is specifically tailored for modelling the phenomena involved in Locally Resonant Acoustic Metamaterials (LRAM). In this view, several additional hypotheses based on scale separation are used to split the fully coupled micro-macro set of equations into a quasi-static and an inertial system. These are then solved by considering a projection of the microscale equations into their natural modes, which allows for a low-cost computational treatment of the multiscale problem. On this basis, the issue of numerically capturing the local resonance phenomena in a FE context is addressed. Objectivity of the obtained results in terms of the macroscopic Finite Element (FE) discretization is checked as well as accuracy of the homogenization procedure by comparing with direct numerical simulations (DNS). The appearance of local resonance band-gaps is then modelled for a homogeneous 2D problem and its extension to multi-layered macroscopic material is presented as an initial attempt towards acoustic metamaterial design for tailored band-gap attenuation.Peer Reviewed20182018-03-0120172017-11-28journal articlehttp://purl.org/coar/resource_type/c_6501AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/111284https://dx.doi.org/10.1016/j.cma.2017.10.025reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)InglésengEuropean Commission http://dx.doi.org/10.13039/100011102 Seventh Framework Programme 320815 Advanced tools for computational design of engineering materialsopen accesshttp://purl.org/coar/access_right/c_abf2Attribution-NonCommercial-NoDerivs 3.0 Spainhttp://creativecommons.org/licenses/by-nc-nd/3.0/es/info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/1112842026-05-27T15:37:01Z
dc.title.none.fl_str_mv A computational multiscale homogenization framework accounting for inertial effects: application to acoustic metamaterials modelling
title A computational multiscale homogenization framework accounting for inertial effects: application to acoustic metamaterials modelling
spellingShingle A computational multiscale homogenization framework accounting for inertial effects: application to acoustic metamaterials modelling
Roca Cazorla, David|||0000-0001-6336-6024
Metamaterials--Acoustic properties
Multiscale modelling Computational homogenization Inertial problems Acoustic metamaterials Local resonance phenomena COMP-DES-MAT Project COMPDESMAT Project
Metamaterials
Acústica
Àrees temàtiques de la UPC::Física::Acústica
title_short A computational multiscale homogenization framework accounting for inertial effects: application to acoustic metamaterials modelling
title_full A computational multiscale homogenization framework accounting for inertial effects: application to acoustic metamaterials modelling
title_fullStr A computational multiscale homogenization framework accounting for inertial effects: application to acoustic metamaterials modelling
title_full_unstemmed A computational multiscale homogenization framework accounting for inertial effects: application to acoustic metamaterials modelling
title_sort A computational multiscale homogenization framework accounting for inertial effects: application to acoustic metamaterials modelling
dc.creator.none.fl_str_mv Roca Cazorla, David|||0000-0001-6336-6024
Lloberas Valls, Oriol|||0000-0001-8405-8725
Cante Terán, Juan Carlos|||0000-0002-9887-4448
Oliver Olivella, Xavier|||0000-0001-8717-1483
author Roca Cazorla, David|||0000-0001-6336-6024
author_facet Roca Cazorla, David|||0000-0001-6336-6024
Lloberas Valls, Oriol|||0000-0001-8405-8725
Cante Terán, Juan Carlos|||0000-0002-9887-4448
Oliver Olivella, Xavier|||0000-0001-8717-1483
author_role author
author2 Lloberas Valls, Oriol|||0000-0001-8405-8725
Cante Terán, Juan Carlos|||0000-0002-9887-4448
Oliver Olivella, Xavier|||0000-0001-8717-1483
author2_role author
author
author
dc.subject.none.fl_str_mv Metamaterials--Acoustic properties
Multiscale modelling Computational homogenization Inertial problems Acoustic metamaterials Local resonance phenomena COMP-DES-MAT Project COMPDESMAT Project
Metamaterials
Acústica
Àrees temàtiques de la UPC::Física::Acústica
topic Metamaterials--Acoustic properties
Multiscale modelling Computational homogenization Inertial problems Acoustic metamaterials Local resonance phenomena COMP-DES-MAT Project COMPDESMAT Project
Metamaterials
Acústica
Àrees temàtiques de la UPC::Física::Acústica
description A framework, based on an extended Hill–Mandel principle accounting for inertial effects (Multiscale Virtual Work principle), is developed for application to acoustic problems in the context of metamaterials modelling. The classical restrictions in the mean values of the micro-displacement fluctuations and their gradients are then accounted for in a saddle-point formulation of that variational principle in terms of Lagrange functionals. A physical interpretation of the involved Lagrange multipliers can then be readily obtained. The framework is specifically tailored for modelling the phenomena involved in Locally Resonant Acoustic Metamaterials (LRAM). In this view, several additional hypotheses based on scale separation are used to split the fully coupled micro-macro set of equations into a quasi-static and an inertial system. These are then solved by considering a projection of the microscale equations into their natural modes, which allows for a low-cost computational treatment of the multiscale problem. On this basis, the issue of numerically capturing the local resonance phenomena in a FE context is addressed. Objectivity of the obtained results in terms of the macroscopic Finite Element (FE) discretization is checked as well as accuracy of the homogenization procedure by comparing with direct numerical simulations (DNS). The appearance of local resonance band-gaps is then modelled for a homogeneous 2D problem and its extension to multi-layered macroscopic material is presented as an initial attempt towards acoustic metamaterial design for tailored band-gap attenuation.
publishDate 2017
dc.date.none.fl_str_mv 2017
2017-11-28
2018
2018-03-01
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
AM
http://purl.org/coar/version/c_ab4af688f83e57aa
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/111284
https://dx.doi.org/10.1016/j.cma.2017.10.025
url https://hdl.handle.net/2117/111284
https://dx.doi.org/10.1016/j.cma.2017.10.025
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv European Commission http://dx.doi.org/10.13039/100011102 Seventh Framework Programme 320815 Advanced tools for computational design of engineering materials
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivs 3.0 Spain
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivs 3.0 Spain
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:UPCommons. Portal del coneixement obert de la UPC
instname:Universitat Politècnica de Catalunya (UPC)
instname_str Universitat Politècnica de Catalunya (UPC)
reponame_str UPCommons. Portal del coneixement obert de la UPC
collection UPCommons. Portal del coneixement obert de la UPC
repository.name.fl_str_mv
repository.mail.fl_str_mv
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