Justifying linearization for nonlinear boundary homogenization on a grill-type winkler foundation

We address a nonlinear boundary homogenization problem associated to the deformations of a block of an elastic material with small reaction regions periodically distributed along a plane. We assume a nonlinear Winkler-Robin law which implies that a strong reaction takes place in these reaction regio...

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Autores: Nazarov, Sergey A., Pérez Martínez, María Eugenia|||0000-0001-7863-0043
Tipo de recurso: artículo
Fecha de publicación:2025
País:España
Institución:Universidad de Cantabria (UC)
Repositorio:UCrea Repositorio Abierto de la Universidad de Cantabria
Idioma:inglés
OAI Identifier:oai:repositorio.unican.es:10902/36845
Acceso en línea:https://hdl.handle.net/10902/36845
Access Level:acceso abierto
Palabra clave:Nonlinear Winkler foundations
Boundary homogenization
Elasticity operator
Capacity matrix
Critical relations
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spelling Justifying linearization for nonlinear boundary homogenization on a grill-type winkler foundationNazarov, Sergey A.Pérez Martínez, María Eugenia|||0000-0001-7863-0043Nonlinear Winkler foundationsBoundary homogenizationElasticity operatorCapacity matrixCritical relationsWe address a nonlinear boundary homogenization problem associated to the deformations of a block of an elastic material with small reaction regions periodically distributed along a plane. We assume a nonlinear Winkler-Robin law which implies that a strong reaction takes place in these reaction regions. Outside, on the plane, the surface is traction-free while the rest of the surface is clamped to an absolutely rigid profile. When dealing with critical sizes of the reaction regions, we show that, asymptotically, they behave as stuck regions, the homogenized boundary condition being a linear one with a new reaction term which contains a capacity matrix depending on the macroscopic variable. This matrix is defined through the solution of a parametric family of microscopic problems, the macroscopic variable being its parameter. Among others, to show the convergence of the solutions, we develop techniques that extend those both for nonlinear scalar problems and linear vector problems in the literature. We also address the extreme cases.The authors thank the anonymous Reviewers and the Editor for sharp comments which enabled us to revise and improve some technical questions and to make demonstrations more intelligible. The work of the first author has been financially supported by the Ministry of Science and Higher Education of the Russian Federation, project 124041500009-8. The work of the second author has been partially supported by Grant PID2022-137694NB-I00 funded by MICIU/AEI/10.13039/501100011033 and by ERDF/EU. Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature.Springer NatureUniversidad de Cantabria20252025-01-01journal articlehttp://purl.org/coar/resource_type/c_6501NAhttp://purl.org/coar/version/c_be7fb7dd8ff6fe43info:eu-repo/semantics/articlehttps://hdl.handle.net/10902/36845Journal of Elasticity, 2025, 157, 64reponame:UCrea Repositorio Abierto de la Universidad de Cantabriainstname:Universidad de Cantabria (UC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Attribution 4.0 Internationalhttp://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessoai:repositorio.unican.es:10902/368452026-06-02T12:39:31Z
dc.title.none.fl_str_mv Justifying linearization for nonlinear boundary homogenization on a grill-type winkler foundation
title Justifying linearization for nonlinear boundary homogenization on a grill-type winkler foundation
spellingShingle Justifying linearization for nonlinear boundary homogenization on a grill-type winkler foundation
Nazarov, Sergey A.
Nonlinear Winkler foundations
Boundary homogenization
Elasticity operator
Capacity matrix
Critical relations
title_short Justifying linearization for nonlinear boundary homogenization on a grill-type winkler foundation
title_full Justifying linearization for nonlinear boundary homogenization on a grill-type winkler foundation
title_fullStr Justifying linearization for nonlinear boundary homogenization on a grill-type winkler foundation
title_full_unstemmed Justifying linearization for nonlinear boundary homogenization on a grill-type winkler foundation
title_sort Justifying linearization for nonlinear boundary homogenization on a grill-type winkler foundation
dc.creator.none.fl_str_mv Nazarov, Sergey A.
Pérez Martínez, María Eugenia|||0000-0001-7863-0043
author Nazarov, Sergey A.
author_facet Nazarov, Sergey A.
Pérez Martínez, María Eugenia|||0000-0001-7863-0043
author_role author
author2 Pérez Martínez, María Eugenia|||0000-0001-7863-0043
author2_role author
dc.contributor.none.fl_str_mv Universidad de Cantabria
dc.subject.none.fl_str_mv Nonlinear Winkler foundations
Boundary homogenization
Elasticity operator
Capacity matrix
Critical relations
topic Nonlinear Winkler foundations
Boundary homogenization
Elasticity operator
Capacity matrix
Critical relations
description We address a nonlinear boundary homogenization problem associated to the deformations of a block of an elastic material with small reaction regions periodically distributed along a plane. We assume a nonlinear Winkler-Robin law which implies that a strong reaction takes place in these reaction regions. Outside, on the plane, the surface is traction-free while the rest of the surface is clamped to an absolutely rigid profile. When dealing with critical sizes of the reaction regions, we show that, asymptotically, they behave as stuck regions, the homogenized boundary condition being a linear one with a new reaction term which contains a capacity matrix depending on the macroscopic variable. This matrix is defined through the solution of a parametric family of microscopic problems, the macroscopic variable being its parameter. Among others, to show the convergence of the solutions, we develop techniques that extend those both for nonlinear scalar problems and linear vector problems in the literature. We also address the extreme cases.
publishDate 2025
dc.date.none.fl_str_mv 2025
2025-01-01
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
NA
http://purl.org/coar/version/c_be7fb7dd8ff6fe43
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/10902/36845
url https://hdl.handle.net/10902/36845
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution 4.0 International
http://creativecommons.org/licenses/by/4.0/
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 4.0 International
http://creativecommons.org/licenses/by/4.0/
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv Springer Nature
publisher.none.fl_str_mv Springer Nature
dc.source.none.fl_str_mv Journal of Elasticity, 2025, 157, 64
reponame:UCrea Repositorio Abierto de la Universidad de Cantabria
instname:Universidad de Cantabria (UC)
instname_str Universidad de Cantabria (UC)
reponame_str UCrea Repositorio Abierto de la Universidad de Cantabria
collection UCrea Repositorio Abierto de la Universidad de Cantabria
repository.name.fl_str_mv
repository.mail.fl_str_mv
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