دورية أكاديمية
A two-dimensional labile aether through homogenization
| العنوان: | A two-dimensional labile aether through homogenization |
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| المؤلفون: | Briane, Marc, Francfort, Gilles A. |
| المساهمون: | Institut de Recherche Mathématique de Rennes (IRMAR), Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-École normale supérieure - Rennes (ENS Rennes)-Université de Rennes 2 (UR2)-Centre National de la Recherche Scientifique (CNRS)-INSTITUT AGRO Agrocampus Ouest, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro), Laboratoire Analyse, Géométrie et Applications (LAGA), Université Paris 8 Vincennes-Saint-Denis (UP8)-Université Paris 13 (UP13)-Institut Galilée-Centre National de la Recherche Scientifique (CNRS), DMS- 1615839, National Science Foundation, ANR-11-LABX-0020,LEBESGUE,Centre de Mathématiques Henri Lebesgue : fondements, interactions, applications et Formation(2011) |
| المصدر: | ISSN: 0010-3616. |
| بيانات النشر: | HAL CCSD Springer Verlag |
| سنة النشر: | 2019 |
| المجموعة: | Archive Ouverte de l'Université Rennes (HAL) |
| مصطلحات موضوعية: | lamination, homogenization, Linear elasticity, wave propagation, ellipticity, 35B27, 74B05, 74J15, 74Q15, [PHYS.COND.CM-MS]Physics [physics]/Condensed Matter [cond-mat]/Materials Science [cond-mat.mtrl-sci], [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], [PHYS.MECA.MEMA]Physics [physics]/Mechanics [physics]/Mechanics of materials [physics.class-ph] |
| الوصف: | International audience ; Homogenization in linear elliptic problems usually assumes coercivity of the accompanying Dirichlet form. In linear elasticity, coercivity is not ensured through mere (strong) ellipticity so that the usual estimates that render homogenization meaningful break down unless stronger assumptions, like very strong ellipticity, are put into place. Here, we demonstrate that a L^2-type homogenization process can still be performed, very strong ellipticity notwithstanding, for a specific two-phase two dimensional problem whose significance derives from prior work establishing that one can lose strong ellipticity in such a setting, provided that homogenization turns out to be meaningful.A striking consequence is that, in an elasto-dynamic setting, some two-phase homogenized laminate may support plane wave propagation in the direction of lamination on a bounded domain with Dirichlet boundary conditions, a possibility which does not exist for the associated two-phase microstructure at a fixed scale. Also, that material blocks longitudinal waves in the direction of lamination, thereby acting as a two-dimensional aether in the sense of e.g. Cauchy. |
| نوع الوثيقة: | article in journal/newspaper |
| اللغة: | English |
| العلاقة: | info:eu-repo/semantics/altIdentifier/arxiv/1802.00834; hal-01696161; https://hal.science/hal-01696161Test; https://hal.science/hal-01696161v2/documentTest; https://hal.science/hal-01696161v2/file/MB.periodic_homogenization_revisited_the-L2-theory-22fev18.pdfTest; ARXIV: 1802.00834 |
| DOI: | 10.1007/s00220-019-03333-7 |
| الإتاحة: | https://doi.org/10.1007/s00220-019-03333-7Test https://hal.science/hal-01696161Test https://hal.science/hal-01696161v2/documentTest https://hal.science/hal-01696161v2/file/MB.periodic_homogenization_revisited_the-L2-theory-22fev18.pdfTest |
| حقوق: | info:eu-repo/semantics/OpenAccess |
| رقم الانضمام: | edsbas.E6296C3B |
| قاعدة البيانات: | BASE |
| DOI: | 10.1007/s00220-019-03333-7 |
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