Embedded Corrector Problems for Homogenization in Linear Elasticity
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| Název: | Embedded Corrector Problems for Homogenization in Linear Elasticity |
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| Autoři: | Ehrlacher, Virginie, Legoll, Frederic, Stamm, Benjamin, Xiang, Shuyang |
| Přispěvatelé: | Legoll, Frederic |
| Zdroj: | Multiscale Modeling & Simulation. 23:1236-1273 |
| Publication Status: | Preprint |
| Informace o vydavateli: | Society for Industrial & Applied Mathematics (SIAM), 2025. |
| Rok vydání: | 2025 |
| Témata: | Mathematics - Analysis of PDEs, FOS: Mathematics, Mathematics - Numerical Analysis, Numerical Analysis (math.NA), [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP], Analysis of PDEs (math.AP) |
| Popis: | In this article, we extend the study of embedded corrector problems, that we have previously introduced in the context of the homogenization of scalar diffusive equations, to the context of homogenized elastic properties of materials. This extension is not trivial and requires mathematical arguments specific to the elasticity case. Starting from a linear elasticity model with highly-oscillatory coefficients, we introduce several effective approximations of the homogenized tensor. These approximations are based on the solution to an embedded corrector problem, where a finite-size domain made of the linear elastic heterogeneous material is embedded in a linear elastic homogeneous infinite medium, the constant elasticity tensor of which has to be appropriately determined. The approximations we provide are proven to converge to the homogenized elasticity tensor when the size of the embedded domain tends to infinity. Some particular attention is devoted to the case of isotropic materials. |
| Druh dokumentu: | Article |
| Jazyk: | English |
| ISSN: | 1540-3467 1540-3459 |
| DOI: | 10.1137/23m1620752 |
| DOI: | 10.48550/arxiv.2307.03537 |
| Přístupová URL adresa: | http://arxiv.org/abs/2307.03537 https://hal.science/hal-04157434v1 |
| Rights: | arXiv Non-Exclusive Distribution |
| Přístupové číslo: | edsair.doi.dedup.....190845599ccb6b47a5b06e7ea1d99b47 |
| Databáze: | OpenAIRE |
Nájsť tento článok vo Web of Science | Abstrakt: | In this article, we extend the study of embedded corrector problems, that we have previously introduced in the context of the homogenization of scalar diffusive equations, to the context of homogenized elastic properties of materials. This extension is not trivial and requires mathematical arguments specific to the elasticity case. Starting from a linear elasticity model with highly-oscillatory coefficients, we introduce several effective approximations of the homogenized tensor. These approximations are based on the solution to an embedded corrector problem, where a finite-size domain made of the linear elastic heterogeneous material is embedded in a linear elastic homogeneous infinite medium, the constant elasticity tensor of which has to be appropriately determined. The approximations we provide are proven to converge to the homogenized elasticity tensor when the size of the embedded domain tends to infinity. Some particular attention is devoted to the case of isotropic materials. |
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| ISSN: | 15403467 15403459 |
| DOI: | 10.1137/23m1620752 |