Multi-Scale Asymptotic Expansion for a Small Inclusion in Elastic Media
The aim of this paper is to present an asymptotic expansion of the influence of a small inclusion of different stiffness in an elastic media. The applicative interest of this study is to provide tools which take into account this influence and correct the deformation without inclusion by additive te...
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| Veröffentlicht in: | Journal of elasticity 2018-04, Vol.131 (2), p.207-237 |
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| container_title | Journal of elasticity |
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| creator | Arfaoui, Makrem Ben Hassine, Mohamed Rafik Moakher, Maher Renard, Yves Vial, Grégory |
| description | The aim of this paper is to present an asymptotic expansion of the influence of a small inclusion of different stiffness in an elastic media. The applicative interest of this study is to provide tools which take into account this influence and correct the deformation without inclusion by additive terms that can be precalculated and which depend only on the shape of the inclusion. We treat two problems: an anti-plane linearized elasticity problem and a plane strain problem. On every expansion order we provide corrective terms modeling the influence of the inclusion using techniques of scaling and multi-scale asymptotic expansions. The resulting expansion is validated by comparing it to a test case obtained by solving the Poisson transmission problem in the case of an inclusion of circular shape using the separation of variables method. Proofs of existence and uniqueness of our fields on unbounded domains are also adapted to the bidimensional Poisson problem and the linear elasticity problem. |
| doi_str_mv | 10.1007/s10659-017-9653-2 |
| format | Article |
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The applicative interest of this study is to provide tools which take into account this influence and correct the deformation without inclusion by additive terms that can be precalculated and which depend only on the shape of the inclusion. We treat two problems: an anti-plane linearized elasticity problem and a plane strain problem. On every expansion order we provide corrective terms modeling the influence of the inclusion using techniques of scaling and multi-scale asymptotic expansions. The resulting expansion is validated by comparing it to a test case obtained by solving the Poisson transmission problem in the case of an inclusion of circular shape using the separation of variables method. 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Proofs of existence and uniqueness of our fields on unbounded domains are also adapted to the bidimensional Poisson problem and the linear elasticity problem.</description><subject>Asymptotic properties</subject><subject>Asymptotic series</subject><subject>Automotive Engineering</subject><subject>Classical Mechanics</subject><subject>Deformation</subject><subject>Elastic media</subject><subject>Elasticity</subject><subject>Engineering Sciences</subject><subject>Mathematical Physics</subject><subject>Mathematics</subject><subject>Mechanical engineering</subject><subject>Mechanics</subject><subject>Multiscale analysis</subject><subject>Physics</subject><subject>Physics and Astronomy</subject><subject>Plane strain</subject><subject>Solid mechanics</subject><subject>Stiffness</subject><issn>0374-3535</issn><issn>1573-2681</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2018</creationdate><recordtype>article</recordtype><recordid>eNp1kLFOwzAQhi0EEqXwAGyRmBgCZzt2krGqSlupiKEwW1fHgVRuEuwE0bfHIQgmpjv9-u7T6SfkmsIdBUjvPQUp8hhoGudS8JidkAkVaVhkRk_JBHiaxFxwcU4uvN8DQJ4lMCHLx952VbzVaE0088dD2zVdpaPFZ4u1r5o6KhsXYbQ9oLXRuta2_06rOlpY9AP6aIoKL8lZidabq585JS8Pi-f5Kt48Ldfz2SbWPOddnHFEKUwpkMIOS8GoFgzSZIcM08LgrgyZSCSWaaFFoXUAdJbwXGBiIC_4lNyO3je0qnXVAd1RNVip1WyjhgxoAlIK9sECezOyrWvee-M7tW96V4f3FANKaS7DT4GiI6Vd470z5a-Wghq6VWO3wZyqoVs1mNl44wNbvxr3Z_7_6AuDNHr6</recordid><startdate>20180401</startdate><enddate>20180401</enddate><creator>Arfaoui, Makrem</creator><creator>Ben Hassine, Mohamed Rafik</creator><creator>Moakher, Maher</creator><creator>Renard, Yves</creator><creator>Vial, Grégory</creator><general>Springer Netherlands</general><general>Springer Nature B.V</general><general>Springer Verlag</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SR</scope><scope>7TB</scope><scope>8BQ</scope><scope>8FD</scope><scope>FR3</scope><scope>JG9</scope><scope>KR7</scope><scope>1XC</scope><scope>VOOES</scope><orcidid>https://orcid.org/0000-0003-4701-4488</orcidid></search><sort><creationdate>20180401</creationdate><title>Multi-Scale Asymptotic Expansion for a Small Inclusion in Elastic Media</title><author>Arfaoui, Makrem ; Ben Hassine, Mohamed Rafik ; Moakher, Maher ; Renard, Yves ; Vial, Grégory</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c393t-83aa65ef5a10baf521c52074ba2a7deabff52546af7dc5dcc21cc84395a4e09d3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2018</creationdate><topic>Asymptotic properties</topic><topic>Asymptotic series</topic><topic>Automotive Engineering</topic><topic>Classical Mechanics</topic><topic>Deformation</topic><topic>Elastic media</topic><topic>Elasticity</topic><topic>Engineering Sciences</topic><topic>Mathematical Physics</topic><topic>Mathematics</topic><topic>Mechanical engineering</topic><topic>Mechanics</topic><topic>Multiscale analysis</topic><topic>Physics</topic><topic>Physics and Astronomy</topic><topic>Plane strain</topic><topic>Solid mechanics</topic><topic>Stiffness</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Arfaoui, Makrem</creatorcontrib><creatorcontrib>Ben Hassine, Mohamed Rafik</creatorcontrib><creatorcontrib>Moakher, Maher</creatorcontrib><creatorcontrib>Renard, Yves</creatorcontrib><creatorcontrib>Vial, Grégory</creatorcontrib><collection>CrossRef</collection><collection>Engineered Materials Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>METADEX</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>Materials Research Database</collection><collection>Civil Engineering Abstracts</collection><collection>Hyper Article en Ligne (HAL)</collection><collection>Hyper Article en Ligne (HAL) (Open Access)</collection><jtitle>Journal of elasticity</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Arfaoui, Makrem</au><au>Ben Hassine, Mohamed Rafik</au><au>Moakher, Maher</au><au>Renard, Yves</au><au>Vial, Grégory</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Multi-Scale Asymptotic Expansion for a Small Inclusion in Elastic Media</atitle><jtitle>Journal of elasticity</jtitle><stitle>J Elast</stitle><date>2018-04-01</date><risdate>2018</risdate><volume>131</volume><issue>2</issue><spage>207</spage><epage>237</epage><pages>207-237</pages><issn>0374-3535</issn><eissn>1573-2681</eissn><abstract>The aim of this paper is to present an asymptotic expansion of the influence of a small inclusion of different stiffness in an elastic media. 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| language | eng |
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| source | SpringerNature Journals |
| subjects | Asymptotic properties Asymptotic series Automotive Engineering Classical Mechanics Deformation Elastic media Elasticity Engineering Sciences Mathematical Physics Mathematics Mechanical engineering Mechanics Multiscale analysis Physics Physics and Astronomy Plane strain Solid mechanics Stiffness |
| title | Multi-Scale Asymptotic Expansion for a Small Inclusion in Elastic Media |
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