Homogenization of viscoelastic composites with fibres of diamond-shaped cross-section
The present paper provides details on the application of asymptotic homogenization techniques to the analysis of viscoelastic composite materials with fibres of diamond-shaped cross-section. The Correspondence principle allows transforming the governing boundary value problems to quasistatic ones. T...
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| Veröffentlicht in: | Acta mechanica 2012-05, Vol.223 (5), p.1093-1100 |
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| container_title | Acta mechanica |
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| creator | Andrianov, Igor V. Danishevs’kyy, Vladyslav V. Kholod, Elena G. |
| description | The present paper provides details on the application of asymptotic homogenization techniques to the analysis of viscoelastic composite materials with fibres of diamond-shaped cross-section. The Correspondence principle allows transforming the governing boundary value problems to quasistatic ones. Then, we apply the homogenization approach. For solving the cell problem for small volume fractions, the boundary shape perturbation procedure and the composite cylinder assemblage model are used. For a volume fraction equal to 1/2, we use the Dykhne–Keller–Mendelson formula. Matching of limit solutions by two-point Padé approximants gives a formula for the effective properties valid for any volume fraction from the interval [0, 0.5]. |
| doi_str_mv | 10.1007/s00707-011-0608-6 |
| format | Article |
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The Correspondence principle allows transforming the governing boundary value problems to quasistatic ones. Then, we apply the homogenization approach. For solving the cell problem for small volume fractions, the boundary shape perturbation procedure and the composite cylinder assemblage model are used. For a volume fraction equal to 1/2, we use the Dykhne–Keller–Mendelson formula. 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The Correspondence principle allows transforming the governing boundary value problems to quasistatic ones. Then, we apply the homogenization approach. For solving the cell problem for small volume fractions, the boundary shape perturbation procedure and the composite cylinder assemblage model are used. For a volume fraction equal to 1/2, we use the Dykhne–Keller–Mendelson formula. Matching of limit solutions by two-point Padé approximants gives a formula for the effective properties valid for any volume fraction from the interval [0, 0.5].</description><subject>Analysis</subject><subject>Asymptotic methods</subject><subject>Boundary value problems</subject><subject>Classical and Continuum Physics</subject><subject>Composite materials</subject><subject>Composite materials industry</subject><subject>Control</subject><subject>Cylinders</subject><subject>Diamond crystals</subject><subject>Diamonds</subject><subject>Dynamical Systems</subject><subject>Engineering</subject><subject>Engineering Thermodynamics</subject><subject>Fibres</subject><subject>Heat and Mass Transfer</subject><subject>Homogenization</subject><subject>Homogenizing</subject><subject>Materials science</subject><subject>Mathematical models</subject><subject>Solid Mechanics</subject><subject>Theoretical and Applied Mechanics</subject><subject>Vibration</subject><subject>Viscoelasticity</subject><subject>Volume fraction</subject><issn>0001-5970</issn><issn>1619-6937</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2012</creationdate><recordtype>article</recordtype><sourceid>8G5</sourceid><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>GNUQQ</sourceid><sourceid>GUQSH</sourceid><sourceid>M2O</sourceid><recordid>eNp1kc1qGzEUhUVpIa6bB8huIJts5FxJI2m0DCFNAoZs4vUga65shZmRK41b2qePnMkiBCqB_vjO4YhDyAWDFQPQ17ksoCkwRkFBQ9UXsmCKGaqM0F_JAgAYlUbDGfme80u5cV2zBdk8xCHucAz_7BTiWEVf_Q7ZRextnoKrXBwOMYcJc_UnTPvKh20q54J1wQ5x7Gje2wN2lUsxZ5rRnWx-kG_e9hnP3_cl2fy8e759oOun-8fbmzV1omkm2tXWS6yRS8YRHJdby2oUwmsnFGw5dNo04KTETgrDjOCm25raCSO9Q2HEklzNvocUfx0xT-1QwmPf2xHjMbcMOG-Uargq6OUn9CUe01jSFQoaA0xJXqjVTO1sj20YfZySdWV2OAQXR_ShvN8IWUYjdF0EbBa8_T-hbw8pDDb9La4nY93OzbSlmfbUTHuKwmdNLuy4w_Qxyv9Er0BCkGg</recordid><startdate>20120501</startdate><enddate>20120501</enddate><creator>Andrianov, Igor V.</creator><creator>Danishevs’kyy, Vladyslav V.</creator><creator>Kholod, Elena G.</creator><general>Springer Vienna</general><general>Springer</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>3V.</scope><scope>7TB</scope><scope>7XB</scope><scope>88I</scope><scope>8AO</scope><scope>8FD</scope><scope>8FE</scope><scope>8FG</scope><scope>8FK</scope><scope>8G5</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>FR3</scope><scope>GNUQQ</scope><scope>GUQSH</scope><scope>HCIFZ</scope><scope>KR7</scope><scope>L6V</scope><scope>M2O</scope><scope>M2P</scope><scope>M7S</scope><scope>MBDVC</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope><scope>Q9U</scope><scope>S0W</scope></search><sort><creationdate>20120501</creationdate><title>Homogenization of viscoelastic composites with fibres of diamond-shaped cross-section</title><author>Andrianov, Igor V. ; Danishevs’kyy, Vladyslav V. ; Kholod, Elena G.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c388t-d4af5e4e2512e0c25ba14e33f7c360b20d7980c55ed53919329db94c395fce393</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2012</creationdate><topic>Analysis</topic><topic>Asymptotic methods</topic><topic>Boundary value problems</topic><topic>Classical and Continuum Physics</topic><topic>Composite materials</topic><topic>Composite materials industry</topic><topic>Control</topic><topic>Cylinders</topic><topic>Diamond crystals</topic><topic>Diamonds</topic><topic>Dynamical Systems</topic><topic>Engineering</topic><topic>Engineering Thermodynamics</topic><topic>Fibres</topic><topic>Heat and Mass Transfer</topic><topic>Homogenization</topic><topic>Homogenizing</topic><topic>Materials science</topic><topic>Mathematical models</topic><topic>Solid Mechanics</topic><topic>Theoretical and Applied Mechanics</topic><topic>Vibration</topic><topic>Viscoelasticity</topic><topic>Volume fraction</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Andrianov, Igor V.</creatorcontrib><creatorcontrib>Danishevs’kyy, Vladyslav V.</creatorcontrib><creatorcontrib>Kholod, Elena G.</creatorcontrib><collection>CrossRef</collection><collection>ProQuest Central (Corporate)</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>ProQuest Central (purchase pre-March 2016)</collection><collection>Science Database (Alumni Edition)</collection><collection>ProQuest Pharma Collection</collection><collection>Technology Research Database</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest Central (Alumni) (purchase pre-March 2016)</collection><collection>Research Library (Alumni Edition)</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>Engineering Research Database</collection><collection>ProQuest Central Student</collection><collection>Research Library Prep</collection><collection>SciTech Premium Collection</collection><collection>Civil Engineering Abstracts</collection><collection>ProQuest Engineering Collection</collection><collection>Research Library</collection><collection>Science Database</collection><collection>Engineering Database</collection><collection>Research Library (Corporate)</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering Collection</collection><collection>ProQuest Central Basic</collection><collection>DELNET Engineering & Technology Collection</collection><jtitle>Acta mechanica</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Andrianov, Igor V.</au><au>Danishevs’kyy, Vladyslav V.</au><au>Kholod, Elena G.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Homogenization of viscoelastic composites with fibres of diamond-shaped cross-section</atitle><jtitle>Acta mechanica</jtitle><stitle>Acta Mech</stitle><date>2012-05-01</date><risdate>2012</risdate><volume>223</volume><issue>5</issue><spage>1093</spage><epage>1100</epage><pages>1093-1100</pages><issn>0001-5970</issn><eissn>1619-6937</eissn><coden>AMHCAP</coden><abstract>The present paper provides details on the application of asymptotic homogenization techniques to the analysis of viscoelastic composite materials with fibres of diamond-shaped cross-section. The Correspondence principle allows transforming the governing boundary value problems to quasistatic ones. Then, we apply the homogenization approach. For solving the cell problem for small volume fractions, the boundary shape perturbation procedure and the composite cylinder assemblage model are used. For a volume fraction equal to 1/2, we use the Dykhne–Keller–Mendelson formula. Matching of limit solutions by two-point Padé approximants gives a formula for the effective properties valid for any volume fraction from the interval [0, 0.5].</abstract><cop>Vienna</cop><pub>Springer Vienna</pub><doi>10.1007/s00707-011-0608-6</doi><tpages>8</tpages></addata></record> |
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| subjects | Analysis Asymptotic methods Boundary value problems Classical and Continuum Physics Composite materials Composite materials industry Control Cylinders Diamond crystals Diamonds Dynamical Systems Engineering Engineering Thermodynamics Fibres Heat and Mass Transfer Homogenization Homogenizing Materials science Mathematical models Solid Mechanics Theoretical and Applied Mechanics Vibration Viscoelasticity Volume fraction |
| title | Homogenization of viscoelastic composites with fibres of diamond-shaped cross-section |
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