Simple closed-form expressions for the effective properties of multilaminated flexoelectric composites
A multilayered rectangular flexoelectric structure is considered. This composite has a unit cell of N -constituents which belong to the cubic crystal symmetry. Using the two-scale asymptotic homogenization method, explicit expressions of the local problems are derived. Simple closed-form formulas of...
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| Veröffentlicht in: | Journal of engineering mathematics 2021-04, Vol.127 (1), Article 4 |
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| container_title | Journal of engineering mathematics |
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| creator | Guinovart-Sanjuán, David Vajravelu, Kuppalapalle Rodríguez-Ramos, Reinaldo Guinovart-Díaz, Raúl Sabina, Federico J. Merodio, Jose |
| description | A multilayered rectangular flexoelectric structure is considered. This composite has a unit cell of
N
-constituents which belong to the cubic crystal symmetry. Using the two-scale asymptotic homogenization method, explicit expressions of the local problems are derived. Simple closed-form formulas of the effective stiffness, piezoelectric, dielectric, and flexoelectric tensors are given, based on the solutions of local problems of stratified multilayered composites with perfect contact at the interface. These formulas provide information about the symmetry of the homogenized structure. As a numerical example, a bilaminate composite where the layers are perpendicular to the
x
3
axis is studied, and the constituents are Barium Titanate and Gallium Arsenide. The composite after the homogenization process exhibits flexoelectric properties with tetragonal
4
¯
2
m crystal symmetry. The effective properties are computed for several constituents of volume fractions. |
| doi_str_mv | 10.1007/s10665-021-10096-5 |
| format | Article |
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N
-constituents which belong to the cubic crystal symmetry. Using the two-scale asymptotic homogenization method, explicit expressions of the local problems are derived. Simple closed-form formulas of the effective stiffness, piezoelectric, dielectric, and flexoelectric tensors are given, based on the solutions of local problems of stratified multilayered composites with perfect contact at the interface. These formulas provide information about the symmetry of the homogenized structure. As a numerical example, a bilaminate composite where the layers are perpendicular to the
x
3
axis is studied, and the constituents are Barium Titanate and Gallium Arsenide. The composite after the homogenization process exhibits flexoelectric properties with tetragonal
4
¯
2
m crystal symmetry. The effective properties are computed for several constituents of volume fractions.</description><identifier>ISSN: 0022-0833</identifier><identifier>EISSN: 1573-2703</identifier><identifier>DOI: 10.1007/s10665-021-10096-5</identifier><language>eng</language><publisher>Dordrecht: Springer Netherlands</publisher><subject>Applications of Mathematics ; Arsenic ; Asymptotic methods ; Barium titanates ; Closed form solutions ; Composite materials ; Computational Mathematics and Numerical Analysis ; Constituents ; Exact solutions ; Gallium arsenide ; Homogenization ; Mathematical and Computational Engineering ; Mathematical Modeling and Industrial Mathematics ; Mathematics ; Mathematics and Statistics ; Mechanics of Fibre-reinforced Materials: Theory and Applications ; Part IV ; Piezoelectricity ; Properties (attributes) ; Stiffness ; Symmetry ; Tensors ; Theoretical and Applied Mechanics ; Unit cell</subject><ispartof>Journal of engineering mathematics, 2021-04, Vol.127 (1), Article 4</ispartof><rights>The Author(s), under exclusive licence to Springer Nature B.V. part of Springer Nature 2021</rights><rights>The Author(s), under exclusive licence to Springer Nature B.V. part of Springer Nature 2021.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c319t-8d82ccae2cecd4ed630e8b3b4f082fdeaf40c4162339f98da3c7e7a0207f78ed3</citedby><cites>FETCH-LOGICAL-c319t-8d82ccae2cecd4ed630e8b3b4f082fdeaf40c4162339f98da3c7e7a0207f78ed3</cites><orcidid>0000-0002-3093-6948</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s10665-021-10096-5$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s10665-021-10096-5$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,778,782,27907,27908,41471,42540,51302</link.rule.ids></links><search><creatorcontrib>Guinovart-Sanjuán, David</creatorcontrib><creatorcontrib>Vajravelu, Kuppalapalle</creatorcontrib><creatorcontrib>Rodríguez-Ramos, Reinaldo</creatorcontrib><creatorcontrib>Guinovart-Díaz, Raúl</creatorcontrib><creatorcontrib>Sabina, Federico J.</creatorcontrib><creatorcontrib>Merodio, Jose</creatorcontrib><title>Simple closed-form expressions for the effective properties of multilaminated flexoelectric composites</title><title>Journal of engineering mathematics</title><addtitle>J Eng Math</addtitle><description>A multilayered rectangular flexoelectric structure is considered. This composite has a unit cell of
N
-constituents which belong to the cubic crystal symmetry. Using the two-scale asymptotic homogenization method, explicit expressions of the local problems are derived. Simple closed-form formulas of the effective stiffness, piezoelectric, dielectric, and flexoelectric tensors are given, based on the solutions of local problems of stratified multilayered composites with perfect contact at the interface. These formulas provide information about the symmetry of the homogenized structure. As a numerical example, a bilaminate composite where the layers are perpendicular to the
x
3
axis is studied, and the constituents are Barium Titanate and Gallium Arsenide. The composite after the homogenization process exhibits flexoelectric properties with tetragonal
4
¯
2
m crystal symmetry. The effective properties are computed for several constituents of volume fractions.</description><subject>Applications of Mathematics</subject><subject>Arsenic</subject><subject>Asymptotic methods</subject><subject>Barium titanates</subject><subject>Closed form solutions</subject><subject>Composite materials</subject><subject>Computational Mathematics and Numerical Analysis</subject><subject>Constituents</subject><subject>Exact solutions</subject><subject>Gallium arsenide</subject><subject>Homogenization</subject><subject>Mathematical and Computational Engineering</subject><subject>Mathematical Modeling and Industrial Mathematics</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Mechanics of Fibre-reinforced Materials: Theory and Applications</subject><subject>Part IV</subject><subject>Piezoelectricity</subject><subject>Properties (attributes)</subject><subject>Stiffness</subject><subject>Symmetry</subject><subject>Tensors</subject><subject>Theoretical and Applied Mechanics</subject><subject>Unit cell</subject><issn>0022-0833</issn><issn>1573-2703</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><recordid>eNp9kE1LxDAQhoMouK7-AU8Bz9F8tE17lMUvWPCgnkM2mWiWtqlJVtZ_b7SCN0_DDM87MzwInTN6ySiVV4nRpqkJ5YyUvmtIfYAWrJaCcEnFIVpQyjmhrRDH6CSlLS1QW_EFck9-mHrApg8JLHEhDhj2U4SUfBgTLgOc3wCDc2Cy_wA8xTBBzB4SDg4Puz77Xg9-1Bksdj3sA_QFjd5gE4YpJJ8hnaIjp_sEZ791iV5ub55X92T9ePewul4TI1iXSWtbbowGbsDYCmwjKLQbsakcbbmzoF1FTcUaLkTnutZqYSRITTmVTrZgxRJdzHvLl-87SFltwy6O5aTiVScYk1I2heIzZWJIKYJTU_SDjp-KUfXtU80-VfGpfnyquoTEHEoFHl8h_q3-J_UFj9l7wg</recordid><startdate>20210401</startdate><enddate>20210401</enddate><creator>Guinovart-Sanjuán, David</creator><creator>Vajravelu, Kuppalapalle</creator><creator>Rodríguez-Ramos, Reinaldo</creator><creator>Guinovart-Díaz, Raúl</creator><creator>Sabina, Federico J.</creator><creator>Merodio, Jose</creator><general>Springer Netherlands</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0002-3093-6948</orcidid></search><sort><creationdate>20210401</creationdate><title>Simple closed-form expressions for the effective properties of multilaminated flexoelectric composites</title><author>Guinovart-Sanjuán, David ; Vajravelu, Kuppalapalle ; Rodríguez-Ramos, Reinaldo ; Guinovart-Díaz, Raúl ; Sabina, Federico J. ; Merodio, Jose</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c319t-8d82ccae2cecd4ed630e8b3b4f082fdeaf40c4162339f98da3c7e7a0207f78ed3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</creationdate><topic>Applications of Mathematics</topic><topic>Arsenic</topic><topic>Asymptotic methods</topic><topic>Barium titanates</topic><topic>Closed form solutions</topic><topic>Composite materials</topic><topic>Computational Mathematics and Numerical Analysis</topic><topic>Constituents</topic><topic>Exact solutions</topic><topic>Gallium arsenide</topic><topic>Homogenization</topic><topic>Mathematical and Computational Engineering</topic><topic>Mathematical Modeling and Industrial Mathematics</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Mechanics of Fibre-reinforced Materials: Theory and Applications</topic><topic>Part IV</topic><topic>Piezoelectricity</topic><topic>Properties (attributes)</topic><topic>Stiffness</topic><topic>Symmetry</topic><topic>Tensors</topic><topic>Theoretical and Applied Mechanics</topic><topic>Unit cell</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Guinovart-Sanjuán, David</creatorcontrib><creatorcontrib>Vajravelu, Kuppalapalle</creatorcontrib><creatorcontrib>Rodríguez-Ramos, Reinaldo</creatorcontrib><creatorcontrib>Guinovart-Díaz, Raúl</creatorcontrib><creatorcontrib>Sabina, Federico J.</creatorcontrib><creatorcontrib>Merodio, Jose</creatorcontrib><collection>CrossRef</collection><jtitle>Journal of engineering mathematics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Guinovart-Sanjuán, David</au><au>Vajravelu, Kuppalapalle</au><au>Rodríguez-Ramos, Reinaldo</au><au>Guinovart-Díaz, Raúl</au><au>Sabina, Federico J.</au><au>Merodio, Jose</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Simple closed-form expressions for the effective properties of multilaminated flexoelectric composites</atitle><jtitle>Journal of engineering mathematics</jtitle><stitle>J Eng Math</stitle><date>2021-04-01</date><risdate>2021</risdate><volume>127</volume><issue>1</issue><artnum>4</artnum><issn>0022-0833</issn><eissn>1573-2703</eissn><abstract>A multilayered rectangular flexoelectric structure is considered. This composite has a unit cell of
N
-constituents which belong to the cubic crystal symmetry. Using the two-scale asymptotic homogenization method, explicit expressions of the local problems are derived. Simple closed-form formulas of the effective stiffness, piezoelectric, dielectric, and flexoelectric tensors are given, based on the solutions of local problems of stratified multilayered composites with perfect contact at the interface. These formulas provide information about the symmetry of the homogenized structure. As a numerical example, a bilaminate composite where the layers are perpendicular to the
x
3
axis is studied, and the constituents are Barium Titanate and Gallium Arsenide. The composite after the homogenization process exhibits flexoelectric properties with tetragonal
4
¯
2
m crystal symmetry. The effective properties are computed for several constituents of volume fractions.</abstract><cop>Dordrecht</cop><pub>Springer Netherlands</pub><doi>10.1007/s10665-021-10096-5</doi><orcidid>https://orcid.org/0000-0002-3093-6948</orcidid></addata></record> |
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| source | Springer Nature - Complete Springer Journals |
| subjects | Applications of Mathematics Arsenic Asymptotic methods Barium titanates Closed form solutions Composite materials Computational Mathematics and Numerical Analysis Constituents Exact solutions Gallium arsenide Homogenization Mathematical and Computational Engineering Mathematical Modeling and Industrial Mathematics Mathematics Mathematics and Statistics Mechanics of Fibre-reinforced Materials: Theory and Applications Part IV Piezoelectricity Properties (attributes) Stiffness Symmetry Tensors Theoretical and Applied Mechanics Unit cell |
| title | Simple closed-form expressions for the effective properties of multilaminated flexoelectric composites |
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