Non-local theory solution of a mode-I crack in a piezoelectric/piezomagnetic composite material plane
The non-local theory solution of a mode-I permeable crack in a piezoelectric/piezomagnetic composite material plane was given by using the generalized Almansi’s theorem and the Schmidt method in this paper. The problem was formulated through Fourier transform into two pairs of dual integral equation...
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| Veröffentlicht in: | International journal of fracture 2010-08, Vol.164 (2), p.213-229 |
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| creator | Zhang, Pei-Wei Zhou, Zhen-Gong Wu, Lin-Zhi |
| description | The non-local theory solution of a mode-I permeable crack in a piezoelectric/piezomagnetic composite material plane was given by using the generalized Almansi’s theorem and the Schmidt method in this paper. The problem was formulated through Fourier transform into two pairs of dual integral equations, in which the unknown variables are the displacement jumps across the crack surfaces. To solve the dual integral equations, the displacement jumps across the crack surfaces were directly expanded as a series of Jacobi polynomials. Numerical examples were provided to show the effects of the crack length and the lattice parameter on the stress field, the electric displacement field and the magnetic flux field near the crack tips. Unlike the classical elasticity solutions, it is found that no stress, electric displacement and magnetic flux singularities are present at the crack tips in piezoelectric/piezomagnetic composite materials. The non-local elastic solution yields a finite hoop stress at the crack tip, thus allowing us to use the maximum stress as a fracture criterion. |
| doi_str_mv | 10.1007/s10704-010-9477-6 |
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The problem was formulated through Fourier transform into two pairs of dual integral equations, in which the unknown variables are the displacement jumps across the crack surfaces. To solve the dual integral equations, the displacement jumps across the crack surfaces were directly expanded as a series of Jacobi polynomials. Numerical examples were provided to show the effects of the crack length and the lattice parameter on the stress field, the electric displacement field and the magnetic flux field near the crack tips. Unlike the classical elasticity solutions, it is found that no stress, electric displacement and magnetic flux singularities are present at the crack tips in piezoelectric/piezomagnetic composite materials. The non-local elastic solution yields a finite hoop stress at the crack tip, thus allowing us to use the maximum stress as a fracture criterion.</description><identifier>ISSN: 0376-9429</identifier><identifier>EISSN: 1573-2673</identifier><identifier>DOI: 10.1007/s10704-010-9477-6</identifier><identifier>CODEN: IJFRAP</identifier><language>eng</language><publisher>Dordrecht: Springer Netherlands</publisher><subject>Automotive Engineering ; Characterization and Evaluation of Materials ; Chemistry and Materials Science ; Civil Engineering ; Classical Mechanics ; Composite materials ; Crack tips ; Displacements (lattice) ; Elasticity ; Exact sciences and technology ; Fourier transforms ; Fracture mechanics ; Fracture mechanics (crack, fatigue, damage...) ; Fundamental areas of phenomenology (including applications) ; Hoop stress ; Inelasticity (thermoplasticity, viscoplasticity...) ; Integral equations ; Magnetic flux ; Magnetic permeability ; Materials Science ; Mathematical analysis ; Mathematical models ; Mechanical Engineering ; Original Paper ; Physics ; Piezoelectricity ; Planes ; Polynomials ; Schmidt method ; Singularities ; Solid mechanics ; Static elasticity (thermoelasticity...) ; Stress distribution ; Stresses ; Structural and continuum mechanics</subject><ispartof>International journal of fracture, 2010-08, Vol.164 (2), p.213-229</ispartof><rights>Springer Science+Business Media B.V. 2010</rights><rights>2015 INIST-CNRS</rights><rights>International Journal of Fracture is a copyright of Springer, (2010). All Rights Reserved.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c379t-7c7ad4de9d79626b45812072ee2b0b30e54bc68fc7a019b5be58bae60a789b7f3</citedby><cites>FETCH-LOGICAL-c379t-7c7ad4de9d79626b45812072ee2b0b30e54bc68fc7a019b5be58bae60a789b7f3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s10704-010-9477-6$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s10704-010-9477-6$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=22955434$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Zhang, Pei-Wei</creatorcontrib><creatorcontrib>Zhou, Zhen-Gong</creatorcontrib><creatorcontrib>Wu, Lin-Zhi</creatorcontrib><title>Non-local theory solution of a mode-I crack in a piezoelectric/piezomagnetic composite material plane</title><title>International journal of fracture</title><addtitle>Int J Fract</addtitle><description>The non-local theory solution of a mode-I permeable crack in a piezoelectric/piezomagnetic composite material plane was given by using the generalized Almansi’s theorem and the Schmidt method in this paper. 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The non-local elastic solution yields a finite hoop stress at the crack tip, thus allowing us to use the maximum stress as a fracture criterion.</description><subject>Automotive Engineering</subject><subject>Characterization and Evaluation of Materials</subject><subject>Chemistry and Materials Science</subject><subject>Civil Engineering</subject><subject>Classical Mechanics</subject><subject>Composite materials</subject><subject>Crack tips</subject><subject>Displacements (lattice)</subject><subject>Elasticity</subject><subject>Exact sciences and technology</subject><subject>Fourier transforms</subject><subject>Fracture mechanics</subject><subject>Fracture mechanics (crack, fatigue, damage...)</subject><subject>Fundamental areas of phenomenology (including applications)</subject><subject>Hoop stress</subject><subject>Inelasticity (thermoplasticity, viscoplasticity...)</subject><subject>Integral equations</subject><subject>Magnetic flux</subject><subject>Magnetic permeability</subject><subject>Materials Science</subject><subject>Mathematical analysis</subject><subject>Mathematical models</subject><subject>Mechanical Engineering</subject><subject>Original Paper</subject><subject>Physics</subject><subject>Piezoelectricity</subject><subject>Planes</subject><subject>Polynomials</subject><subject>Schmidt method</subject><subject>Singularities</subject><subject>Solid mechanics</subject><subject>Static elasticity (thermoelasticity...)</subject><subject>Stress distribution</subject><subject>Stresses</subject><subject>Structural and continuum mechanics</subject><issn>0376-9429</issn><issn>1573-2673</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2010</creationdate><recordtype>article</recordtype><sourceid>AFKRA</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><recordid>eNp1kE1LHTEUhoNY8Gr7A7oLlIKb6MnHJJOliF8gumnXIZN7RmNnJmMyd2F_fXO9YkFwFZLznIc3LyHfOZxwAHNaOBhQDDgwq4xheo-seGMkE9rIfbICaXSdCHtADkt5AgBrWrUieJcmNqTgB7o8YsovtKRhs8Q00dRTT8e0RnZDQ_bhD41TfZkj_k04YFhyDKevt9E_TLjEQEMa51TignT0C-ZYrfPgJ_xKvvR-KPjt7Twivy8vfp1fs9v7q5vzs1sWpLELM8H4tVqjXRurhe5U03IBRiCKDjoJ2Kgu6LavGHDbNR02bedRgzet7Uwvj8jxzjvn9LzBsrgxloDDNkPaFMe14VKo-veK_viAPqVNnmo6J0RjW2EbkJXiOyrkVErG3s05jj6_OA5uW7zbFe9q8W5bvNN15-eb2Zfaa5_9FGJ5XxTV3CipKid2XKmj6QHz_wSfy_8BydSTNQ</recordid><startdate>20100801</startdate><enddate>20100801</enddate><creator>Zhang, Pei-Wei</creator><creator>Zhou, Zhen-Gong</creator><creator>Wu, Lin-Zhi</creator><general>Springer Netherlands</general><general>Springer</general><general>Springer Nature B.V</general><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>8FE</scope><scope>8FG</scope><scope>ABJCF</scope><scope>AFKRA</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>D1I</scope><scope>DWQXO</scope><scope>HCIFZ</scope><scope>KB.</scope><scope>L6V</scope><scope>M7S</scope><scope>PDBOC</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope><scope>7SR</scope><scope>7TB</scope><scope>8BQ</scope><scope>8FD</scope><scope>FR3</scope><scope>JG9</scope><scope>KR7</scope></search><sort><creationdate>20100801</creationdate><title>Non-local theory solution of a mode-I crack in a piezoelectric/piezomagnetic composite material plane</title><author>Zhang, Pei-Wei ; Zhou, Zhen-Gong ; Wu, Lin-Zhi</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c379t-7c7ad4de9d79626b45812072ee2b0b30e54bc68fc7a019b5be58bae60a789b7f3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2010</creationdate><topic>Automotive Engineering</topic><topic>Characterization and Evaluation of Materials</topic><topic>Chemistry and Materials Science</topic><topic>Civil Engineering</topic><topic>Classical Mechanics</topic><topic>Composite materials</topic><topic>Crack tips</topic><topic>Displacements (lattice)</topic><topic>Elasticity</topic><topic>Exact sciences and technology</topic><topic>Fourier transforms</topic><topic>Fracture mechanics</topic><topic>Fracture mechanics (crack, fatigue, damage...)</topic><topic>Fundamental areas of phenomenology (including applications)</topic><topic>Hoop stress</topic><topic>Inelasticity (thermoplasticity, viscoplasticity...)</topic><topic>Integral equations</topic><topic>Magnetic flux</topic><topic>Magnetic permeability</topic><topic>Materials Science</topic><topic>Mathematical analysis</topic><topic>Mathematical models</topic><topic>Mechanical Engineering</topic><topic>Original Paper</topic><topic>Physics</topic><topic>Piezoelectricity</topic><topic>Planes</topic><topic>Polynomials</topic><topic>Schmidt method</topic><topic>Singularities</topic><topic>Solid mechanics</topic><topic>Static elasticity (thermoelasticity...)</topic><topic>Stress distribution</topic><topic>Stresses</topic><topic>Structural and continuum mechanics</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Zhang, Pei-Wei</creatorcontrib><creatorcontrib>Zhou, Zhen-Gong</creatorcontrib><creatorcontrib>Wu, Lin-Zhi</creatorcontrib><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central UK/Ireland</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Materials Science Collection</collection><collection>ProQuest Central Korea</collection><collection>SciTech Premium Collection</collection><collection>Materials Science Database</collection><collection>ProQuest Engineering Collection</collection><collection>Engineering Database</collection><collection>Materials Science Collection</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>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><jtitle>International journal of fracture</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Zhang, Pei-Wei</au><au>Zhou, Zhen-Gong</au><au>Wu, Lin-Zhi</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Non-local theory solution of a mode-I crack in a piezoelectric/piezomagnetic composite material plane</atitle><jtitle>International journal of fracture</jtitle><stitle>Int J Fract</stitle><date>2010-08-01</date><risdate>2010</risdate><volume>164</volume><issue>2</issue><spage>213</spage><epage>229</epage><pages>213-229</pages><issn>0376-9429</issn><eissn>1573-2673</eissn><coden>IJFRAP</coden><abstract>The non-local theory solution of a mode-I permeable crack in a piezoelectric/piezomagnetic composite material plane was given by using the generalized Almansi’s theorem and the Schmidt method in this paper. The problem was formulated through Fourier transform into two pairs of dual integral equations, in which the unknown variables are the displacement jumps across the crack surfaces. To solve the dual integral equations, the displacement jumps across the crack surfaces were directly expanded as a series of Jacobi polynomials. Numerical examples were provided to show the effects of the crack length and the lattice parameter on the stress field, the electric displacement field and the magnetic flux field near the crack tips. Unlike the classical elasticity solutions, it is found that no stress, electric displacement and magnetic flux singularities are present at the crack tips in piezoelectric/piezomagnetic composite materials. The non-local elastic solution yields a finite hoop stress at the crack tip, thus allowing us to use the maximum stress as a fracture criterion.</abstract><cop>Dordrecht</cop><pub>Springer Netherlands</pub><doi>10.1007/s10704-010-9477-6</doi><tpages>17</tpages></addata></record> |
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| subjects | Automotive Engineering Characterization and Evaluation of Materials Chemistry and Materials Science Civil Engineering Classical Mechanics Composite materials Crack tips Displacements (lattice) Elasticity Exact sciences and technology Fourier transforms Fracture mechanics Fracture mechanics (crack, fatigue, damage...) Fundamental areas of phenomenology (including applications) Hoop stress Inelasticity (thermoplasticity, viscoplasticity...) Integral equations Magnetic flux Magnetic permeability Materials Science Mathematical analysis Mathematical models Mechanical Engineering Original Paper Physics Piezoelectricity Planes Polynomials Schmidt method Singularities Solid mechanics Static elasticity (thermoelasticity...) Stress distribution Stresses Structural and continuum mechanics |
| title | Non-local theory solution of a mode-I crack in a piezoelectric/piezomagnetic composite material plane |
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