{"id":"https://openalex.org/W3107818955","doi":"https://doi.org/10.3390/sym12121935","title":"Effect of Axial Porosities on Flexomagnetic Response of In-Plane Compressed Piezomagnetic Nanobeams","display_name":"Effect of Axial Porosities on Flexomagnetic Response of In-Plane Compressed Piezomagnetic Nanobeams","publication_year":2020,"publication_date":"2020-11-24","ids":{"openalex":"https://openalex.org/W3107818955","doi":"https://doi.org/10.3390/sym12121935","mag":"3107818955"},"language":"en","primary_location":{"id":"doi:10.3390/sym12121935","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym12121935","pdf_url":"https://www.mdpi.com/2073-8994/12/12/1935/pdf?version=1606298531","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/12/12/1935/pdf?version=1606298531","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5068183982","display_name":"Mohammad Malikan","orcid":"https://orcid.org/0000-0001-7356-2168"},"institutions":[{"id":"https://openalex.org/I169333911","display_name":"Gda\u0144sk University of Technology","ror":"https://ror.org/006x4sc24","country_code":"PL","type":"education","lineage":["https://openalex.org/I169333911"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Mohammad Malikan","raw_affiliation_strings":["Department of Mechanics of Materials and Structures, Faculty of Civil and Environmental Engineering, Gdansk University of Technology, 80-233 Gdansk, Poland"],"raw_orcid":"https://orcid.org/0000-0001-7356-2168","affiliations":[{"raw_affiliation_string":"Department of Mechanics of Materials and Structures, Faculty of Civil and Environmental Engineering, Gdansk University of Technology, 80-233 Gdansk, Poland","institution_ids":["https://openalex.org/I169333911"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5043372900","display_name":"Victor A. Eremeyev","orcid":"https://orcid.org/0000-0002-8128-3262"},"institutions":[{"id":"https://openalex.org/I169333911","display_name":"Gda\u0144sk University of Technology","ror":"https://ror.org/006x4sc24","country_code":"PL","type":"education","lineage":["https://openalex.org/I169333911"]},{"id":"https://openalex.org/I172446870","display_name":"University of Cagliari","ror":"https://ror.org/003109y17","country_code":"IT","type":"education","lineage":["https://openalex.org/I172446870"]},{"id":"https://openalex.org/I4210097717","display_name":"Don State Technical University","ror":"https://ror.org/00x5je630","country_code":"RU","type":"education","lineage":["https://openalex.org/I4210097717"]}],"countries":["IT","PL","RU"],"is_corresponding":false,"raw_author_name":"Victor Eremeyev","raw_affiliation_strings":["Department of Civil and Environmental Engineering and Architecture (DICAAR), University of Cagliari, Via Marengo, 2, 09123 Cagliari, Italy","Department of Mechanics of Materials and Structures, Faculty of Civil and Environmental Engineering, Gdansk University of Technology, 80-233 Gdansk, Poland","Laboratory of Mechanics of Biomaterials, Research and Education Center \u201cMaterials\u201d, Don State Technical University, Gagarina sq., 1, 344000 Rostov on Don, Russia","Laboratory of Mechanics of Biomaterials, Research and Education Center \"Materials\", Don State Technical University, Gagarina sq., 1, 344000 Rostov on Don, Russia"],"raw_orcid":"https://orcid.org/0000-0002-8128-3262","affiliations":[{"raw_affiliation_string":"Department of Civil and Environmental Engineering and Architecture (DICAAR), University of Cagliari, Via Marengo, 2, 09123 Cagliari, Italy","institution_ids":["https://openalex.org/I172446870"]},{"raw_affiliation_string":"Department of Mechanics of Materials and Structures, Faculty of Civil and Environmental Engineering, Gdansk University of Technology, 80-233 Gdansk, Poland","institution_ids":["https://openalex.org/I169333911"]},{"raw_affiliation_string":"Laboratory of Mechanics of Biomaterials, Research and Education Center \u201cMaterials\u201d, Don State Technical University, Gagarina sq., 1, 344000 Rostov on Don, Russia","institution_ids":["https://openalex.org/I4210097717"]},{"raw_affiliation_string":"Laboratory of Mechanics of Biomaterials, Research and Education Center \"Materials\", Don State Technical University, Gagarina sq., 1, 344000 Rostov on Don, Russia","institution_ids":["https://openalex.org/I4210097717"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5005113182","display_name":"Krzysztof Kamil \u017bur","orcid":"https://orcid.org/0000-0003-1367-9609"},"institutions":[{"id":"https://openalex.org/I1323121030","display_name":"Bialystok University of Technology","ror":"https://ror.org/02bzfsy61","country_code":"PL","type":"education","lineage":["https://openalex.org/I1323121030"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"Krzysztof \u017bur","raw_affiliation_strings":["Faculty of Mechanical Engineering, Bialystok University of Technology, 15-351 Bialystok, Poland"],"raw_orcid":"https://orcid.org/0000-0003-1367-9609","affiliations":[{"raw_affiliation_string":"Faculty of Mechanical Engineering, Bialystok University of Technology, 15-351 Bialystok, Poland","institution_ids":["https://openalex.org/I1323121030"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5005113182"],"corresponding_institution_ids":["https://openalex.org/I1323121030"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":2.7684,"has_fulltext":false,"cited_by_count":51,"citation_normalized_percentile":{"value":0.91424612,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":"12","issue":"12","first_page":"1935","last_page":"1935"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11646","display_name":"Nonlocal and gradient elasticity in micro/nano structures","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11646","display_name":"Nonlocal and gradient elasticity in micro/nano structures","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11565","display_name":"Thermoelastic and Magnetoelastic Phenomena","score":0.9940999746322632,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10221","display_name":"Composite Structure Analysis and Optimization","score":0.9865999817848206,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/materials-science","display_name":"Materials science","score":0.7212140560150146},{"id":"https://openalex.org/keywords/axial-symmetry","display_name":"Axial symmetry","score":0.6447815895080566},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.541058361530304},{"id":"https://openalex.org/keywords/elasticity","display_name":"Elasticity (physics)","score":0.5073849558830261},{"id":"https://openalex.org/keywords/porosity","display_name":"Porosity","score":0.5039200186729431},{"id":"https://openalex.org/keywords/transverse-plane","display_name":"Transverse plane","score":0.4940093159675598},{"id":"https://openalex.org/keywords/deflection","display_name":"Deflection (physics)","score":0.4927835762500763},{"id":"https://openalex.org/keywords/buckling","display_name":"Buckling","score":0.4834064543247223},{"id":"https://openalex.org/keywords/magnetic-field","display_name":"Magnetic field","score":0.43723300099372864},{"id":"https://openalex.org/keywords/magnetization","display_name":"Magnetization","score":0.42895346879959106},{"id":"https://openalex.org/keywords/condensed-matter-physics","display_name":"Condensed matter physics","score":0.3737811744213104},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2950146794319153},{"id":"https://openalex.org/keywords/composite-material","display_name":"Composite material","score":0.28268885612487793},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.26315221190452576},{"id":"https://openalex.org/keywords/structural-engineering","display_name":"Structural engineering","score":0.14157405495643616}],"concepts":[{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.7212140560150146},{"id":"https://openalex.org/C35377427","wikidata":"https://www.wikidata.org/wiki/Q3886264","display_name":"Axial symmetry","level":2,"score":0.6447815895080566},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.541058361530304},{"id":"https://openalex.org/C121854251","wikidata":"https://www.wikidata.org/wiki/Q62932","display_name":"Elasticity (physics)","level":2,"score":0.5073849558830261},{"id":"https://openalex.org/C6648577","wikidata":"https://www.wikidata.org/wiki/Q622669","display_name":"Porosity","level":2,"score":0.5039200186729431},{"id":"https://openalex.org/C154954056","wikidata":"https://www.wikidata.org/wiki/Q1604164","display_name":"Transverse plane","level":2,"score":0.4940093159675598},{"id":"https://openalex.org/C2781355719","wikidata":"https://www.wikidata.org/wiki/Q2080698","display_name":"Deflection (physics)","level":2,"score":0.4927835762500763},{"id":"https://openalex.org/C85476182","wikidata":"https://www.wikidata.org/wiki/Q693104","display_name":"Buckling","level":2,"score":0.4834064543247223},{"id":"https://openalex.org/C115260700","wikidata":"https://www.wikidata.org/wiki/Q11408","display_name":"Magnetic field","level":2,"score":0.43723300099372864},{"id":"https://openalex.org/C32546565","wikidata":"https://www.wikidata.org/wiki/Q856711","display_name":"Magnetization","level":3,"score":0.42895346879959106},{"id":"https://openalex.org/C26873012","wikidata":"https://www.wikidata.org/wiki/Q214781","display_name":"Condensed matter physics","level":1,"score":0.3737811744213104},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2950146794319153},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.28268885612487793},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.26315221190452576},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.14157405495643616},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/sym12121935","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym12121935","pdf_url":"https://www.mdpi.com/2073-8994/12/12/1935/pdf?version=1606298531","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:c98bd5ea8f754b9c8bcdcefd421099f0","is_oa":true,"landing_page_url":"https://doaj.org/article/c98bd5ea8f754b9c8bcdcefd421099f0","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 12, Iss 12, p 1935 (2020)","raw_type":"article"},{"id":"pmh:oai:iris.unica.it:11584/307263","is_oa":true,"landing_page_url":"http://hdl.handle.net/11584/307263","pdf_url":null,"source":{"id":"https://openalex.org/S4377196293","display_name":"UNICA IRIS Institutional Research Information System (University of Cagliari)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I172446870","host_organization_name":"University of Cagliari","host_organization_lineage":["https://openalex.org/I172446870"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:mdpi.com:/2073-8994/12/12/1935/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym12121935","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym12121935","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym12121935","pdf_url":"https://www.mdpi.com/2073-8994/12/12/1935/pdf?version=1606298531","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3107818955.pdf","grobid_xml":"https://content.openalex.org/works/W3107818955.grobid-xml"},"referenced_works_count":74,"referenced_works":["https://openalex.org/W1515137979","https://openalex.org/W1966330485","https://openalex.org/W1976547406","https://openalex.org/W1979737264","https://openalex.org/W1989604748","https://openalex.org/W1998189944","https://openalex.org/W1999180226","https://openalex.org/W2003271585","https://openalex.org/W2017965666","https://openalex.org/W2021052111","https://openalex.org/W2034036934","https://openalex.org/W2038733853","https://openalex.org/W2045673424","https://openalex.org/W2054808773","https://openalex.org/W2055990100","https://openalex.org/W2057754058","https://openalex.org/W2072411809","https://openalex.org/W2073050705","https://openalex.org/W2076436283","https://openalex.org/W2078248053","https://openalex.org/W2120977559","https://openalex.org/W2121809600","https://openalex.org/W2166346770","https://openalex.org/W2171904197","https://openalex.org/W2237885336","https://openalex.org/W2394511056","https://openalex.org/W2403695180","https://openalex.org/W2551592702","https://openalex.org/W2589926384","https://openalex.org/W2727680925","https://openalex.org/W2732945110","https://openalex.org/W2765771158","https://openalex.org/W2773020731","https://openalex.org/W2793988398","https://openalex.org/W2801992198","https://openalex.org/W2809858442","https://openalex.org/W2827037829","https://openalex.org/W2887937035","https://openalex.org/W2889118618","https://openalex.org/W2889995754","https://openalex.org/W2893031975","https://openalex.org/W2895445186","https://openalex.org/W2903538118","https://openalex.org/W2906533956","https://openalex.org/W2907986015","https://openalex.org/W2947628223","https://openalex.org/W2949173711","https://openalex.org/W2953579378","https://openalex.org/W2955995563","https://openalex.org/W2966211079","https://openalex.org/W2979675875","https://openalex.org/W2986565148","https://openalex.org/W2990295617","https://openalex.org/W2991464456","https://openalex.org/W2994649250","https://openalex.org/W2995642085","https://openalex.org/W2997270779","https://openalex.org/W2998910175","https://openalex.org/W3000168924","https://openalex.org/W3004229953","https://openalex.org/W3011717837","https://openalex.org/W3016308700","https://openalex.org/W3033468770","https://openalex.org/W3045627705","https://openalex.org/W3083187382","https://openalex.org/W3087249929","https://openalex.org/W3087431853","https://openalex.org/W3093041159","https://openalex.org/W3094518907","https://openalex.org/W3208523588","https://openalex.org/W4211209218","https://openalex.org/W6779369561","https://openalex.org/W6784064411","https://openalex.org/W6802631727"],"related_works":["https://openalex.org/W4385491145","https://openalex.org/W120984554","https://openalex.org/W1554885640","https://openalex.org/W2053604103","https://openalex.org/W2349021974","https://openalex.org/W2941013975","https://openalex.org/W8641448","https://openalex.org/W3034644892","https://openalex.org/W4226484441","https://openalex.org/W792917412"],"abstract_inverted_index":{"We":[0,61,120],"investigated":[1],"the":[2,12,20,46,63,71,84,106,113,126],"stability":[3,64],"of":[4,70,91,105,133],"an":[5,40],"axially":[6],"loaded":[7],"Euler\u2013Bernoulli":[8],"porous":[9],"nanobeam":[10],"considering":[11],"flexomagnetic":[13,31,114],"material":[14],"properties.":[15],"The":[16,75],"flexomagneticity":[17,47],"relates":[18],"to":[19,44,82],"magnetization":[21],"with":[22,36,66],"strain":[23,72],"gradients.":[24],"Here":[25],"we":[26],"assume":[27],"both":[28],"piezomagnetic":[29,134],"and":[30,94,135],"phenomena":[32],"are":[33,98],"coupled":[34],"simultaneously":[35],"elastic":[37],"relations":[38],"in":[39],"inverse":[41],"magnetization.":[42],"Similar":[43],"flexoelectricity,":[45],"is":[48,55,80],"a":[49,67,117,129],"size-dependent":[50],"property.":[51],"Therefore,":[52],"its":[53],"effect":[54,115],"more":[56],"pronounced":[57],"at":[58,116],"small":[59,118],"scales.":[60],"merge":[62],"equation":[65],"nonlocal":[68],"model":[69],"gradient":[73],"elasticity.":[74],"Navier":[76],"sinusoidal":[77],"transverse":[78],"deflection":[79],"employed":[81],"attain":[83],"critical":[85],"buckling":[86],"load.":[87],"Furthermore,":[88],"different":[89],"types":[90],"axial":[92],"symmetric":[93],"asymmetric":[95],"porosity":[96],"distributions":[97],"studied.":[99],"It":[100],"was":[101],"revealed":[102],"that":[103,124],"regardless":[104],"high":[107],"magnetic":[108],"field,":[109],"one":[110],"can":[111],"realize":[112],"scale.":[119],"demonstrate":[121],"as":[122],"well":[123],"for":[125],"larger":[127],"thicknesses":[128],"difference":[130],"between":[131],"responses":[132],"piezo-flexomagnetic":[136],"nanobeams":[137],"would":[138],"not":[139],"be":[140],"significant.":[141]},"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":8},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":9},{"year":2021,"cited_by_count":17},{"year":2020,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2020-12-07T00:00:00"}