{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,31]],"date-time":"2026-03-31T01:46:36Z","timestamp":1774921596352,"version":"3.50.1"},"reference-count":71,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2020,11,24]],"date-time":"2020-11-24T00:00:00Z","timestamp":1606176000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>We investigated the stability of an axially loaded Euler\u2013Bernoulli porous nanobeam considering the flexomagnetic material properties. The flexomagneticity relates to the magnetization with strain gradients. Here we assume both piezomagnetic and flexomagnetic phenomena are coupled simultaneously with elastic relations in an inverse magnetization. Similar to flexoelectricity, the flexomagneticity is a size-dependent property. Therefore, its effect is more pronounced at small scales. We merge the stability equation with a nonlocal model of the strain gradient elasticity. The Navier sinusoidal transverse deflection is employed to attain the critical buckling load. Furthermore, different types of axial symmetric and asymmetric porosity distributions are studied. It was revealed that regardless of the high magnetic field, one can realize the flexomagnetic effect at a small scale. We demonstrate as well that for the larger thicknesses a difference between responses of piezomagnetic and piezo-flexomagnetic nanobeams would not be significant.<\/jats:p>","DOI":"10.3390\/sym12121935","type":"journal-article","created":{"date-parts":[[2020,11,24]],"date-time":"2020-11-24T22:22:38Z","timestamp":1606256558000},"page":"1935","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":50,"title":["Effect of Axial Porosities on Flexomagnetic Response of In-Plane Compressed Piezomagnetic Nanobeams"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7356-2168","authenticated-orcid":false,"given":"Mohammad","family":"Malikan","sequence":"first","affiliation":[{"name":"Department of Mechanics of Materials and Structures, Faculty of Civil and Environmental Engineering, Gdansk University of Technology, 80-233 Gdansk, Poland"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8128-3262","authenticated-orcid":false,"given":"Victor","family":"Eremeyev","sequence":"additional","affiliation":[{"name":"Department of Mechanics of Materials and Structures, Faculty of Civil and Environmental Engineering, Gdansk University of Technology, 80-233 Gdansk, Poland"},{"name":"Laboratory of Mechanics of Biomaterials, Research and Education Center \u201cMaterials\u201d, Don State Technical University, Gagarina sq., 1, 344000 Rostov on Don, Russia"},{"name":"Department of Civil and Environmental Engineering and Architecture (DICAAR), University of Cagliari, Via Marengo, 2, 09123 Cagliari, Italy"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1367-9609","authenticated-orcid":false,"given":"Krzysztof","family":"\u017bur","sequence":"additional","affiliation":[{"name":"Faculty of Mechanical Engineering, Bialystok University of Technology, 15-351 Bialystok, Poland"}]}],"member":"1968","published-online":{"date-parts":[[2020,11,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"980","DOI":"10.1134\/S1063784219070144","article-title":"Flexomagnetic and Flexoantiferromagnetic Effects in Centrosymmetric Antiferromagnetic Materials","volume":"64","author":"Kabychenkov","year":"2019","journal-title":"Tech. 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