{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T16:37:28Z","timestamp":1773247048315,"version":"3.50.1"},"reference-count":14,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2016,4,16]],"date-time":"2016-04-16T00:00:00Z","timestamp":1460764800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>During the manufacturing process and use of ferromagnetic sheets, operations such as rolling, cutting, and tightening induce anisotropy that changes the material\u2019s behavior. Consequently for more accuracy in magnetization and magnetostriction calculations in electric devices such as transformers, anisotropic effects should be considered. In the following sections, we give an overview of a macroscopic model which takes into account the magnetic and magnetoelastic anisotropy of the material for both magnetization and magnetostriction computing. Firstly, a comparison between the model results and measurements from a Single Sheet Tester (SST) and values will be shown. Secondly, the model is integrated in a finite elements code to predict magnetostrictive deformation of an in-house test bench which is a stack of 40 sheets glued together by the Vacuum-Pressure Impregnation (VPI) method. Measurements on the test bench and Finite Elements results are presented.<\/jats:p>","DOI":"10.3390\/s16040553","type":"journal-article","created":{"date-parts":[[2016,4,18]],"date-time":"2016-04-18T10:37:17Z","timestamp":1460975837000},"page":"553","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["An Anisotropic Model for Magnetostriction and Magnetization Computing for Noise Generation in Electric Devices"],"prefix":"10.3390","volume":"16","author":[{"given":"Serigne","family":"Mbengue","sequence":"first","affiliation":[{"name":"Sorbonne universit\u00e9s, Universit\u00e9 de Technologie de Compi\u00e8gne (UTC) Laboratoire Roberval (CNRS UMR7337), 60203 Compi\u00e8gne Cedex, France"},{"name":"Sorbonne universit\u00e9s, UTC Laboratoire Electrom\u00e9canique de Compi\u00e8gne (EA1006), 60203 Compi\u00e8gne Cedex, France"}]},{"given":"Nicolas","family":"Buiron","sequence":"additional","affiliation":[{"name":"Sorbonne universit\u00e9s, Universit\u00e9 de Technologie de Compi\u00e8gne (UTC) Laboratoire Roberval (CNRS UMR7337), 60203 Compi\u00e8gne Cedex, France"}]},{"given":"Vincent","family":"Lanfranchi","sequence":"additional","affiliation":[{"name":"Sorbonne universit\u00e9s, UTC Laboratoire Electrom\u00e9canique de Compi\u00e8gne (EA1006), 60203 Compi\u00e8gne Cedex, France"}]}],"member":"1968","published-online":{"date-parts":[[2016,4,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1549","DOI":"10.1109\/TMAG.2011.2173563","article-title":"Acoustic noise characteristics and magnetostriction of Fe\u2013Si powder cores","volume":"48","author":"Jang","year":"2012","journal-title":"IEEE Trans. Magn."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"3759","DOI":"10.1109\/20.908346","article-title":"Relevance of magnetostriction and forces for the generation of audible noise of transformer cores","volume":"36","author":"Weiser","year":"2000","journal-title":"IEEE Trans. Magn."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"20","DOI":"10.1108\/03321640110359697","article-title":"Finite element based expressions for Lorentz, reluctance and magnetostriction forces","volume":"20","author":"Delaere","year":"2001","journal-title":"COMPEL"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"3388","DOI":"10.1109\/20.952620","article-title":"Coupled magnetoelastic finite element formulation including anisotropic reluctivity tensor and magnetostriction effects for machinery applications","volume":"37","author":"Mohammed","year":"2001","journal-title":"IEEE Trans. Magn."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"352","DOI":"10.1016\/S0304-8853(02)00850-8","article-title":"Experimental analysis of the magnetoelastic anisotropy of a non-oriented silicon iron alloy","volume":"254\u2013255","author":"Hubert","year":"2003","journal-title":"J. Magn. Magn. Mater."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Moses, A.J., Anderson, P.I., and Somkun, S. (2015). Modeling 2-D Magnetostriction in Nonoriented Electrical Steels Using a Simple Magnetic Domain Model. IEEE Trans. Magn., 51.","DOI":"10.1109\/TMAG.2015.2402111"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Belahcen, A., Singh, D., Rasilo, P., Martin, F., Ghalamestani, S.G., and Vandevelde, L. (2015). Anisotropic and Strain-Dependent Model of Magnetostriction in Electrical Steel Sheets. IEEE Trans. Magn., 51.","DOI":"10.1109\/TMAG.2014.2361681"},{"key":"ref_8","unstructured":"Lundgren, A. (1999). On Measurement and Modelling of 2D Magnetization and Magnetostriction of Sife Sheets. [Ph.D. Thesis, Royal Institute of Technology]."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"302","DOI":"10.1109\/TMAG.2009.2033123","article-title":"Magnetostriction Anisotropy and Rotational Magnetostriction of a nonoriented Electrical Steel","volume":"46","author":"Somkun","year":"2010","journal-title":"IEEE Trans. Magn."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Du Tr\u00e9molet de Lacheisserie, E. (2000). Magn\u00e9tisme, EDP Sciences. [1st ed.].","DOI":"10.1051\/978-2-7598-0131-2"},{"key":"ref_11","first-page":"1","article-title":"Equivalence of magnetoelastic, elastic and mechanical work energies with stress-induced anisotropy","volume":"6929","author":"Mudivarthi","year":"2008","journal-title":"Behav. Mech. Multifunct. Compos. Mater."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"74","DOI":"10.1016\/j.jmmm.2015.12.001","article-title":"Macroscopic modeling of anisotropic magnetostriction and magnetization in soft ferromagnetic materials","volume":"404","author":"Mbengue","year":"2016","journal-title":"J. Magn. Magn. Mater."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"614","DOI":"10.1016\/S0304-8853(00)00241-9","article-title":"Anisotropy and texture influence on 2D magnetic behaviour for silicon, cobalt and nickel iron alloys","volume":"215\u2013216","author":"Spornic","year":"2000","journal-title":"J. Magn. Magn. Mater."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Cullity, B.D., and Graham, C.D. (2009). Introduction to Magnetic Materials, Wiley. [2nd ed.].","DOI":"10.1002\/9780470386323"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/16\/4\/553\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T19:22:24Z","timestamp":1760210544000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/16\/4\/553"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,4,16]]},"references-count":14,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2016,4]]}},"alternative-id":["s16040553"],"URL":"https:\/\/doi.org\/10.3390\/s16040553","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,4,16]]}}}