{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,5]],"date-time":"2026-05-05T15:52:39Z","timestamp":1777996359245,"version":"3.51.4"},"reference-count":29,"publisher":"MDPI AG","issue":"14","license":[{"start":{"date-parts":[[2022,7,19]],"date-time":"2022-07-19T00:00:00Z","timestamp":1658188800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["11872104"],"award-info":[{"award-number":["11872104"]}]},{"name":"National Natural Science Foundation of China","award":["CSCEC-2021-Q-5"],"award-info":[{"award-number":["CSCEC-2021-Q-5"]}]},{"name":"National Natural Science Foundation of China","award":["2019JBM82"],"award-info":[{"award-number":["2019JBM82"]}]},{"name":"China State Construction Engineering Corporation","award":["11872104"],"award-info":[{"award-number":["11872104"]}]},{"name":"China State Construction Engineering Corporation","award":["CSCEC-2021-Q-5"],"award-info":[{"award-number":["CSCEC-2021-Q-5"]}]},{"name":"China State Construction Engineering Corporation","award":["2019JBM82"],"award-info":[{"award-number":["2019JBM82"]}]},{"name":"Fundamental Research Funds for the Central Universities","award":["11872104"],"award-info":[{"award-number":["11872104"]}]},{"name":"Fundamental Research Funds for the Central Universities","award":["CSCEC-2021-Q-5"],"award-info":[{"award-number":["CSCEC-2021-Q-5"]}]},{"name":"Fundamental Research Funds for the Central Universities","award":["2019JBM82"],"award-info":[{"award-number":["2019JBM82"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>In this letter, we propose a nonlinear Magnetoelastic Energy (ME) with a material parameter related to electron interactions. An attenuating term is contained in the formula of the proposed nonlinear ME, which can predict the variation in the anisotropic magneto-crystalline constants induced by external stress more accurately than the classical linear ME. The domain wall velocity under stress and magnetic field can be predicted accurately based on the nonlinear ME. The proposed nonlinear ME model is concise and easy to use. It is important in sensor analysis and production, magneto-acoustic coupling motivation, magnetoelastic excitation, etc.<\/jats:p>","DOI":"10.3390\/s22145371","type":"journal-article","created":{"date-parts":[[2022,7,19]],"date-time":"2022-07-19T05:37:53Z","timestamp":1658209073000},"page":"5371","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["A Nonlinear Magnetoelastic Energy Model and Its Application in Domain Wall Velocity Prediction"],"prefix":"10.3390","volume":"22","author":[{"given":"Li-Bo","family":"Wu","sequence":"first","affiliation":[{"name":"Department of Mechanics, School of Civil Engineering, Beijing Jiaotong University, Beijing 100044, China"},{"name":"China Construction Second Bureau Installation Engineering Co., Ltd., Beijing 100176, China"}]},{"given":"Yu-Feng","family":"Fan","sequence":"additional","affiliation":[{"name":"China Construction Second Bureau Installation Engineering Co., Ltd., Beijing 100176, China"}]},{"given":"Feng-Bo","family":"Sun","sequence":"additional","affiliation":[{"name":"China Construction Second Engineering Bureau Co., Ltd., Beijing 100160, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6763-2772","authenticated-orcid":false,"given":"Kai","family":"Yao","sequence":"additional","affiliation":[{"name":"Department of Mechanics, School of Civil Engineering, Beijing Jiaotong University, Beijing 100044, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0043-8411","authenticated-orcid":false,"given":"Yue-Sheng","family":"Wang","sequence":"additional","affiliation":[{"name":"Department of Mechanics, School of Civil Engineering, Beijing Jiaotong University, Beijing 100044, China"},{"name":"Department of Mechanics, School of Mechanical Engineering, Tianjin University, Tianjin 300350, China"}]}],"member":"1968","published-online":{"date-parts":[[2022,7,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1022","DOI":"10.1038\/nphys3465","article-title":"Long-distance transport of magnon spin information in a magnetic insulator at room temperature","volume":"11","author":"Cornelissen","year":"2015","journal-title":"Nat. Phys."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1055","DOI":"10.1016\/j.physleta.2017.01.044","article-title":"Tunability of band structures in a two-dimensional magnetostrictive phononic crystal plate with stress and magnetic loadings","volume":"381","author":"Zhang","year":"2017","journal-title":"Phys. Lett. A"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"064409","DOI":"10.1103\/PhysRevB.74.064409","article-title":"Weakly coupled motion of individual layers in ferromagnetic resonance","volume":"74","author":"Arena","year":"2006","journal-title":"Phys. Rev. B"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Dai, M., Chen, X., Sun, T., Yu, L., Chen, M., Lin, H., and Chen, S. (2018). A 2D Magneto-Acousto-Electrical Tomography method to detect conductivity variation using multifocus image method. Sensors, 18.","DOI":"10.3390\/s18072373"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"158555","DOI":"10.1016\/j.jallcom.2020.158555","article-title":"Influence of the magnetic domain structure in the mass sensitivity of magnetoelastic sensors with different geometries","volume":"863","author":"Saiz","year":"2021","journal-title":"J. Alloys Compd."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Grenda, P., Kuty\u0142a, M., Nowicki, M., and Charubin, T. (2021). Bendductor\u2014Transformer Steel Magnetomechanical Force Sensor. Sensors, 21.","DOI":"10.3390\/s21248250"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"192","DOI":"10.1016\/S0924-4247(97)80172-0","article-title":"Enhancement of magnetorestrictive properties of amorphous ribbons for a biomedical application","volume":"59","author":"Meydan","year":"1997","journal-title":"Sens. Actuators A Phys."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Samourgkanidis, G., and Kouzoudis, D. (2021). Magnetoelastic Ribbons as Vibration Sensors for Real-Time Health Monitoring of Rotating Metal Beams. Sensors, 21.","DOI":"10.3390\/s21238122"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"126657","DOI":"10.1016\/j.physleta.2020.126657","article-title":"Giant magneto-impedance variation in amorphous CoFeSiB ribbons as a function of tensile stress and frequency","volume":"384","author":"Mansourian","year":"2020","journal-title":"Phys. Lett. A"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Sisniega, B., Sagasti Sedano, A., Guti\u00e9rrez, J., and Garc\u00eda-Arribas, A. (2020). Real time monitoring of calcium oxalate precipitation reaction by using corrosion resistant magnetoelastic resonance sensors. Sensors, 20.","DOI":"10.3390\/s20102802"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"2451","DOI":"10.1016\/j.physleta.2019.05.017","article-title":"Absence of a spontaneous long-range order in a mixed spin-(1\/2, 3\/2) ising model on a decorated square lattice due to anomalous spin frustration driven by a magnetoelastic coupling","volume":"383","author":"Strecka","year":"2019","journal-title":"Phys. Lett. A"},{"key":"ref_12","unstructured":"Chikazumi, S., and Graham, C.D. (2009). Physics of Ferromagnetism 2e, Oxford University Press on Demand."},{"key":"ref_13","unstructured":"Gurevich, A.G., and Melkov, G.A. (1996). Magnetization Oscillations and Waves, CRC Press."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"867","DOI":"10.1038\/nature03183","article-title":"Tomographic imaging of molecular orbitals","volume":"432","author":"Itatani","year":"2004","journal-title":"Nature"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"086101","DOI":"10.1103\/PhysRevLett.125.086101","article-title":"Potential of attosecond coherent diffractive imaging","volume":"125","author":"Rana","year":"2020","journal-title":"Phys. Rev. Lett."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"793","DOI":"10.1103\/PhysRevLett.29.793","article-title":"New magnetoelastic interaction","volume":"29","author":"Liu","year":"1972","journal-title":"Phys. Rev. Lett."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"184412","DOI":"10.1103\/PhysRevB.84.184412","article-title":"Magnetoelastic coupling in la2\/3sr1\/3mno3 thin films on srtio3","volume":"84","author":"Pesquera","year":"2011","journal-title":"Phys. Rev. B"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"3051","DOI":"10.1103\/PhysRevB.31.3051","article-title":"Theory of linear magnetoelastic effects","volume":"31","author":"Rinaldi","year":"1985","journal-title":"Phys. Rev. B"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"142403","DOI":"10.1063\/1.4999493","article-title":"Determination of stress-coefficient of magnetoelastic anisotropy in flexible amorphous CoFeB film by anisotropic magnetoresistance","volume":"111","author":"Wen","year":"2017","journal-title":"Appl. Phys. Lett."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"10C906","DOI":"10.1063\/1.1848355","article-title":"Magnetostriction effect of amorphous CoFeB thin films and application in spin-dependent tunnel junctions","volume":"97","author":"Wang","year":"2005","journal-title":"J. Appl. Phys."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"34","DOI":"10.1557\/S0883769400037337","article-title":"Magnetostrictive materials","volume":"18","author":"Hathaway","year":"1993","journal-title":"MRS Bull."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"162406","DOI":"10.1063\/1.5121458","article-title":"A micro-statistical constructive model for magnetization and magnetostriction under applied stress and magnetic fields","volume":"115","author":"Wu","year":"2019","journal-title":"Appl. Phys. Lett."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1016\/0304-8853(80)90522-3","article-title":"Theory of first order magnetization processes: Uniaxial anisotropy","volume":"20","author":"Asti","year":"1980","journal-title":"J. Magn. Magn. Mater."},{"key":"ref_24","unstructured":"Song, O. (1994). Magnetoelastic Coupling in Thin Films. [Ph.D. Thesis, Massachusetts Institute of Technology]."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"024432","DOI":"10.1103\/PhysRevB.79.024432","article-title":"Nonlinear magnetoelastic coupling of epitaxial layers of Fe, Co, and Ni on Ir(100)","volume":"79","author":"Tian","year":"2009","journal-title":"Phys. Rev. B"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"66","DOI":"10.1016\/j.eml.2015.03.004","article-title":"180 magnetization switching in nanocylinders by a mechanical strain","volume":"3","author":"Yi","year":"2015","journal-title":"Extrem. Mech. Lett."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1757","DOI":"10.1016\/j.physleta.2016.02.037","article-title":"Simultaneous microwave photonic and phononic band gaps in piezoelectric\u2013piezomagnetic superlattices with three types of domains in a unit cell","volume":"380","author":"Tang","year":"2016","journal-title":"Phys. Lett. A"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1109\/TMAG.2014.2321114","article-title":"Domain wall propagation in Co-based glass-coated microwires: Effect of stress annealing and tensile applied stresses","volume":"50","author":"Talaat","year":"2014","journal-title":"IEEE Trans. Magn."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"053004","DOI":"10.7567\/APEX.6.053004","article-title":"Anisotropic Magnetostriction and Domain Wall Motion in Sm10Co90 Amorphous Films","volume":"6","author":"Moubah","year":"2013","journal-title":"Appl. Phys. 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