{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,9]],"date-time":"2026-03-09T13:48:09Z","timestamp":1773064089555,"version":"3.50.1"},"reference-count":54,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2025,11,7]],"date-time":"2025-11-07T00:00:00Z","timestamp":1762473600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2025,11,7]],"date-time":"2025-11-07T00:00:00Z","timestamp":1762473600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100001824","name":"Grant Agency of the Czech Republic","doi-asserted-by":"crossref","award":["23-04766S"],"award-info":[{"award-number":["23-04766S"]}],"id":[{"id":"10.13039\/501100001824","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001824","name":"Grant Agency of the Czech Republic","doi-asserted-by":"crossref","award":["23-04766S"],"award-info":[{"award-number":["23-04766S"]}],"id":[{"id":"10.13039\/501100001824","id-type":"DOI","asserted-by":"crossref"}]},{"name":"INdAM-GNFM"},{"name":"Italian Ministry of University and Research","award":["PRIN 2022NNTZNM DISCOVER"],"award-info":[{"award-number":["PRIN 2022NNTZNM DISCOVER"]}]},{"name":"Institute of Information Theory and Automation of the Czech Academy of Sciences"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Nonlinear Sci"],"published-print":{"date-parts":[[2026,2]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>We investigate a homogenization problem for a linearly elastic magnetic material that incorporates elastically rigid magnetic inclusions firmly bonded to the matrix. By considering a periodic arrangement of this material, we identify an effective magnetoelastic energy, obtained by homogenization when the period approaches zero. For comparison, we also briefly discuss alternative, essentially equivalent magnetic models naturally linked by a Legendre-Fenchel transform of magnetic energy density where the elastic deformation enters as a parameter.<\/jats:p>","DOI":"10.1007\/s00332-025-10219-7","type":"journal-article","created":{"date-parts":[[2025,11,7]],"date-time":"2025-11-07T14:22:48Z","timestamp":1762525368000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Homogenization of Magnetoelastic Materials with Rigid Magnetic Inclusions at Small Strains"],"prefix":"10.1007","volume":"36","author":[{"given":"Raffaele","family":"Grande","sequence":"first","affiliation":[]},{"given":"Stefan","family":"Kr\u00f6mer","sequence":"additional","affiliation":[]},{"given":"Martin","family":"Kru\u017e\u00edk","sequence":"additional","affiliation":[]},{"given":"Giuseppe","family":"Tomassetti","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,11,7]]},"reference":[{"issue":"6","key":"10219_CR1","doi-asserted-by":"publisher","first-page":"1482","DOI":"10.1137\/0523084","volume":"23","author":"G Allaire","year":"1992","unstructured":"Allaire, G.: Homogenization and two-scale convergence. SIAM J. Math. Anal. 23(6), 1482\u20131518 (1992)","journal-title":"SIAM J. Math. Anal."},{"key":"10219_CR2","unstructured":"Almi, S., Kru\u017e\u00edk, M., Molchanova, A.: Linearization in magnetoelasticity. Prepint arXiv 2401, 09586 (2024)"},{"issue":"2","key":"10219_CR3","doi-asserted-by":"publisher","first-page":"45","DOI":"10.3390\/act8020045","volume":"8","author":"V Apicella","year":"2019","unstructured":"Apicella, V., et al.: Review of modeling and control of magnetostrictive actuators. Actuators 8(2), 45 (2019)","journal-title":"Actuators"},{"key":"10219_CR4","volume-title":"Homogenisation: averaging processes in periodic media: mathematical problems in the mechanics of composite materials","author":"NS Bakhvalov","year":"2012","unstructured":"Bakhvalov, N.S., Panasenko, G.: Homogenisation: averaging processes in periodic media: mathematical problems in the mechanics of composite materials. Springer, Berlin (2012)"},{"key":"10219_CR5","doi-asserted-by":"crossref","unstructured":"Behera, A.: Magnetostrictive materials. In Advanced Materials: An Introduction to Modern Materials Science, pages 101\u2013125. Springer, (2022)","DOI":"10.1007\/978-3-030-80359-9_3"},{"issue":"12","key":"10219_CR6","doi-asserted-by":"publisher","first-page":"2877","DOI":"10.1016\/S0022-5096(01)00108-9","volume":"49","author":"L Borcea","year":"2001","unstructured":"Borcea, L., Bruno, O.: On the magneto-elastic properties of elastomer\u2013ferromagnet composites. J. Mech. Phys. Solids 49(12), 2877\u20132919 (2001)","journal-title":"J. Mech. Phys. Solids"},{"issue":"4","key":"10219_CR7","doi-asserted-by":"publisher","first-page":"543","DOI":"10.1142\/S0218202595000322","volume":"5","author":"A Braides","year":"1995","unstructured":"Braides, A., Garroni, A.: Homogenization of periodic nonlinear media with stiff and soft inclusions. Math. Models Methods Appl. Sci. 5(4), 543\u2013564 (1995)","journal-title":"Math. Models Methods Appl. Sci."},{"key":"10219_CR8","doi-asserted-by":"crossref","unstructured":"Bresciani, M., Davoli, E., Kru\u017e\u00edk, M.: Existence results in large-strain magnetoelasticity. Ann. Inst. H. Poincar\u00e9 C Anal. Non Lin\u00e9aire, 40(3):557\u2013592, (2023)","DOI":"10.4171\/aihpc\/51"},{"issue":"4","key":"10219_CR9","doi-asserted-by":"publisher","first-page":"3108","DOI":"10.1137\/21M1446836","volume":"55","author":"M Bresciani","year":"2023","unstructured":"Bresciani, M., Kru\u017e\u00edk, M.: A reduced model for plates arising as low-energy $$\\Gamma $$-limit in nonlinear magnetoelasticity. SIAM J. Math. Anal. 55(4), 3108\u20133168 (2023)","journal-title":"SIAM J. Math. Anal."},{"key":"10219_CR10","volume-title":"Micromagnetics","author":"W Brown","year":"1963","unstructured":"Brown, W.: Micromagnetics. Krieger Publishing Co., New York (1963)"},{"key":"10219_CR11","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-87396-6","volume-title":"Magnetoelastic Interactions. Springer Tracts in Natural Philosophy.","author":"W Brown","year":"1966","unstructured":"Brown, W.: Magnetoelastic Interactions. Springer Tracts in Natural Philosophy. Springer, Berlin (1966)"},{"issue":"3\u20134","key":"10219_CR12","doi-asserted-by":"publisher","first-page":"183","DOI":"10.1007\/s00707-009-0193-0","volume":"210","author":"R Bustamante","year":"2010","unstructured":"Bustamante, R.: Transversely isotropic nonlinear magneto-active elastomers. Acta Mech. 210(3\u20134), 183\u2013214 (2010)","journal-title":"Acta Mech."},{"issue":"8","key":"10219_CR13","doi-asserted-by":"publisher","first-page":"725","DOI":"10.1177\/1081286507079832","volume":"13","author":"R Bustamante","year":"2008","unstructured":"Bustamante, R., Dorfmann, A., Ogden, R.W.: On variational formulations in nonlinear magnetoelastostatics. Math. Mech. Solids 13(8), 725\u2013745 (2008)","journal-title":"Math. Mech. Solids"},{"issue":"10","key":"10219_CR14","doi-asserted-by":"publisher","first-page":"1057","DOI":"10.1177\/1045389X06072358","volume":"18","author":"FT Calkins","year":"2007","unstructured":"Calkins, F.T., Flatau, A.B., Dapino, M.J.: Overview of magnetostrictive sensor technology. J. Intell. Mater. Syst. Struct. 18(10), 1057\u20131066 (2007)","journal-title":"J. Intell. Mater. Syst. Struct."},{"issue":"2","key":"10219_CR15","doi-asserted-by":"publisher","first-page":"445","DOI":"10.1007\/s00205-011-0481-4","volume":"204","author":"M Cherdantsev","year":"2012","unstructured":"Cherdantsev, M., Cherednichenko, K.: Two-scale $$\\gamma $$-convergence of integral functionals and its application to homogenisation of nonlinear high-contrast periodic composites. Arch. Ration. Mech. Anal. 204(2), 445\u2013478 (2012)","journal-title":"Arch. Ration. Mech. Anal."},{"issue":"1\u20132","key":"10219_CR16","first-page":"67","volume":"104","author":"M Cherdantsev","year":"2017","unstructured":"Cherdantsev, M., Cherednichenko, K., Neukamm, S.: High contrast homogenisation in nonlinear elasticity under small loads. Asymptot. Anal. 104(1\u20132), 67\u2013102 (2017)","journal-title":"Asymptot. Anal."},{"key":"10219_CR17","doi-asserted-by":"publisher","first-page":"607","DOI":"10.1007\/s11401-010-0606-3","volume":"31","author":"PG Ciarlet","year":"2010","unstructured":"Ciarlet, P.G.: On Korn\u2019s inequality. Chinese Ann. Math., Ser B 31, 607\u2013618 (2010)","journal-title":"Chinese Ann. Math., Ser B"},{"issue":"5","key":"10219_CR18","doi-asserted-by":"publisher","first-page":"1435","DOI":"10.1137\/040620898","volume":"37","author":"D Cioranescu","year":"2006","unstructured":"Cioranescu, D., Damlamian, A., De Arcangelis, R.: Homogenization of quasiconvex integrals via the periodic unfolding method. SIAM J. Math. Anal. 37(5), 1435\u20131453 (2006)","journal-title":"SIAM J. Math. Anal."},{"key":"10219_CR19","doi-asserted-by":"crossref","unstructured":"Cioranescu, D., Damlamian, A., Griso, G.: The periodic unfolding method, volume\u00a03 of Series in Contemporary Mathematics. Springer, Singapore, (2018). Theory and applications to partial differential problems","DOI":"10.1007\/978-981-13-3032-2"},{"key":"10219_CR20","doi-asserted-by":"publisher","DOI":"10.1093\/oso\/9780198565543.001.0001","volume-title":"An Introduction to Homogenization","author":"D Cioranescu","year":"1999","unstructured":"Cioranescu, D., Donato, P.: An Introduction to Homogenization. Oxford University Press (1999)"},{"key":"10219_CR21","volume-title":"An Introduction to $$\\Gamma $$-Convergence","author":"G Dal Maso","year":"2012","unstructured":"Dal Maso, G.: An Introduction to $$\\Gamma $$-Convergence. Springer, Berlin (2012)"},{"key":"10219_CR22","doi-asserted-by":"publisher","first-page":"25","DOI":"10.1016\/j.jmps.2017.04.016","volume":"105","author":"K Danas","year":"2017","unstructured":"Danas, K.: Effective response of classical, auxetic and chiral magnetoelastic materials by use of a new variational principle. J. Mech. Phys. Solids 105, 25\u201353 (2017)","journal-title":"J. Mech. Phys. Solids"},{"key":"10219_CR23","doi-asserted-by":"crossref","unstructured":"Davoli, E., Kru\u017e\u00edk, M., Pagliari, V.: Homogenization of high-contrast composites under differential constraints. Adv. Calc. Var., (2022)","DOI":"10.1515\/acv-2022-0009"},{"issue":"10","key":"10219_CR24","doi-asserted-by":"publisher","DOI":"10.1088\/1361-665X\/aa8347","volume":"26","author":"Z Deng","year":"2017","unstructured":"Deng, Z., Dapino, M.J.: Review of magnetostrictive vibration energy harvesters. Smart Mat. Struct. 26(10), 103001 (2017)","journal-title":"Smart Mat. Struct."},{"issue":"2","key":"10219_CR25","doi-asserted-by":"publisher","first-page":"283","DOI":"10.1016\/S0022-5096(01)00050-3","volume":"50","author":"A DeSimone","year":"2002","unstructured":"DeSimone, A., James, R.: A constrained theory of magnetoelasticity. J. Mech. Phys. Solids 50(2), 283\u2013320 (2002)","journal-title":"J. Mech. Phys. Solids"},{"issue":"8","key":"10219_CR26","doi-asserted-by":"publisher","first-page":"5706","DOI":"10.1063\/1.364643","volume":"81","author":"A DeSimone","year":"1997","unstructured":"DeSimone, A., James, R.D.: A theory of magnetostriction oriented towards applications. J. Appl. Phys. 81(8), 5706\u20135708 (1997)","journal-title":"J. Appl. Phys."},{"issue":"4","key":"10219_CR27","doi-asserted-by":"publisher","first-page":"599","DOI":"10.1093\/qjmam\/57.4.599","volume":"57","author":"A Dorfmann","year":"2004","unstructured":"Dorfmann, A.: Nonlinear magnetoelastic deformations. Q. J. Mech. Appl. Math. 57(4), 599\u2013622 (2004)","journal-title":"Q. J. Mech. Appl. Math."},{"issue":"3","key":"10219_CR28","doi-asserted-by":"publisher","first-page":"270","DOI":"10.1016\/j.commatsci.2003.10.004","volume":"29","author":"A Dorfmann","year":"2004","unstructured":"Dorfmann, A., Brigadnov, I.: Constitutive modelling of magneto-sensitive Cauchy-elastic solids. Comput. Mater. Sci. 29(3), 270\u2013282 (2004)","journal-title":"Comput. Mater. Sci."},{"issue":"4","key":"10219_CR29","doi-asserted-by":"publisher","first-page":"497","DOI":"10.1016\/S0997-7538(03)00067-6","volume":"22","author":"A Dorfmann","year":"2003","unstructured":"Dorfmann, A., Ogden, R.: Magnetoelastic modelling of elastomers. Eur. J. Mech. A\/Solids 22(4), 497\u2013507 (2003)","journal-title":"Eur. J. Mech. A\/Solids"},{"key":"10219_CR30","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4614-9596-3","volume-title":"Nonlinear Theory of Electroelastic and Magnetoelastic Interactions","author":"L Dorfmann","year":"2014","unstructured":"Dorfmann, L., Ogden, R.W.: Nonlinear Theory of Electroelastic and Magnetoelastic Interactions. Springer, New York (2014)"},{"key":"10219_CR31","doi-asserted-by":"crossref","unstructured":"du Tr\u00e9molet, E., de Lacheisserie, D., Gignoux, and M. Schlenker.: Magnetostrictive materials. In: du Tr\u00e9molet, E., de Lacheisserie, D., Gignoux, and M. Schlenker, (eds.) Magnetism. Springer: Boston (2002)","DOI":"10.1007\/978-0-387-23062-7"},{"issue":"1","key":"10219_CR32","doi-asserted-by":"publisher","first-page":"38","DOI":"10.1177\/1081286506069847","volume":"13","author":"J Ericksen","year":"2007","unstructured":"Ericksen, J.: Magnetizable and polarizable elastic materials. Math. Mech. Solids 13(1), 38\u201354 (2007)","journal-title":"Math. Mech. Solids"},{"issue":"6","key":"10219_CR33","doi-asserted-by":"publisher","first-page":"1355","DOI":"10.1137\/S0036141098339885","volume":"30","author":"I Fonseca","year":"1999","unstructured":"Fonseca, I., M\u00fcller, S.: $$\\cal{A} $$-quasiconvexity, lower semicontinuity, and Young measures. SIAM J. Math. Anal. 30(6), 1355\u20131390 (1999)","journal-title":"SIAM J. Math. Anal."},{"issue":"1","key":"10219_CR34","doi-asserted-by":"publisher","first-page":"22","DOI":"10.1016\/j.jmaa.2025.129705","volume":"552","author":"J Fotso Tachago","year":"2025","unstructured":"Fotso Tachago, J., Gargiulo, G., Nnang, H., Zappale, E.: Homogenization of non-convex integral energies with Orlicz growth via periodic unfolding. J. Math. Anal. Appl. 552(1), 22 (2025)","journal-title":"J. Math. Anal. Appl."},{"key":"10219_CR35","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmps.2022.105081","volume":"169","author":"J Furer","year":"2022","unstructured":"Furer, J., Ponte Casta\u00f1eda, P.: Homogenization, macroscopic instabilities and domain formation in magnetoactive composites: Theory and applications. J. Mech. Phys. Solids 169, 105081 (2022)","journal-title":"J. Mech. Phys. Solids"},{"key":"10219_CR36","volume-title":"Smart Structures and Materials 1999: Smart Materials Technologies","author":"J Ginder","year":"1999","unstructured":"Ginder, J., Nichols, M., Elie, L., Tardiff, J.: Magnetorheological elastomers: Properties and applications. In: Wuttig, M. (ed.) Smart Structures and Materials 1999: Smart Materials Technologies. SPIE, Bellingham, WA (1999)"},{"issue":"2","key":"10219_CR37","doi-asserted-by":"publisher","first-page":"237","DOI":"10.1080\/01418639308226405","volume":"68","author":"R James","year":"1993","unstructured":"James, R., Kinderlehrer, D.: Theory of magnetostriction with applications to Tb$$_x$$Dy$$_{1-x}$$Fe$$_2$$. Philosophical Magazine B 68(2), 237\u2013274 (1993)","journal-title":"Philosophical Magazine B"},{"issue":"5","key":"10219_CR38","doi-asserted-by":"publisher","first-page":"607","DOI":"10.1088\/0964-1726\/5\/5\/009","volume":"5","author":"M Jolly","year":"1996","unstructured":"Jolly, M., Carlson, J., Muoz, B.: A model of the behaviour of magnetorheological materials. Smart Mat. Struct. 5(5), 607\u2013614 (1996)","journal-title":"Smart Mat. Struct."},{"issue":"199","key":"10219_CR39","first-page":"76","volume":"30","author":"J Joule","year":"1847","unstructured":"Joule, J.: Xvii. on the effects of magnetism upon the dimensions of iron and steel bars. Lond. Edinb. Dubl. Phil. Mag. J. Sci. 30(199), 76\u201387 (1847)","journal-title":"Lond. Edinb. Dubl. Phil. Mag. J. Sci."},{"issue":"12","key":"10219_CR40","doi-asserted-by":"publisher","first-page":"2869","DOI":"10.1016\/j.jmps.2004.04.007","volume":"52","author":"S Kankanala","year":"2004","unstructured":"Kankanala, S., Triantafyllidis, N.: On finitely strained magnetorheological elastomers. J. Mech. Phys. Solids 52(12), 2869\u20132908 (2004)","journal-title":"J. Mech. Phys. Solids"},{"key":"10219_CR41","series-title":"Progress in Nonlinear Differential Equations and Their Applications","doi-asserted-by":"publisher","first-page":"177","DOI":"10.1007\/978-3-0348-9244-5_17","volume-title":"Variational Methods for Discontinuous Structures","author":"D Kinderlehrer","year":"1996","unstructured":"Kinderlehrer, D.: Magnetoelastic interactions. In: Serapioni, R., Tomarelli, F. (eds.) Variational Methods for Discontinuous Structures. Progress in Nonlinear Differential Equations and Their Applications, vol. 25, pp. 177\u2013189. Birkh\u00e4user Basel, Basel (1996)"},{"key":"10219_CR42","doi-asserted-by":"publisher","DOI":"10.1093\/oso\/9780198506041.001.0001","volume-title":"Electromagnetic Theory","author":"A Kovetz","year":"2000","unstructured":"Kovetz, A.: Electromagnetic Theory. Oxford Science Publications. Oxford University Press, Oxford (2000)"},{"issue":"3","key":"10219_CR43","doi-asserted-by":"publisher","first-page":"269","DOI":"10.4171\/zaa\/1435","volume":"30","author":"S Kr\u00f6mer","year":"2011","unstructured":"Kr\u00f6mer, S.: On compactness of minimizing sequences subject to a linear differential constraint. Z. Anal. Anwend. 30(3), 269\u2013303 (2011)","journal-title":"Z. Anal. Anwend."},{"issue":"3","key":"10219_CR44","doi-asserted-by":"publisher","first-page":"189","DOI":"10.1007\/BF00284506","volume":"99","author":"S M\u00fcller","year":"1987","unstructured":"M\u00fcller, S.: Homogenization of nonconvex integral functionals and cellular elastic materials. Arch. Rational Mech. Anal. 99(3), 189\u2013212 (1987)","journal-title":"Arch. Rational Mech. Anal."},{"issue":"2","key":"10219_CR45","doi-asserted-by":"publisher","first-page":"295","DOI":"10.1051\/cocv:2004008","volume":"10","author":"G Pisante","year":"2004","unstructured":"Pisante, G.: Homogenization of micromagnetics large bodies. ESAIM Control Optim. Calc. Var. 10(2), 295\u2013314 (2004)","journal-title":"ESAIM Control Optim. Calc. Var."},{"issue":"2","key":"10219_CR46","doi-asserted-by":"publisher","first-page":"194","DOI":"10.1016\/j.jmps.2010.11.004","volume":"59","author":"P Ponte Casta\u00f1eda","year":"2011","unstructured":"Ponte Casta\u00f1eda, P., Galipeau, E.: Homogenization-based constitutive models for magnetorheological elastomers at finite strain. J. Mech. Phys. Solids 59(2), 194\u2013215 (2011)","journal-title":"J. Mech. Phys. Solids"},{"issue":"3","key":"10219_CR47","doi-asserted-by":"publisher","first-page":"267","DOI":"10.1016\/0304-8853(83)90055-0","volume":"37","author":"Z Rigbi","year":"1983","unstructured":"Rigbi, Z., Jilk\u00e9n, L.: The response of an elastomer filled with soft ferrite to mechanical and magnetic influences. J. Magnetism Mag. Mat. 37(3), 267\u2013276 (1983)","journal-title":"J. Magnetism Mag. Mat."},{"key":"10219_CR48","volume-title":"Convex analysis, volume No 28 of Princeton Mathematical Series","author":"RT Rockafellar","year":"1970","unstructured":"Rockafellar, R.T.: Convex analysis, volume No 28 of Princeton Mathematical Series. Princeton, Princeton University Press (1970)"},{"issue":"2","key":"10219_CR49","doi-asserted-by":"publisher","first-page":"16","DOI":"10.3390\/act7020016","volume":"7","author":"A Rossi","year":"2018","unstructured":"Rossi, A., Orsini, F., Scorza, A., Botta, F., Belfiore, N.P., Sciuto, S.A.: A review on parametric dynamic models of magnetorheological dampers and their characterization methods. Actuators 7(2), 16 (2018)","journal-title":"Actuators"},{"issue":"10","key":"10219_CR50","doi-asserted-by":"publisher","first-page":"1424","DOI":"10.1177\/1081286520975808","volume":"26","author":"BL Sharma","year":"2021","unstructured":"Sharma, B.L., Saxena, P.: Variational principles of nonlinear magnetoelastostatics and their correspondences. Math. Mech. Solids 26(10), 1424\u20131454 (2021)","journal-title":"Math. Mech. Solids"},{"issue":"11","key":"10219_CR51","doi-asserted-by":"publisher","first-page":"2453","DOI":"10.1007\/s00707-013-0948-5","volume":"224","author":"C Spieler","year":"2013","unstructured":"Spieler, C., K\u00e4stner, M., Goldmann, J., Brummund, J., Ulbricht, V.: XFEM modeling and homogenization of magnetoactive composites. Acta Mech. 224(11), 2453\u20132469 (2013)","journal-title":"Acta Mech."},{"issue":"4","key":"10219_CR52","doi-asserted-by":"publisher","first-page":"390","DOI":"10.1177\/1081286507080808","volume":"14","author":"DJ Steigmann","year":"2007","unstructured":"Steigmann, D.J.: On the formulation of balance laws for electromagnetic continua. Math. Mech. Solids 14(4), 390\u2013402 (2007)","journal-title":"Math. Mech. Solids"},{"issue":"6","key":"10219_CR53","doi-asserted-by":"publisher","first-page":"907","DOI":"10.1177\/1081286517696536","volume":"23","author":"M \u0160ilhav\u00fd","year":"2018","unstructured":"\u0160ilhav\u00fd, M.: A variational approach to nonlinear electro-magneto-elasticity: Convexity conditions and existence theorems. Math. Mech. Solids 23(6), 907\u2013928 (2018)","journal-title":"Math. Mech. Solids"},{"issue":"3","key":"10219_CR54","doi-asserted-by":"publisher","first-page":"738","DOI":"10.1177\/1081286518754567","volume":"24","author":"M \u0160ilhav\u00fd","year":"2019","unstructured":"\u0160ilhav\u00fd, M.: Isotropic polyconvex electromagnetoelastic bodies. Math. Mech. Solids 24(3), 738\u2013747 (2019)","journal-title":"Math. Mech. Solids"}],"container-title":["Journal of Nonlinear Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00332-025-10219-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00332-025-10219-7","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00332-025-10219-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,9]],"date-time":"2026-03-09T10:03:47Z","timestamp":1773050627000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00332-025-10219-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,11,7]]},"references-count":54,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2026,2]]}},"alternative-id":["10219"],"URL":"https:\/\/doi.org\/10.1007\/s00332-025-10219-7","relation":{},"ISSN":["0938-8974","1432-1467"],"issn-type":[{"value":"0938-8974","type":"print"},{"value":"1432-1467","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,11,7]]},"assertion":[{"value":"25 June 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 October 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"7 November 2025","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare no Conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"4"}}