Abstract
The elongation of a ferroelastic material sample (whose initial shape is a sphere or an ellipsoid of revolution) under the action of an external magnetic field is studied in an in approximation of small strains. For a sphere, there is a classical estimate obtained under the assumption that elongating in the direction of the field, it becomes a spheroid and the stress and strain fields remain uniform. In the present calculation, it is assumed that the body is an ellipsoid (a sphere in a particular case) only in the absence of an external field; the shape of the sample in the presence of a field is not specified in advance but is found from the condition of balance of surface forces (elastic and magnetic). For the spherical case, the problem is solved exactly: it is shown, that the contour of the deformed body is described by a third-order algebraic equation. The case where the initial configuration is an ellipsoid of revolution is studied numerically. It is shown that in all versions, the refined solution leads to an appreciable increase in the elongation of the sample compared to the classical estimate.
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REFERENCES
M. Zrínyi, L. Barsi, and A. Büki, “Strain of ferrogels induced by nonuniform magnetic fields,” J. Chem. Phys., 104, No. 21, 8750–8756 (1996).
N. Kato, Y. Takizawa, and F. Takahashi, “Magnetically driven chemomechanical device with poly (N-isopropylacrylamide) hydrogel containing γ-Fe2O3”, J. Intellig. Mater. Syst. Struct., 8, No. 7, 588–596 (1997).
M. Zrínyi, L. Barsi, D. Szabo, and H.-G. Kilian, “Direct observation of abrupt shape transition in ferrogels induced by nonuniform magnetic field,” J. Chem. Phys., 106, No. 13, 5685–5692 (1997).
M. Zrínyi, L. Barsi, and A. Büki, “Ferrogel: A new magneto-controlled elastic medium,” Polymer Gels Networks, 5, 415–427 (1997).
L. V. Nikitin, L. S. Mironova, G. V. Stepanov, and A. N. Samus’, “Effect of a magnetic field on the elastic and viscous properties of magnetoelastic materials,” Vysokomol. Soed., 43, No. 4, 698–706 (2001).
J. A. Galicia, O. Sandre, F. Cousin, et al., “Designing magnetic composite materials using aqueous magnetic uids,” J. Phys. Condens. Matter, 15, No. 15, 1379–1402 (2003).
K. G. Kornev, L. V. Nikitin, and L. S. Mironova, “Change in the form of a spherical ferroelastic sample in a uniform magnetic field,” in: Abstracts of the XVI Int. Workshop on New Magnetic Materials for Microelectronics, Part 2, Moscow (1998), pp. 387–388.
Yu. L. Raikher and O. V. Stolbov, “Magnetic-deformation effect in a ferroelastic material,” Pis’ma Zh. Tekh. Fiz., 26, No. 4, 47–53 (2000).
L. D. Landau and E. M. Lifshits, Course of Theoretical Physics, Vol. 8: Electrodynamics of Continuous Media, Pergamon, New York (1984).
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 3, pp. 153–164, May–June, 2005.
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Raikher, Y.L., Stolbov, O.V. Deformation of an ellipsoidal ferrogel sample in a uniform magnetic field. J Appl Mech Tech Phys 46, 434–443 (2005). https://doi.org/10.1007/s10808-005-0094-5
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DOI: https://doi.org/10.1007/s10808-005-0094-5