zbMATH — the first resource for mathematics

Magnetostriction of a hard ferromagnetic and elastic thin-film structure. (English) Zbl 1175.74035
Summary: In this paper, the magnetostriction of a thin film ferromagnetic and elastic structure is investigated. The structure is composed of an elastic layer confined between two perfectly bonded thin ferromagnetic layers in a plane strain setting. The ferromagnetic layers are saturated insulators and their magnetization is assumed at every stage parallel to the relevant layer’s axis (latent microstructure). The structure is studied within the theory of magneto-elastic interaction and focus is set on reducing the problem to a manageable one-dimensional form. This is accomplished employing the Euler-Bernoulli kinematics in conjunction with Maxwell equations. Once the model is stated, a system of coupled nonlinear integro-differential equations is obtained in the deformation components. Integral terms spring from the non-local character of the magnetic interaction. Some features of the solution are pointed out through an asymptotic analysis. The system is solved through the spectral method and a collocation technique, employing Gaussian quadrature at a second grid to assess the magnetic field and an iterative solver for nonlinear systems. Plots of the deformed configuration, of the internal action and of the layers’s interaction are given. A parametric analysis brings out the role of some dimensionless quantities. Finally, solutions are compared with experimental results on Nickel magnetostriction.

74F15 Electromagnetic effects in solid mechanics
74K35 Thin films
74E30 Composite and mixture properties
HYBRJ; minpack
Full Text: DOI
[1] Bozorth, R.M., The Bell Telephone Laboratories Series (1951)
[2] Toupin, R., Journal of Rational Mechanics and Analysis 5 pp 849– (1956)
[3] Brown, Jr, W.F., Magnetoelastic Interaction, Tracts in Natural Philosophy (1966) · doi:10.1007/978-3-642-87396-6
[4] Tiersten, H.F., Journal of Mathematical Physics 5 pp 1298– (1994) · Zbl 0131.42803 · doi:10.1063/1.1704239
[5] Brown, Jr, W.F., Selected Topics in Solid State Physics (1962)
[6] Moon, F.C., Magneto-Solid Mechanics (1984)
[7] Pao, Y.-H., International Journal of Engineering Science 11 pp 415– (1973) · Zbl 0252.73070 · doi:10.1016/0020-7225(73)90059-1
[8] Dorfmann, A., Quarterly Journal of Mechanics and Applied Mathematics 56 pp 1– (2004)
[9] Moon, F.C., Journal of Applied Mechanics (1968)
[10] Wallerstein. D. V., Journal of Applied Mechanics E 39 pp 451– (1972) · doi:10.1115/1.3422699
[11] Nobili, A., A hard ferromagnetic and elastic beam-plate sandwich structure, Zeitschrift für Angewandte Mathematik und Physik (ZAMP) (2006) · Zbl 1161.74023
[12] Zhou, Y.-H., International Journal of Engineering Science 35 pp 1405– (1997) · Zbl 0916.73041 · doi:10.1016/S0020-7225(97)00051-7
[13] Pao, Y.-H., Mechanics Today 4 pp 209– (1978) · doi:10.1016/B978-0-08-021792-5.50012-4
[14] Funaro, D., Lecture Notes in Physics 8 (1992) · Zbl 0762.65076
[15] Garbow, B.S., MinPack project (1980)
[16] Mikhlin, S.G., Multidimensional Singular Integrals and Integral Equations (1965) · Zbl 0129.07701
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.