Abstract
This paper presents a fully coupled model to account for the flux pinning induced giant magnetostriction in type-II superconductors under alternating magnetic field The superconductor E-J constitutive law is characterized by power law where the critical current density is assumed to depend exponentially on the flux density. The governing equations of the two-field problem (i.e., the interactions of elastic and magnetic effects) are formulated in a two-dimensional model. The magnetostriction curves and magnetization loops are calculated over a wide range of parameters. The effects of applied magnetic field frequency f and amplitude B0 and critical current density on magnetostriction and magnetization are discussed. Results show that the critical current density of high temperature superconductor (HTS) YBCO has a significant effect on the magnetization and magnetostriction. The pinning-induced magnetostriction which has been observed in experiment can be qualitatively simulated by this model.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Murakami, M., Progress in applications of bulk high temperature superconductors. Superconductor Science and Technology, 2000, 13: 448–450.
Hong, Z., Jiang, Q., Pei, R., Campbell, A.M. and Coombs, T.A., A numerical method to estimate AC loss in superconducting coated conductors by finite element modeling. Superconductor Science and Technology, 2007, 20: 331–337.
Ikuta, H., Hirota, N. and Nakayama, Y., Giant magnetostriction in Bi2Sr2CaCu2O8 single crystal in the superconducting state and its mechanism. Physical Review Letters, 1993, 70: 2166–2169.
Ikuta, H., Kishio, K. and Kitazawa, K., Critical state models for fllux-pinning-induced magnetostriction in type-II superconductors. Journal of Applied Physics, 1994, 76: 4776–4786.
Çelebi, S., Inanir, F. and LeBlanc, M.AR., Coexistence of critical and normal state magnetostrictions in type II superconductors: A model exploration. Journal of Applied Physics, 2007, 101: 013906 1–4.
Inanir, F., Okutan, M. and Yakuphanog, F., Modeling of normal-state like contribution on the pinning induced magnetostriction. Physica C, 2008, 468: 39–46.
Johansen, T.H., Shape distortion by irreversible flux-pinning-induced magnetostriction. Physical Review Letters, 1998, 80: 4757–4760.
Johansen, T.H., Flux-pinning-induced stress and strain in superconductors: Long rectangular slab. Physical Review B, 1999, 59: 11187–11190.
Johansen, T.H., Flux-pinning-induced stress and strain in superconductors: Case of a long circular cylinder. Physical Review B, 1999, 60: 9690–9703.
Johansen, T.H., Wang, C., Chen, Q.Y. and Chu, W., Enhancement of tensile stress near a hole in superconducting trapped-field magnets. Journal of Applied Physics , 2000, 88: 2730–2733.
Zhou, Y. and Yong, H., Crack problem for a long rectangular slab of superconductor under an electromagnetic force. Physical Review B, 2007, 76: 094523 1–5.
Ren, Y. and Weinstein, R., Damage caused by magnetic pressure at high trapped field in quasi-permanent magnets composed of melt-textured Y-Ba-Cu-O superconductor. Physica C, 1995, 251: 15–26.
Johansen, T.H. and Shantsev, D.V., Magnetostrictive behaviour of thin superconducting disks. Superconductor Science and Technology, 2003, 16: 1109–1114.
Yong, H., Jing, Z. and Zhou, Y., Magnetostriction and magnetization in deformable superconductors. Physica C, 2012, 483: 51–54.
Gao, Z., Zhou, Y. and Lee, K.Y., The interaction of two collinear cracks in a rectangular superconductor slab under an electromagnetic force. Physica C, 2010 , 470: 654–658.
Gao, Z. and Zhou, Y., Crack growth for a long rectangular slab of superconducting trapped-field magnets. Superconductor Science and Technology, 2008, 21: 095010 1–5.
Gao, Z., Zhou, Y. and Lee, K.Y., Crack–inclusion problem for a long rectangular slab of superconductor under an electromagnetic force. Computational Materials Science, 2010, 50: 279–282.
Zhang, M., Kvitkovic, J., Kim, J., Kim, C.H. and Pamidi, S.V., Alternating current loss of second-generation high-temperature superconducting coils with magnetic and non-magnetic substrate. Applied Physics letters, 2012, 101: 102602 1–4.
Benatar, J.G., FEM Implementations of Magnetostrictive-based Applications. University of Maryland, 2005.
Hong, Z., Campbell, A.M. and Coombs, T.A., Numerical solution of critical state in superconductivity by finite element software. Superconductor Science and Technology, 2006, 19: 1246–1252.
Datta, S. and Flatau, A.B., Smart Structures and Materials 2005: Smart Structures and Integrated Systems, 2005.
Kannan, K.S., Galerkin Finite Element Scheme for Magnetostrictive Structures and Composites. PhD thesis, University of Maryland, 1997.
Author information
Authors and Affiliations
Corresponding author
Additional information
Project supported by the National Natural Science Foundation of China (Nos. 11272140, 10902046, 11032006 and 11121202), the Fundamental Research Funds for the Central Universities (lzujbky-2015-176), and National Key Project of Magneto-Constrained Fusion Energy Development Program (2013GB110002).
Rights and permissions
About this article
Cite this article
Gao, Z., Zhou, Y. A magneto-mechanical fully coupled model for giant magnetostriction in high temperature superconductor. Acta Mech. Solida Sin. 28, 353–359 (2015). https://doi.org/10.1016/S0894-9166(15)30021-5
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1016/S0894-9166(15)30021-5