In order to study the influences of interfaces on magnetoelectric (ME) coupling, a finite element model for multiferroics composites was suggested by employing cohesive zone elements for the interfaces. Piezoelectric elements were utilized for both piezoelectric and piezomagnetic phases based on the analogy between piezoelectric and piezomagnetic constitutive relations. And cohesive zone models (CZM) were employed to represent the relation between tractions and displacement discontinuities on imperfect interfaces, which characterized the stiffness and toughness of interfaces and were implemented by cohesive zone elements. Imperfect interfaces can be modeled by adopting CZM parameters, and perfect interfaces are also possible to be approximately modeled by CZM with enhanced interfacial stiffness. Example results of laminated multiferroics composites with ideal interfaces show good agreement with those in literature. The influences of imperfect interfaces on ME coupling were analyzed by the present finite element model, the corresponding ME coefficients were calculated. The simulation results indicate that the interface stiffness plays a significant role on ME coefficient of the composites. When the interfaces are stiff enough, they tend to be perfect and the ME coefficient tends to a constant. The present method and results are of reference significance to process of interfacial bonding and prediction of ME properties.
[1] EERENSTEIN W, MATHUR N D, SCOTT J F. Multiferroic and magnetoelectric materials[J]. Nature, 2006, 442(7104): 759-765.
[2] YUAN Guoliang, OR S W. Multiferroicity in polarized singlephaseBi0.875Sm0.125FeO3ceramics[J]. Journal of Applied Physics , 2006 , 100(2): 024109.
[3] YUAN Guoliang, OR SW, LIU Junming, et al. Structural transformation and ferroelectromagnetic behavior in singlephaseBi1xNdxFeO3multiferroic ceramics [J]. Applied Physics Letters, 2006, 89(5): 052905.
[4] WANG Yiping, YUAN Guoliang, CHEN Xiaoyuan, et al. Electrical and magnetic properties of singlephased and highly resistive ferroelectromagnet BiFeO3ceramic[J]. Journal of Physics D: Applied Physics, 2006, 39(10): 2019-2023.
[5] SPALDIN N A, FIEBIG M. The renaissance of magnetoelectric multiferroics [J]. Science, 2005, 309(5733): 391-392.
[6] NAN Cewen. Magnetoelectric effect in composites of piezoelectric and piezomagnetic phases [J]. Physical Review B, 1994(50): 6082-6088.
[7] PAN E, WANG R. Effects of geometric size and mechanical boundary conditions on magnetoelectric coupling in multiferroic composites [J]. Journal of Physics D:Applied Physics, 2009, 42(24):245503.
[8] NAN Cewen, BICHURIN M I, DONG Shuxiang, et al. Multiferroic magnetoelectric composites: Historical perspective, status, and future directions [J]. Journal of Applied Physics, 2008, 103: 031101.
[9] NEEDLEMAN A. A continuum model for void nucleation by inclusion debonding [J]. Journal of Applied Mechanics Transactions of The Asme, 1987, 54(3): 525-531.
[10] NEEDLEMAN A. An analysis of tensile decohesion along an interface [J]. Journal of The Mechanics and Physics of Solids, 1990, 38(3): 289-324.
[11] CAMACHO G T, ORTIZ M. Computational modeling of impact damage in brittle materials [J]. International Journal of Solids and Structures,1996,33(20/22): 2899-2938.
[12] GEUBELLE P H, BAYLOR J . Impactinduced delamination of laminated composites: A 2D simulation [J]. Composites Part BEngineering, 1998, 29: 589-602.
[13] 闫亚宾, 尚福林. PZT薄膜界面分层破坏的内聚力模拟[J]. 中国科学, 2009, 39(7): 1007-1017.
YAN Yabin, SHANG Fulin. Choesive zone modeling of interfacial delamination in PZT thin films [J]. Science in China, 2009, 39(7): 1007-1017.
[14] 曲凯, 张旭东, 李高春. 基于内聚力界面脱黏的复合固体推进剂力学性能研究[J], 火炸药学报, 2008, 31(6): 77-81.
QU Kai, ZHANG Xudong, LI Gaochun. Research on mechanical performance of composite propellant with cohesive interface debonding [J]. Chinese Journal of Explosives and Propellants, 2008, 31(6): 77-81.
[15] 周储伟,杨卫,方岱宁. 内聚力界面单元与复合材料的界面损伤分析[J]. 力学学报,1999,31(3): 372-377.
ZHOU Chuwei, YANG Wei, FANG Daining. Cohesive interface element and interfacial damage analysis of composites [J]. Acta Mechanica Sinica, 1999, 31(3): 372-377.
[16] BLACKBURN J F, VOPSAROIU M, CAIN M G. Verified finite element simulation of multiferroic structures: Solutions for conducting and insulating systems [J]. Journal of Applied Physics, 2008, 104: 074104.