铁磁形状记忆合金马氏体变体重取向行为的热力学模型及其应用
|
摘要
铁磁形状记忆合金(Ferromagnetic Shape Memory Alloys,简称为FSMAs)且有强铁磁性、大磁致应变、响应频率高、磁控形状记忆效应等优点,是一种极具应用潜力的铁磁性功能材料。针对铁磁形状记忆合金材料在横向磁场和轴向应力场作用下的马氏体变体重取向的力磁耦合行为和大磁致应变输出等行为,本文开展了相关的理论研究和数值模拟。
首先我们基于复合材料细观力学Eshelby等效夹杂理论和Mori-Tanaka场平均方法,将铁磁形状记忆合金材料内部马氏体变体重取向过程中长大的马氏体变体看作夹杂相、变小的马氏体变体看作基体相,推导出了铁磁形状记忆合金材料在力磁耦合重取向过程中的总应变表达式。其次根据热力学原理,建立了描述马氏体变体力磁耦合重取向行为的热力学模型,其中提出了一形式简单、相关系数实验可测并具有力学意义的马氏体变体重取向的热力学阻力公式,并由此建立了其与驱动马氏体变体孪晶界移动的广义热力学驱动力间的热力学平衡方程。
通过选取适当的描述材料马氏体变体重取向过程中微结构变化的内部状态变量,将细观力学理论与宏观热力学原理结合,实现了对铁磁形状记忆合金材料内部马氏体变体力磁耦合重取向行为的描述。进而模拟了描述材料内部马氏体变体微结构变化的三个内部状态变量及磁化强度的演化过程。相关结果表明：本文的模型可以很好地预测铁磁形状记忆合金马氏体变体发生重取向以及逆取向的相关力磁耦合行为；并可以预测马氏体变体重取向过程发生和结束的临界磁场值及变体逆取向过程发生和结束的临界应力值。最后我们还对马氏体变体重取向过程完全不发生、部分发生和完全发生的机理或外界场限制条件进行了讨论。
Ferromagnetic shape memory alloys (FSMAs) are a potential application of ferromagnetic functional material, which exhibit advantages such as high ferromagnetism, huge output strains, high response frequencies etc. The shape memory effect (SME) of FSMAs can be controlled not only by a thermal field or a stress field, but also by a magnetic field. The theoretical studies and numerical simulations for FSMAs are conducted, aiming at their mechanical-magnetic coupling behaviors of martensite variants rearrangement and huge output magnetic field-induced strain behaviors caused by applied both of transversal magnetic field and axial compressive stress.
Firstly, the total strain of FSMAs is derived from the Eshelby equivalent inclusion method and the Mori-Tanaka averaged scheme during the martensite variants mechanical-magnetic coupling rearrangement process, by treating the growth variant as inclusion phase and the decrease variant as parent phase. Secondly, the thermodynamic model based on thermodynamic principle is proposed to describe the mechanical-magnetic coupling behaviors during the martensite variants rearrangement process. Furthermore, a simple form thermodynamic resistance formula for martensite variants rearrangement process is proposed, which has the mechanical significant. And the correlation coefficients can be measured by experiment. Thus, a thermodynamic balance equation is established for the thermodynamic resistance formula and the generalized thermodynamic driving force leading to martensite variants twin boundary motion.
The proper internal state variables, which combine the micromechanics theory with the thermodynamic principle, are chosen to describe the microstucture change during the martensite variants rearrangement process. The above method realizes to describe the mechanical-magnetic coupling rearrangement behaviors of the martensite variants. The evolution process of the three internal state variables and the magnetization are numerical simulated to describe the microstructure change of martensite variants. The results show that, the model can give the good predictions on the mechanical-magnetic coupling behaviors during the martensite variants rearrangement or inverse rearrangement process of the FSMAs under either the loading of magnetic field or compressive stress. The model can well predict the critical field for the start and end of the martensite variants rearrangement process and the critical stress for the start and end of the inverse rearrangement process. Lastly, the model discusses the mechanism and the applied field conditions of how the martensite variants rearrangement process could not happen, partly happen or completely happen.
首先我们基于复合材料细观力学Eshelby等效夹杂理论和Mori-Tanaka场平均方法,将铁磁形状记忆合金材料内部马氏体变体重取向过程中长大的马氏体变体看作夹杂相、变小的马氏体变体看作基体相,推导出了铁磁形状记忆合金材料在力磁耦合重取向过程中的总应变表达式。其次根据热力学原理,建立了描述马氏体变体力磁耦合重取向行为的热力学模型,其中提出了一形式简单、相关系数实验可测并具有力学意义的马氏体变体重取向的热力学阻力公式,并由此建立了其与驱动马氏体变体孪晶界移动的广义热力学驱动力间的热力学平衡方程。
通过选取适当的描述材料马氏体变体重取向过程中微结构变化的内部状态变量,将细观力学理论与宏观热力学原理结合,实现了对铁磁形状记忆合金材料内部马氏体变体力磁耦合重取向行为的描述。进而模拟了描述材料内部马氏体变体微结构变化的三个内部状态变量及磁化强度的演化过程。相关结果表明：本文的模型可以很好地预测铁磁形状记忆合金马氏体变体发生重取向以及逆取向的相关力磁耦合行为；并可以预测马氏体变体重取向过程发生和结束的临界磁场值及变体逆取向过程发生和结束的临界应力值。最后我们还对马氏体变体重取向过程完全不发生、部分发生和完全发生的机理或外界场限制条件进行了讨论。
Ferromagnetic shape memory alloys (FSMAs) are a potential application of ferromagnetic functional material, which exhibit advantages such as high ferromagnetism, huge output strains, high response frequencies etc. The shape memory effect (SME) of FSMAs can be controlled not only by a thermal field or a stress field, but also by a magnetic field. The theoretical studies and numerical simulations for FSMAs are conducted, aiming at their mechanical-magnetic coupling behaviors of martensite variants rearrangement and huge output magnetic field-induced strain behaviors caused by applied both of transversal magnetic field and axial compressive stress.
Firstly, the total strain of FSMAs is derived from the Eshelby equivalent inclusion method and the Mori-Tanaka averaged scheme during the martensite variants mechanical-magnetic coupling rearrangement process, by treating the growth variant as inclusion phase and the decrease variant as parent phase. Secondly, the thermodynamic model based on thermodynamic principle is proposed to describe the mechanical-magnetic coupling behaviors during the martensite variants rearrangement process. Furthermore, a simple form thermodynamic resistance formula for martensite variants rearrangement process is proposed, which has the mechanical significant. And the correlation coefficients can be measured by experiment. Thus, a thermodynamic balance equation is established for the thermodynamic resistance formula and the generalized thermodynamic driving force leading to martensite variants twin boundary motion.
The proper internal state variables, which combine the micromechanics theory with the thermodynamic principle, are chosen to describe the microstucture change during the martensite variants rearrangement process. The above method realizes to describe the mechanical-magnetic coupling rearrangement behaviors of the martensite variants. The evolution process of the three internal state variables and the magnetization are numerical simulated to describe the microstructure change of martensite variants. The results show that, the model can give the good predictions on the mechanical-magnetic coupling behaviors during the martensite variants rearrangement or inverse rearrangement process of the FSMAs under either the loading of magnetic field or compressive stress. The model can well predict the critical field for the start and end of the martensite variants rearrangement process and the critical stress for the start and end of the inverse rearrangement process. Lastly, the model discusses the mechanism and the applied field conditions of how the martensite variants rearrangement process could not happen, partly happen or completely happen.
引文
[1]宫峰飞.铁磁NiMnGa形状记忆合金研究的新进展[J].材料导报,2003,17(8)：1-4.
[2]李健靓,张羊换,郭世海,祁炎,全白云,王新林.铁磁形状记忆合金Ni2MnGa的研究现状及发展[J].金属功能材料,2003,10(5)：25-30.
[3]徐祖耀,金学军.形状记忆材料的新进展[J].功能材料,2004,35：6-10.
[4]谢建宏,张为公,梁大开.智能材料结构的研究现状及未来发展[J].材料导报,2006,20(11)：6-9.
[5]裘进浩,边义祥,季宏丽,朱孔军.智能材料结构在航空领域中的应用[J].航空制造技术,2009,3：26-29.
[6]蒋海涛,颜令辉.智能材料在飞行器翼面结构中的应用探索[J].飞航导弹,2008,1：56-60.
[7]朱玉萍.形状记忆合金材料的细观力学模型若干问题研究[D].北京：北京交通大学,2007.
[8]魏融冰.基于细观力学的铁磁形状记忆合金NiMnGa热力学本构关系研究[D].兰州：兰州大学,2010.
[9]肖恩忠.形状记忆合金的应用现状与发展趋势[J].工具技术,2005,39(12)：10-13.
[10]Chernenko, V.A., and Besseghini, S. Ferromagnetic shape memory alloys:Scientific and applied aspects[J]. Sensors and Actuators A.2008,142(2):542-548.
[11]Adaptive Materials Technology-AdaptaMat Ltd, Finland, http://www.adaptamat.com/. 2012-03-11.
[12]Wutting, M, J.L., and Craciunescu, C. A new Ferromagnetic shape memory alloy system[J]. Scripta mater.2001,44(10):2393-2397.
[13]James, R.D., and Hane, K.F. Martensite transformations and shape-memory materials[J]. Acta Mater.2000,48(1):197-222.
[14]Chernenko, V.A., Segui, C., Cesari, E., Pons, J., and Kokorin, V.V. Sequence of martensitic transformations in NiMnGa alloys[J]. Physical Review B.1998,57(5):2659-2662.
[15]Pons, J., Chernenko, V.A., Santamarta, R., and Cesari, E. Crystal structure of matrensitic phases in NiMnGa shape memory alloys[J]. Acta Mater.2000,48:3027-3038.
[16]James, R.D., Tickle, R., and Wutting, M. Large-field induced strains in ferromagnetic shape memory materials[J]. Mater. Sci. Eng. A.1999,273-275:320-325.
[17]Sozinov, A., Ezer, Y., Kimmel, G., Yakovenko, P., Giller, D., Wolfus, Y, Yeshurun, Y, Ullakko, K., and Lindroos, V.K. Large magnetic-field-induced strains in Ni-Mn-Ga alloys in rotating magnetic field[J]. J.Phys. IV.2001,11(8):311-316.
[18]Ge, Y., Heczko, O., Soderberg, O., and Hannula, S.P. Direct optical observation of magnetic domains in a Ni-Mn-Ga martensite[J]. Appl.Phys.Lett.2006,89:082502-1-3.
[19]Ge, Y, Heczko, O., Soderberg, O., and Lindroos, V.K. Various magnetic domain structures in a Ni-Mn-Ga martensite exhibiting magnetic shape memory effect[J]. J.Appl.Phys. 2004,96(4):2159-2163.
[20]Enkovaara, J., Ayuela, A., Zayak, A.T., Entel, P., Nordstrom, L., Dube, M., Jalkanen, J., Impola, J., and Nieminen, R.M. Magnetically driven shape memory alloys[J]. Mater. Sci. Eng. A.2004,378(1-2):52-60.
[21]Kiefer, B., and Lagoudas, D.C. Modeling of magnetic field-induced martensitic variant reorientation and the associated magnetic shape memory effect in MSMAs[J]. Smart Structures and Materials,2005,5761:454-465.
[22]Kiefer, B., and Lagoudas, D.C. Magnetic field-induced martensite variant reorientation in magnetic shape memory alloys[J]. Philosophical Magazine.2005,85(33-35):4289-4329.
[23]Armstrong, J.N., Sullivan, M.R., Romancer, M.L., Chernenko, V.A., and Chopra, H.D. Role of magnetostatic interactions in micromagnetic structure of multiferroics[J]. J.Appl.Phys. 2008,103(2):023905-1-5.
[24]James, R.D., and Wutting, M. Magnetostriction of martensite[J]. Phil. Mag. A. 1998,77(5):1273-1299.
[25]DeSimone, A., and James, R.D. Energetics of magnetoelastic domains in ferromagnetic shape memory alloys[J]. J. de Phys.2003,112:969-972.
[26]Ma, Y.F., and Li, J.Y. Magnetization rotation and rearrangement of martensite variants in ferromagnetic shape memory alloys[J]. Appl. Phys. Lett.2007,90(17):172504-1-3.
[27]Li, J.Y., and Ma, Y.F. Magnetoelastic modeling of magnetization rotation and variant rearrangement in ferromagnetic shape memory alloys[J]. Mech. Mater. 2008,40(12):1022-1036.
[28]Zhu, Y., and Dui G. Micromechanical modeling of the stress-induced superelastic strain in magnetic shape memory alloy[J]. Mech. Mater,2007,39(12):1025-1034.
[29]Zhu, Y, and Dui G Model for field-induced reorientation strain in magnetic shape memory alloy with tensile and compressive loads[J] J. Alloys Compd.459(1-2):55-60.
[30]Landis, C.M. A continuum thermodynamics formulation for micro-magneto-mechanics with applications to ferromagnetic shape memory alloys[J]. J. Mech. Phys. Solids. 2008,56(10):3059-3076.
[31]Landis, C.M. A continuum thermodynamics formulation for micro-magneto-mechanics with applications to ferromagnetic shape memory alloys: application to domain wall-twin boundary dissociation[J]. Proc. SPIE.2008,6929:692910-1-8.
[32]O'Handley, R.C. Model for strain and magnetization in magnetic shape memory alloys[J]. 1998,83(6):3263-3270.
[33]Hirsinger, L., and Lexcellent, C. Internal variable model for magneto-mechanical behavior of ferromagnetic shape memory alloys Ni-Mn-Ga[J]. J. Phys. Ⅳ.2003,112:977-980.
[34]Hirsinger, L., and Lexcellent, C. Modeling detwinning of martensite platelets under magnetic and(or) stress actions on Ni-Mn-Ga alloys[J]. J. Magn. Magn. Mater.2003,254-255:275-277.
[35]Kiefer, B., and Lagoudas, D.C. Phenomenological modeling of ferromagnetic shape memory alloys[J]. Proc. SPIE.2004,5387:164-176.
[36]Kiefer, B., Karaca, H.E., Lagoudas, D.C., and Karaman, I. Characterization and modeling of the magnetic field-induced strain and work output in Ni2MnGa magnetic shape memory alloys[J]. J. Magn. Magn. Mater.2007,312(1):164-175.
[37]Sarawate, N.N., and Dapino, M.J. A continuum thermodynamics model for the sensing effect in ferromagnetic shape memory Ni-Mn-Ga[J]. J. Appl. Phys.2007,101(12):123522-1-11.
[38]Sarawate, N.N., and Dapino, M.J. Magnetic-field-induced stress and magnetization in mechanically blocked Ni-Mn-Ga[J]. J. Appl. Phys.2008,103(8):083902-1-4.
[39]Sarawate, N.N., and Dapino, M.J. Magnetization dependence on dynamic strain in ferromagnetic shape memory Ni-Mn-Ga[J]. Appl. Phys. Lett.2008,93(6):062501-1-3.
[40]Sarawate, N.N., and Dapino, M.J. Magnetomechanical characterization and unified energy model for the quasistatic behavior of ferromagnetic shape memory Ni-Mn-Ga[J]. Smart Mater. Struct.2010,19(3):035001-1-20.
[41]李芳.铁磁形状记忆合金马氏体变体重取向及其多场耦合行为研究[D].兰州：兰州大学,2011.
[42]Wang, X.Z., and Li, F. A kinetic model for martensite variants rearrangement in ferromagnetic shape memory alloys[J]. Journal of Applied Physics,2010,108(113921):1-7.
[43]Zhou, Y.H., Zheng, X.J., and Miya, K. Magnetoelastic bending and snapping of ferromagnetic plates in oblique magnetic field[J]. Fusion Eng. Design.1995,30(4):325-337.
[44]Zhou, Y.H., and Zheng, X.J. A theoretical model of magnetoelastic bucking for soft ferromagnetic thin plates[J]. Acta Mech. Sinina.1996,12(3):213-224.
[45]Zhou, Y.H., and Zheng, X.J. A variational principle on magnetoelastic interaction of ferromagnetic thin plates[J]. Acta Mech. Sinina.1997,10(1):1-10.
[46]Zhou, Y.H., and Zheng, X.J. A general expression of magnetic force for soft ferromagnetic plates in complex magnetic fields[J]. Int. J. Eng. Sci.1997,35(15):1405-1417.
[47]周又和,郑晓静.电磁固体结构力学[M].北京：科学出版社.1999.
[48]Zheng, X.J., and Wang, X. Analysis of magnetoelastic interaction of rectangular ferromagnetic plates with nonlinear magnetization[J]. Int. J. Solids and Structures. 2001,38(48-49):8641-8652.
[49]Wang, X., Zhou, Y.H., and Zheng, X.J. A generalized variational model of magneto-thermo-elasticity for nonlinearly magnetized ferroelastic bodies[J]. Int. J. Eng. Sci. 2002,40(17):1957-1973.
[50]Zheng, X.J., and Wang, X. Large-deflection deformation of ferromagnetic plates in magnetic fields[J]. J. Eng. Mech.2003,129(2):245-248.
[51]Wang, X., Lee, J.S., and Zheng, X.J. Magneto-thermo-elastic instability of ferromagnetic plates in thermal and magnetic field[J]. Int. J. Solids and Structures.2003,40(22):6125-6142.
[52]王省哲,郑晓静.铁磁梁式板热弹性屈曲分析[J].兰州大学学报.2005,41(1)：86-90.
[53]Wang, X., and Lee, J.S. Dynamic stability of ferromagnetic beam-plates with magnetoelastic interaction and magnetic damping in transverse magnetic fields[J]. J. Eng. Mech. 2006,132(4):422-428.
[54]Wang, X., and Huang, X. Feedback control and optimization for rotating disk flutter suppression with actuator patches[J]. AIAA Journal.2006,44(4):892-900.
[55]Zheng, X.J., and Liu, X.E. A nonlinear constitutive model for Terfenol-D Rods[J]. J. Appl. Phys.2005,97(5):053901-1-8.
[56]Liu, X.E., and Zheng, X.J. A nonlinear constitutive model for magnetostrictive materials[J]. Acta Mech. Sinica.2005,21(3):278-285.
[57]Zheng, X.J., and Sun, L. A nonlinear constitutive model of magneto-thermo-mechanical coupling for giant magnetostrictive materials[J]. J. Appl. Phys.2006,100(6):063906-1-6.
[58]Zheng, X.J., and Sun, L. A one-dimension coupled hysteresis model for giant magnetostrictive materials[J]. J. Magn. Magn. Mater.2007,309(2):263-271.
[59]Zhou, H.M., Zhou, Y.H., and Zheng, X.J. A general theoretical model of magnetostrictive constitutive relationships for soft ferromagnetic material rods[J]. J. Appl. Phys. 2008,104(2):023907-1-9.
[60]Zhou, H.M., and Zhou, Y.H. Vibration suppression of laminated composite beams using actuators of giant magnetostrictive materials[J]. Smart Mater. Struct.2007,16(1):198-206.
[61]Wang, T.Z., and Zhou, Y.H. A nonlinear transient constitutive model with eddy current effects for giant magnetostrictive materials[J]. J. Appl. Phys.2010,108(12):123905-1-9.
[62]Jin, K., Liang, Y.Y., and Zheng, X.J. Effects of hysteresis losses on dynamic behavior of magnetostrictive actuators[J]. J. Appl. Phys.2011,110,093908.
[63]杜善义,王彪.复合材料细观力学[M].北京：科学出版社,1997.
[64]沈观林,胡更开.复合材料力学[M].北京：清华大学出版社,2006.
[65]Eshelby, J.D. The determination of the elastic field of an Ellipsoidal inclusion, and related problems[J]. Mathematical and Physical Sciences.1957,241(1226):376-396.
[66]Mori. T., and Tanaka, K. Average stress in matrix and average elastic energy of material with misfitting inclusions[J]. Acta Metall.1973,21(5):571-571.
[67]Heczko, O. Magnetic shape memory effect and magnetization reversal[J]. Journal of Magnetism and Magnetic Materials.2005,290-291(2):787-794.
[68]S J Murray, M Marioni, S M Allen, R C O'Handley.6% magnetic-field-induced strain by twin-boundary motion in ferromagnetic NiMnGa[J]. Applied Physics Letters,2000, 77(6):886-888.
[69]Heczko, O., Sozinov, A., and Ullakko, K. Giant Field-Induced Reversible Strain in Magnetic Shape Memory NiMnGa Alloy [J]. IEEE transactions on magnetics.2000,36(5):3266-3268.
[70]Callaway, J.D., Sehitoglu, H., Hamilton, R.F, Aslantas, K., Miller, N., Maier, H.J., and Chumlyakov, Y. Magnetic shape memory in Ni2MnGa as influenced by applied stress [J]. Appl. Phys. Lett.2006,89(22):221905-1-3.
[2]李健靓,张羊换,郭世海,祁炎,全白云,王新林.铁磁形状记忆合金Ni2MnGa的研究现状及发展[J].金属功能材料,2003,10(5)：25-30.
[3]徐祖耀,金学军.形状记忆材料的新进展[J].功能材料,2004,35：6-10.
[4]谢建宏,张为公,梁大开.智能材料结构的研究现状及未来发展[J].材料导报,2006,20(11)：6-9.
[5]裘进浩,边义祥,季宏丽,朱孔军.智能材料结构在航空领域中的应用[J].航空制造技术,2009,3：26-29.
[6]蒋海涛,颜令辉.智能材料在飞行器翼面结构中的应用探索[J].飞航导弹,2008,1：56-60.
[7]朱玉萍.形状记忆合金材料的细观力学模型若干问题研究[D].北京：北京交通大学,2007.
[8]魏融冰.基于细观力学的铁磁形状记忆合金NiMnGa热力学本构关系研究[D].兰州：兰州大学,2010.
[9]肖恩忠.形状记忆合金的应用现状与发展趋势[J].工具技术,2005,39(12)：10-13.
[10]Chernenko, V.A., and Besseghini, S. Ferromagnetic shape memory alloys:Scientific and applied aspects[J]. Sensors and Actuators A.2008,142(2):542-548.
[11]Adaptive Materials Technology-AdaptaMat Ltd, Finland, http://www.adaptamat.com/. 2012-03-11.
[12]Wutting, M, J.L., and Craciunescu, C. A new Ferromagnetic shape memory alloy system[J]. Scripta mater.2001,44(10):2393-2397.
[13]James, R.D., and Hane, K.F. Martensite transformations and shape-memory materials[J]. Acta Mater.2000,48(1):197-222.
[14]Chernenko, V.A., Segui, C., Cesari, E., Pons, J., and Kokorin, V.V. Sequence of martensitic transformations in NiMnGa alloys[J]. Physical Review B.1998,57(5):2659-2662.
[15]Pons, J., Chernenko, V.A., Santamarta, R., and Cesari, E. Crystal structure of matrensitic phases in NiMnGa shape memory alloys[J]. Acta Mater.2000,48:3027-3038.
[16]James, R.D., Tickle, R., and Wutting, M. Large-field induced strains in ferromagnetic shape memory materials[J]. Mater. Sci. Eng. A.1999,273-275:320-325.
[17]Sozinov, A., Ezer, Y., Kimmel, G., Yakovenko, P., Giller, D., Wolfus, Y, Yeshurun, Y, Ullakko, K., and Lindroos, V.K. Large magnetic-field-induced strains in Ni-Mn-Ga alloys in rotating magnetic field[J]. J.Phys. IV.2001,11(8):311-316.
[18]Ge, Y., Heczko, O., Soderberg, O., and Hannula, S.P. Direct optical observation of magnetic domains in a Ni-Mn-Ga martensite[J]. Appl.Phys.Lett.2006,89:082502-1-3.
[19]Ge, Y, Heczko, O., Soderberg, O., and Lindroos, V.K. Various magnetic domain structures in a Ni-Mn-Ga martensite exhibiting magnetic shape memory effect[J]. J.Appl.Phys. 2004,96(4):2159-2163.
[20]Enkovaara, J., Ayuela, A., Zayak, A.T., Entel, P., Nordstrom, L., Dube, M., Jalkanen, J., Impola, J., and Nieminen, R.M. Magnetically driven shape memory alloys[J]. Mater. Sci. Eng. A.2004,378(1-2):52-60.
[21]Kiefer, B., and Lagoudas, D.C. Modeling of magnetic field-induced martensitic variant reorientation and the associated magnetic shape memory effect in MSMAs[J]. Smart Structures and Materials,2005,5761:454-465.
[22]Kiefer, B., and Lagoudas, D.C. Magnetic field-induced martensite variant reorientation in magnetic shape memory alloys[J]. Philosophical Magazine.2005,85(33-35):4289-4329.
[23]Armstrong, J.N., Sullivan, M.R., Romancer, M.L., Chernenko, V.A., and Chopra, H.D. Role of magnetostatic interactions in micromagnetic structure of multiferroics[J]. J.Appl.Phys. 2008,103(2):023905-1-5.
[24]James, R.D., and Wutting, M. Magnetostriction of martensite[J]. Phil. Mag. A. 1998,77(5):1273-1299.
[25]DeSimone, A., and James, R.D. Energetics of magnetoelastic domains in ferromagnetic shape memory alloys[J]. J. de Phys.2003,112:969-972.
[26]Ma, Y.F., and Li, J.Y. Magnetization rotation and rearrangement of martensite variants in ferromagnetic shape memory alloys[J]. Appl. Phys. Lett.2007,90(17):172504-1-3.
[27]Li, J.Y., and Ma, Y.F. Magnetoelastic modeling of magnetization rotation and variant rearrangement in ferromagnetic shape memory alloys[J]. Mech. Mater. 2008,40(12):1022-1036.
[28]Zhu, Y., and Dui G. Micromechanical modeling of the stress-induced superelastic strain in magnetic shape memory alloy[J]. Mech. Mater,2007,39(12):1025-1034.
[29]Zhu, Y, and Dui G Model for field-induced reorientation strain in magnetic shape memory alloy with tensile and compressive loads[J] J. Alloys Compd.459(1-2):55-60.
[30]Landis, C.M. A continuum thermodynamics formulation for micro-magneto-mechanics with applications to ferromagnetic shape memory alloys[J]. J. Mech. Phys. Solids. 2008,56(10):3059-3076.
[31]Landis, C.M. A continuum thermodynamics formulation for micro-magneto-mechanics with applications to ferromagnetic shape memory alloys: application to domain wall-twin boundary dissociation[J]. Proc. SPIE.2008,6929:692910-1-8.
[32]O'Handley, R.C. Model for strain and magnetization in magnetic shape memory alloys[J]. 1998,83(6):3263-3270.
[33]Hirsinger, L., and Lexcellent, C. Internal variable model for magneto-mechanical behavior of ferromagnetic shape memory alloys Ni-Mn-Ga[J]. J. Phys. Ⅳ.2003,112:977-980.
[34]Hirsinger, L., and Lexcellent, C. Modeling detwinning of martensite platelets under magnetic and(or) stress actions on Ni-Mn-Ga alloys[J]. J. Magn. Magn. Mater.2003,254-255:275-277.
[35]Kiefer, B., and Lagoudas, D.C. Phenomenological modeling of ferromagnetic shape memory alloys[J]. Proc. SPIE.2004,5387:164-176.
[36]Kiefer, B., Karaca, H.E., Lagoudas, D.C., and Karaman, I. Characterization and modeling of the magnetic field-induced strain and work output in Ni2MnGa magnetic shape memory alloys[J]. J. Magn. Magn. Mater.2007,312(1):164-175.
[37]Sarawate, N.N., and Dapino, M.J. A continuum thermodynamics model for the sensing effect in ferromagnetic shape memory Ni-Mn-Ga[J]. J. Appl. Phys.2007,101(12):123522-1-11.
[38]Sarawate, N.N., and Dapino, M.J. Magnetic-field-induced stress and magnetization in mechanically blocked Ni-Mn-Ga[J]. J. Appl. Phys.2008,103(8):083902-1-4.
[39]Sarawate, N.N., and Dapino, M.J. Magnetization dependence on dynamic strain in ferromagnetic shape memory Ni-Mn-Ga[J]. Appl. Phys. Lett.2008,93(6):062501-1-3.
[40]Sarawate, N.N., and Dapino, M.J. Magnetomechanical characterization and unified energy model for the quasistatic behavior of ferromagnetic shape memory Ni-Mn-Ga[J]. Smart Mater. Struct.2010,19(3):035001-1-20.
[41]李芳.铁磁形状记忆合金马氏体变体重取向及其多场耦合行为研究[D].兰州：兰州大学,2011.
[42]Wang, X.Z., and Li, F. A kinetic model for martensite variants rearrangement in ferromagnetic shape memory alloys[J]. Journal of Applied Physics,2010,108(113921):1-7.
[43]Zhou, Y.H., Zheng, X.J., and Miya, K. Magnetoelastic bending and snapping of ferromagnetic plates in oblique magnetic field[J]. Fusion Eng. Design.1995,30(4):325-337.
[44]Zhou, Y.H., and Zheng, X.J. A theoretical model of magnetoelastic bucking for soft ferromagnetic thin plates[J]. Acta Mech. Sinina.1996,12(3):213-224.
[45]Zhou, Y.H., and Zheng, X.J. A variational principle on magnetoelastic interaction of ferromagnetic thin plates[J]. Acta Mech. Sinina.1997,10(1):1-10.
[46]Zhou, Y.H., and Zheng, X.J. A general expression of magnetic force for soft ferromagnetic plates in complex magnetic fields[J]. Int. J. Eng. Sci.1997,35(15):1405-1417.
[47]周又和,郑晓静.电磁固体结构力学[M].北京：科学出版社.1999.
[48]Zheng, X.J., and Wang, X. Analysis of magnetoelastic interaction of rectangular ferromagnetic plates with nonlinear magnetization[J]. Int. J. Solids and Structures. 2001,38(48-49):8641-8652.
[49]Wang, X., Zhou, Y.H., and Zheng, X.J. A generalized variational model of magneto-thermo-elasticity for nonlinearly magnetized ferroelastic bodies[J]. Int. J. Eng. Sci. 2002,40(17):1957-1973.
[50]Zheng, X.J., and Wang, X. Large-deflection deformation of ferromagnetic plates in magnetic fields[J]. J. Eng. Mech.2003,129(2):245-248.
[51]Wang, X., Lee, J.S., and Zheng, X.J. Magneto-thermo-elastic instability of ferromagnetic plates in thermal and magnetic field[J]. Int. J. Solids and Structures.2003,40(22):6125-6142.
[52]王省哲,郑晓静.铁磁梁式板热弹性屈曲分析[J].兰州大学学报.2005,41(1)：86-90.
[53]Wang, X., and Lee, J.S. Dynamic stability of ferromagnetic beam-plates with magnetoelastic interaction and magnetic damping in transverse magnetic fields[J]. J. Eng. Mech. 2006,132(4):422-428.
[54]Wang, X., and Huang, X. Feedback control and optimization for rotating disk flutter suppression with actuator patches[J]. AIAA Journal.2006,44(4):892-900.
[55]Zheng, X.J., and Liu, X.E. A nonlinear constitutive model for Terfenol-D Rods[J]. J. Appl. Phys.2005,97(5):053901-1-8.
[56]Liu, X.E., and Zheng, X.J. A nonlinear constitutive model for magnetostrictive materials[J]. Acta Mech. Sinica.2005,21(3):278-285.
[57]Zheng, X.J., and Sun, L. A nonlinear constitutive model of magneto-thermo-mechanical coupling for giant magnetostrictive materials[J]. J. Appl. Phys.2006,100(6):063906-1-6.
[58]Zheng, X.J., and Sun, L. A one-dimension coupled hysteresis model for giant magnetostrictive materials[J]. J. Magn. Magn. Mater.2007,309(2):263-271.
[59]Zhou, H.M., Zhou, Y.H., and Zheng, X.J. A general theoretical model of magnetostrictive constitutive relationships for soft ferromagnetic material rods[J]. J. Appl. Phys. 2008,104(2):023907-1-9.
[60]Zhou, H.M., and Zhou, Y.H. Vibration suppression of laminated composite beams using actuators of giant magnetostrictive materials[J]. Smart Mater. Struct.2007,16(1):198-206.
[61]Wang, T.Z., and Zhou, Y.H. A nonlinear transient constitutive model with eddy current effects for giant magnetostrictive materials[J]. J. Appl. Phys.2010,108(12):123905-1-9.
[62]Jin, K., Liang, Y.Y., and Zheng, X.J. Effects of hysteresis losses on dynamic behavior of magnetostrictive actuators[J]. J. Appl. Phys.2011,110,093908.
[63]杜善义,王彪.复合材料细观力学[M].北京：科学出版社,1997.
[64]沈观林,胡更开.复合材料力学[M].北京：清华大学出版社,2006.
[65]Eshelby, J.D. The determination of the elastic field of an Ellipsoidal inclusion, and related problems[J]. Mathematical and Physical Sciences.1957,241(1226):376-396.
[66]Mori. T., and Tanaka, K. Average stress in matrix and average elastic energy of material with misfitting inclusions[J]. Acta Metall.1973,21(5):571-571.
[67]Heczko, O. Magnetic shape memory effect and magnetization reversal[J]. Journal of Magnetism and Magnetic Materials.2005,290-291(2):787-794.
[68]S J Murray, M Marioni, S M Allen, R C O'Handley.6% magnetic-field-induced strain by twin-boundary motion in ferromagnetic NiMnGa[J]. Applied Physics Letters,2000, 77(6):886-888.
[69]Heczko, O., Sozinov, A., and Ullakko, K. Giant Field-Induced Reversible Strain in Magnetic Shape Memory NiMnGa Alloy [J]. IEEE transactions on magnetics.2000,36(5):3266-3268.
[70]Callaway, J.D., Sehitoglu, H., Hamilton, R.F, Aslantas, K., Miller, N., Maier, H.J., and Chumlyakov, Y. Magnetic shape memory in Ni2MnGa as influenced by applied stress [J]. Appl. Phys. Lett.2006,89(22):221905-1-3.