基于颗粒动力学演化的磁弹体力磁耦合数值模型
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摘要
基于颗粒动力学演化的磁致微观结构建立了横观各向同性磁弹体(MREs)三维几何模型,在考虑了磁场和变形耦合作用的基础上,依据当前MREs研究较热的两种磁颗粒作用模型构建了颗粒的控制方程,从而建立MREs多颗粒的力磁耦合数值模型,从细观角度研究MREs的力磁耦合性能。数值模型和剪切实验对比表明,点偶极子作用力模拟的MREs磁流变效应远低于实验数据,而多极作用力在量级上更接近实验数据。基于构建的数值模型,还详细探究了磁感应强度和颗粒浓度对磁致剪切模量的影响,模拟结果和实验趋势吻合较好,颗粒体积分数在20%附近时,相对磁流变效应达到最大。
Based on the evolution of magneto-induced microstructure by particle dynamics simulation,the 3 Dgeometric model was established for transversely isotropic magnetorheological elastomers(MREs).On the basis of the current two main theories for the interaction between magnetic particles,the control equations on particles were built considering the coupling effect between deformation and magnetic field.The mechanics-magnetic coupling properties were studied in the mesoscopic level by establishing the multi-particles numerical model of MREs.The comparison result between numerical model and shear experiments indicates that multipole force model is closer to the test data than point-dipoles model.The influences of magnetic flux density and particle volume fraction on magneto-induced shear modulus were also discussed,that is,the numerical model gives an excellent agreement with experiments.The optimum particle volume fraction for the largest relative magnetorheological effect is about 20%.
Based on the evolution of magneto-induced microstructure by particle dynamics simulation,the 3 Dgeometric model was established for transversely isotropic magnetorheological elastomers(MREs).On the basis of the current two main theories for the interaction between magnetic particles,the control equations on particles were built considering the coupling effect between deformation and magnetic field.The mechanics-magnetic coupling properties were studied in the mesoscopic level by establishing the multi-particles numerical model of MREs.The comparison result between numerical model and shear experiments indicates that multipole force model is closer to the test data than point-dipoles model.The influences of magnetic flux density and particle volume fraction on magneto-induced shear modulus were also discussed,that is,the numerical model gives an excellent agreement with experiments.The optimum particle volume fraction for the largest relative magnetorheological effect is about 20%.
引文
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[28]RAY S,SHANMUGHARAJ A M,BHOWMICK A K.A new parameter for interpretation of polymer-filler and fillerfiller interactions in rubber vulcanizates[J].Journal of Materials Science Letters,2002,21(14):1097-1100.
[29]LI W H,ZHOU Y,TIAN T F.Viscoelastic properties of MR elastomers under harmonic loading[J].Rheologica Acta,2010,49(7):733-740.
[2]ZHOU G Y.Shear properties of a magnetorheological elastomer[J].Smart Materials and Structures,2003,12(1):139.
[3]GONG X L,ZHANG X Z,ZHANG P Q.Fabrication and characterization of isotropic magnetorheological elastomers[J].Polymer Testing,2005,24(5):669-676.
[4]YANG J,DU H,LI W,et al.Experimental study and modeling of a novel magnetorheological elastomer isolator[J].Smart Materials and Structures,2013,22(11):117001.
[5]许阳光,龚兴龙,万强,等.磁敏智能软材料及磁流变机理研究[J].力学进展,2015,45:201508.XU Y G,GONG X L,WAN Q,et al.Magneto-sensitive smart soft material and magnetorheological mechanism[J].Advances in Mechanics,2015,45:201508(in Chinese).
[6]JOLLY M R,CARLSON J D,MUNOZ B C.A model of the behaviour of magnetorheological materials[J].Smart Materials and Structures,1996,5(5):607-614.
[7]DAVIS L C.Model of magnetorheological elastomers[J].Journal of Applied Physics,1999,85(6):3348-3351.
[8]SHEN Y,GOLNARAGHI M F,HEPPLER G R.Experimental research and modeling of magnetorheological elastomers[J].Journal of Intelligent Material Systems and Structures,2004,15(1):27-35.
[9]DORFMANN A,OGDEN R W.Magnetoelastic modelling of elastomers[J].European Journal of Mechanics A:Solids,2003,22(4):497-507.
[10]KANKANALA S V,TRIANTAFYLLIDIS N.On finitely strained magnetorheological elastomers[J].Journal of the Mechanics and Physics of Solids,2004,52(12):2869-2908.
[11]BUSTAMANTE R.Transversely isotropic nonlinear magneto-active elastomers[J].Acta Mechanica,2010,210(3-4):183-214.
[12]DANAS K,KANKANALA S V,TRIANTAFYLLIDIS N.Experiments and modeling of iron-particle-filled magnetorheological elastomers[J].Journal of the Mechanics and Physics of Solids,2012,60(1):120-138.
[13]高伟,王省哲.具有倾斜链结构的磁流变弹性体的磁致剪切模量模型与分析[J].中国科技论文,2015,10(4):433-437.GAO W,WANG S Z.Model and analysis on magnetic fieldinduced shear modulus of magnetorheological elastomer with tilted chain[J].China Sciencepaper,2015,10(4):433-437(in Chinese).
[14]索思,徐赵东,许飞鸿.磁流变弹性体基于卡方分布的磁偶极子模型[J].功能材料,2016,47(9):9063-9067.SUO S,XU Z D,XU F H.A model of magnetorheological elastomer based on chi-square distribution[J].Journal of functional materials,2016,47(9):9063-9067(in Chinese).
[15]LY H V,REITICH F,JOLLY M R,et al.Simulations of particle dynamics in magnetorheological fluids[J].Journal of Computational Physics,1999,155(1):160-177.
[16]HAGHGOOIE R,DOYLE P S.Structural analysis of a dipole system in two-dimensional channels[J].Physical Review E,2004,70(6):061408.
[17]CLIMENT E,MAXEY M R,KARNIADAKIS G E.Dynamics of self-assembled chaining in magnetorheological fluids[J].Langmuir,2004,20(2):507-513.
[18]LIU T,GONG X,XU Y,et al.Simulation of magnetoinduced rearrangeable microstructures of magnetorheological plastomers[J].Soft Matter,2013,9(42):10069-10080.
[19]METSCH P,KALINA K A,SPIELER C,et al.A numerical study on magnetostrictive phenomena in magnetorheological elastomers[J].Computational Materials Science,2016,124:364-374.
[20]HAN Y,ZHANG Z,FAIDLEY L A E,et al.Microstructure-based modeling of magneto-rheological elastomers[C]//Proceedings of SPIE.Bellingham:SPIE,2012:83421B.
[21]HAN Y,HONG W,FAIDLEY L A E.Field-stiffening effect of magneto-rheological elastomers[J].International Journal of Solids and Structures,2013,50(14):2281-2288.
[22]CHEN S W,LI R,ZHANG Z,et al.Micromechanical analysis on tensile modulus of structured magneto-rheological elastomer[J].Smart Materials and Structures,2016,25(3):035001.
[23]CHEN L,GONG X L,LI W H.Microstructures and viscoelastic properties of anisotropic magnetorheological elastomers[J].Smart Materials and Structures,2007,16(6):2645-2650.
[24]KEAVENY E E,MAXEY M R.Modeling the magnetic interactions between paramagnetic beads in magnetorheological fluids[J].Journal of Computational Physics,2008,227(22):9554-9571.
[25]BILLER A M,STOLBOV O V,RAIKHER Y L.Modeling of particle interactions in magnetorheological elastomers[J].Journal of Applied Physics,2014,116(11):114904.
[26]DE VICENTE J,BOSSIS G,LACIS S,et al.Permeability measurements in cobalt ferrite and carbonyl iron powders and suspensions[J].Journal of Magnetism and Magnetic Materials,2002,251(1):100-108.
[27]LIU G R.A step-by-step method of rule-of-mixture of fiberand particle-reinforced composite materials[J].Composite Structures,1997,40(3-4):313-322.
[28]RAY S,SHANMUGHARAJ A M,BHOWMICK A K.A new parameter for interpretation of polymer-filler and fillerfiller interactions in rubber vulcanizates[J].Journal of Materials Science Letters,2002,21(14):1097-1100.
[29]LI W H,ZHOU Y,TIAN T F.Viscoelastic properties of MR elastomers under harmonic loading[J].Rheologica Acta,2010,49(7):733-740.