基于均匀化理论分析磁流变弹性体(MR)磁致剪切模量
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摘要
本文考虑了磁流变弹性体(MR弹性体)内颗粒与基体间磁场的相互影响,基于均匀化理论计算磁流变弹性体的磁致剪切模量,并与已有磁偶极子理论的解进行对比分析。结果表明,铁磁颗粒磁导率的变化对磁致剪切模量的影响不大;当颗粒体积分数为30%时,基于均匀化理论获得的磁致剪切模量呈现最大值,其整体变化规律与实验数据基本吻合,可预测磁致剪切模量最大时的颗粒体积分数;而基于磁偶极子理论的计算结果与实验数据有一定差距。
Considering the mutual influence of magnetic field between the particles and the matrix in magnetorheological elastomers(MR elastomers), the magnetic shear modulus of MR elastomers was calculated based on homogenization theory. As compared with those from the magnetic dipole theory, the calculation results show that: the change of magnetic permeability of ferromagnetic particles has little effect on the magnetic shear modulus; when the volume fraction of particles is 30%, magnetic shear modulus obtained by homogenization theory reaches the maximum value, and the whole variation law agrees well with experimental data, it can be predicted when magnetic shear modulus gets the largest; but the calculated results based on the magnetic dipole theory have some deviation from the experimental data. This work can provide guidance and reference for the production of magnetorheological elastomers as well as the analysis of magneto-mechanical properties.
Considering the mutual influence of magnetic field between the particles and the matrix in magnetorheological elastomers(MR elastomers), the magnetic shear modulus of MR elastomers was calculated based on homogenization theory. As compared with those from the magnetic dipole theory, the calculation results show that: the change of magnetic permeability of ferromagnetic particles has little effect on the magnetic shear modulus; when the volume fraction of particles is 30%, magnetic shear modulus obtained by homogenization theory reaches the maximum value, and the whole variation law agrees well with experimental data, it can be predicted when magnetic shear modulus gets the largest; but the calculated results based on the magnetic dipole theory have some deviation from the experimental data. This work can provide guidance and reference for the production of magnetorheological elastomers as well as the analysis of magneto-mechanical properties.
引文
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[2] 王宇飞,何琳,杨雪,等. 磁流变弹性体的研究现状及工程应用 [J]. 材料科学与工程学报, 2010, 28(4): 633～636.
[3] 黄炼,查长松. 磁流变弹性体的磁致性能 [J]. 材料科学与工程学报, 2016, 34(1): 139～141.
[4] 张海宇,王省哲. 磁流变弹性体中铁磁颗粒尺寸大小随机分布下的磁致剪切模量的分析[J].功能材料, 2011, 42(1): 233～240.
[5] A Javili, G Chatzigeorgiou, P Steinmann. Computional Homogenization in Magetomechanics [J]. International Journal of Solids & Structures, 2013, 50(25～26): 4197～4216.
[6] J T Zhu, Z D Xu, X C Zhang. Main Chain Adsorption Model of Magnetorheological Elastomer[J]. Journal of Southeast University, 2011, 41(2): 342～346.
[7] X Lu, X Qiao, H Watanabe, et al. Mechanical and Structural Investigation of Isotropic and Anisotropic Thermoplastic Magnetorheological Elastomer Composites Based on Poly [J]. Rheologica Acta, 2011, 51(1): 37～50.
[8] M Dai, P Schiavone, Cun F G. Prediction of the Stress Field and Effective Shear Modulus of Composites Containing Periodic Inclusions Incorporating Interface Effects in Anti-plane Shear [J]. Journal of Elasticity, 2016, 125(2): 217～230.
[9] E M Furst, A P Gast. Micromechanics of Magnetorheological Suspensions [J]. Physical Review E, 2000, 61(6): 6732.
[10] Y Shen, M F Golnaraghi, G R Heppler. Experimental Research and Modeling of Magnetorheological Elastomers [J]. Journal of Intelligent Material Systems and Structures, 2004, 15(1): 27～35.
[11] G J Liao, X L Gong, S H Xuan. Influence of Shear Deformation on the Normal Force of Magnetorheological Elastomer [J]. Journal of Intelligent Material Systems and Structures, 2013, 106(106): 270～272.
[12] H Waki, H Igarashi, T Honma. Analysis of Magnetic Shielding Effect of Layered Shields Based on Homogenization [J]. IEEE Transactions on Magnetics, 2006, 42(4): 847～850.
[13] PP Castaneda, E Galipeau. Homogenization-based Constitutive Models for Magnetorheological Elastomers at Finite Strain [J]. Journal of the Mechanics and Physics of Solids, 2011, 59(2): 194～215.
[14] T M Simon, F Reitich, M R Jolly, et al. Estimation of the Effective Permeability in Magnetorheological Fluids [J]. Journal of Intelligent Material Systems & Structures, 1999, 10(11): 872～879.
[15] E Coquelle, G Bossis. Mullins Effect in Elastomers filled with particles aligned by a Magnetic field [J]. InternationalJournal of Solids and Structures, 2006, 43(25): 7659～7672.
[16] H M Yin, L Z Sun. Effective Magnetic Permeability of Composites Containing Chain-structured Particles[J].Acta Materialia, 2006, 54(9): 2317～2323.
[17] H M Yin, L Z Sun, J S Chen. Magneto-elastic Modeling of Composites Containing Chain-structured Magnetostrictive Particles [J]. Journal of the Mechanics and Physics of Solids, 2006, 54(5): 975～1003.
[18] T Mura, D M Barnett. Micromechanics of Defects in Solids [M]. Martinus Nijhoff Publishers, 1987.
[19] L C Davis. Model of Magnetorheological Elastomers [J]. Journal of Applied Physics, 1999, 85(6): 3348～3351.
[20] M Lokander, B Stenberg. Performance of isotropic Magnetorheological Rubber Materials[J]. Polymer Testing, 2003, 22(3): 245～251.
[2] 王宇飞,何琳,杨雪,等. 磁流变弹性体的研究现状及工程应用 [J]. 材料科学与工程学报, 2010, 28(4): 633～636.
[3] 黄炼,查长松. 磁流变弹性体的磁致性能 [J]. 材料科学与工程学报, 2016, 34(1): 139～141.
[4] 张海宇,王省哲. 磁流变弹性体中铁磁颗粒尺寸大小随机分布下的磁致剪切模量的分析[J].功能材料, 2011, 42(1): 233～240.
[5] A Javili, G Chatzigeorgiou, P Steinmann. Computional Homogenization in Magetomechanics [J]. International Journal of Solids & Structures, 2013, 50(25～26): 4197～4216.
[6] J T Zhu, Z D Xu, X C Zhang. Main Chain Adsorption Model of Magnetorheological Elastomer[J]. Journal of Southeast University, 2011, 41(2): 342～346.
[7] X Lu, X Qiao, H Watanabe, et al. Mechanical and Structural Investigation of Isotropic and Anisotropic Thermoplastic Magnetorheological Elastomer Composites Based on Poly [J]. Rheologica Acta, 2011, 51(1): 37～50.
[8] M Dai, P Schiavone, Cun F G. Prediction of the Stress Field and Effective Shear Modulus of Composites Containing Periodic Inclusions Incorporating Interface Effects in Anti-plane Shear [J]. Journal of Elasticity, 2016, 125(2): 217～230.
[9] E M Furst, A P Gast. Micromechanics of Magnetorheological Suspensions [J]. Physical Review E, 2000, 61(6): 6732.
[10] Y Shen, M F Golnaraghi, G R Heppler. Experimental Research and Modeling of Magnetorheological Elastomers [J]. Journal of Intelligent Material Systems and Structures, 2004, 15(1): 27～35.
[11] G J Liao, X L Gong, S H Xuan. Influence of Shear Deformation on the Normal Force of Magnetorheological Elastomer [J]. Journal of Intelligent Material Systems and Structures, 2013, 106(106): 270～272.
[12] H Waki, H Igarashi, T Honma. Analysis of Magnetic Shielding Effect of Layered Shields Based on Homogenization [J]. IEEE Transactions on Magnetics, 2006, 42(4): 847～850.
[13] PP Castaneda, E Galipeau. Homogenization-based Constitutive Models for Magnetorheological Elastomers at Finite Strain [J]. Journal of the Mechanics and Physics of Solids, 2011, 59(2): 194～215.
[14] T M Simon, F Reitich, M R Jolly, et al. Estimation of the Effective Permeability in Magnetorheological Fluids [J]. Journal of Intelligent Material Systems & Structures, 1999, 10(11): 872～879.
[15] E Coquelle, G Bossis. Mullins Effect in Elastomers filled with particles aligned by a Magnetic field [J]. InternationalJournal of Solids and Structures, 2006, 43(25): 7659～7672.
[16] H M Yin, L Z Sun. Effective Magnetic Permeability of Composites Containing Chain-structured Particles[J].Acta Materialia, 2006, 54(9): 2317～2323.
[17] H M Yin, L Z Sun, J S Chen. Magneto-elastic Modeling of Composites Containing Chain-structured Magnetostrictive Particles [J]. Journal of the Mechanics and Physics of Solids, 2006, 54(5): 975～1003.
[18] T Mura, D M Barnett. Micromechanics of Defects in Solids [M]. Martinus Nijhoff Publishers, 1987.
[19] L C Davis. Model of Magnetorheological Elastomers [J]. Journal of Applied Physics, 1999, 85(6): 3348～3351.
[20] M Lokander, B Stenberg. Performance of isotropic Magnetorheological Rubber Materials[J]. Polymer Testing, 2003, 22(3): 245～251.