Three-dimensional general magneto-electro-elastic finite element model for multiphysics nonlinear analysis of layered composites

doi:10.1007/s10483-023-2943-8

Abstract

Abstract: In this paper, by defining a general potential energy for the multiphase coupled multiferroics and applying the minimum energy principle, the coupled governing equations are derived. This system of equations is then discretized as a general three-dimensional (3D) finite element (FE) model based on the COMSOL software. After validating the formulation, it is then applied to the analysis and design of the common sandwich structure of multiferroics composites. Under the typical static loading, the effects of general lateral boundary conditions, material grading, nonlinearity, as well as polarization orientation on the composites are analyzed. For the magneto-electro-elastic (MEE) sandwich made of piezoelectric BaTiO₃ and magnetostrictive CoFe₂O₄ with different stacking sequences, various interesting features are observed which should be very helpful for the design of high-performance multiphase composites.

Key words: multiferroics, sandwich composite, magneto-electro-elastic (MEE) material, multilayered plate, nonlinear behavior

2010 MSC Number:

74S05

Zheng GONG, Yinxiao ZHANG, Ernian PAN, Chao ZHANG. Three-dimensional general magneto-electro-elastic finite element model for multiphysics nonlinear analysis of layered composites. Applied Mathematics and Mechanics (English Edition), 2023, 44(1): 53-72.

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References

[1] NAN, C. W. Magnetoelectric effect in composites of piezoelectric and piezomagnetic phases. Physical Review B, 50, 6082–6088(1994)
[2] AVELLANEDA, M. and HARSHÉ, G. Magnetoelectric effect in piezoelectric/magnetostrictive multilayer (2-2) composites. Journal of Intelligent Material Systems and Structures, 5, 501–513(1994)
[3] BENVENISTE, Y. Magnetoelectric effect in fibrous composites with piezoelectric and piezomagnetic phases. Physical Review B, 51, 16424–16427(1995)
[4] BERLINCOURT, D. A., CURRAN, D. R., and JAFFE, H. Piezoelectric and piezomagnetic materials and their function in transducers. Physical Acoustics, 1, 169–270(1964)
[5] NAN, C. W., BICHURIN, M. I., DONG, S., VIEHLAND, D., and SRINIVASAN, G. Multiferroic magnetoelectric composites: historical perspective, status, and future directions. Journal of Applied Physics, 103, 031101(2008)
[6] SUCHTELEN, J. V. Product properties: a new application of composite materials. Philips Research Reports, 27, 28–37(1972)
[7] HUANG, J. H. and KUO, W. S. The analysis of piezoelectric/piezomagnetic composite materials containing ellipsoidal inclusions. Journal of Applied Physics, 81, 1378–1386(1997)
[8] LI, J. Y. and DUNN, M. L. Micromechanics of magnetoelectroelastic composite materials: average fields and effective behavior. Journal of Intelligent Material Systems and Structures, 9, 404–416(1998)
[9] KUO, H. Y. and PENG, C. Y. Magnetoelectricity in coated fibrous composites of piezoelectric and piezomagnetic phases. International Journal of Engineering Science, 62, 70–83(2013)
[10] BENVENISTE, Y. On the micromechanics of fibrous piezoelectric composites. Mechanics of Materials, 18, 183–193(1994)
[11] CARMAN, G. P., CHEUNG, K. S., and WANG, D. Micro-mechanical model of a composite containing a conservative nonlinear electro-magneto-thermo-mechanical material. Journal of Intelligent Material Systems and Structures, 6, 691–699(1995)
[12] JANSSON, S. Homogenized nonlinear constitutive properties and local stress concentrations for composites with periodic internal structure. International Journal of Solids and Structures, 29, 2181–2200(1992)
[13] BANKS-SILLS, L., LEIDERMAN, V., and FANG, D. On the effect of particle shape and orientation on elastic properties of metal matrix composites. Composites Part B, 28, 465–481(1997)
[14] ABOUDI, J. Micromechanical analysis of fully coupled electro-magneto-thermo-elastic multiphase composites. Smart Materials and Structures, 10, 867–877(2001)
[15] JIANG, C. P. and CHEUNG, Y. K. An exact solution for the three-phase piezoelectric cylinder model under antiplane shear and its applications to piezoelectric composites. International Journal of Solids and Structures, 38, 4777–4796(2001)
[16] TONG, Z. H., LO, S. H., JIANG, C. P., and CHEUNG, Y. K. An exact solution for the three-phase thermo-electro-magneto-elastic cylinder model and its application to piezoelectric-magnetic fiber composites. International Journal of Solids and Structures, 45, 5205–5219(2008)
[17] LEE, J., JAMES, I. V., and LAGOUDAS, D. C. Effective properties of three-phase electro-magneto-elastic composites. International Journal of Engineering Science, 43, 790–825(2005)
[18] SLADEK, J., SLADEK, V., REPKA, M., KASALA, J., and BISHAY, P. Evaluation of effective material properties in magneto-electro-elastic composite materials. Composite Structures, 174, 176–186(2017)
[19] HAGHGOO, M., ANSARI, R., HASSANZADEH-AGHDAM, M. K., and DARVIZEH, A. Fully coupled thermo-magneto-electro-elastic properties of unidirectional smart composites with a piezoelectric interphase. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 233, 2813–2829(2019)
[20] CHEN, Q., CHEN, W., and WANG, G. Fully-coupled electro-magneto-elastic behavior of unidirectional multiphased composites via finite-volume homogenization. Mechanics of Materials, 154, 103553(2021)
[21] WANG, Y., LIU, C., YU, H., and WANG, J. Phase field simulations on domain switching-induced toughening or weakening in multiferroic composites. International Journal of Solids and Structures, 178, 48–58(2019)
[22] PAN, E. Exact solution for simply supported and multilayered magneto-electro-elastic plates. Journal of Applied Mechanics, 68, 608–618(2001)
[23] PAN, E. and HEYLIGER, P. R. Exact solutions for magneto-electro-elastic laminates in cylindrical bending. International Journal of Solids and Structures, 40, 6859–6876(2003)
[24] PAN, E. and HAN, F. Exact solution for functionally graded and layered magneto-electro-elastic plates. International Journal of Engineering Science, 43, 321–339(2005)
[25] GUO, J., CHEN, J., and PAN, E. Static deformation of anisotropic layered magnetoelectroelastic plates based on modified couple-stress theory. Composites Part B: Engineering, 107, 84–96(2016)
[26] KUO, H. Y., HUANG, C. S., and PAN, E. Effect of imperfect interfaces on the field response of multilayered magneto-electroelastic composites under surface loading. Smart Materials and Structures, 28, 115006(2019)
[27] VATTRÉ, A. and PAN, E. Semicoherent heterophase interfaces with core-spreading dislocation structures in magneto-electro-elastic multilayers under external surface loads. Journal of the Mechanics and Physics of Solids, 124, 929–956(2019)
[28] WANG, J., CHEN, L., and FANG, S. State vector approach to analysis of multilayered magneto-electro-elastic plates. International Journal of Solids and Structures, 40, 1669–1680(2003)
[29] LI, X. Y., DING, H. J., and CHEN, W. Q. Three-dimensional analytical solution for functionally graded magneto-electro-elastic circular plates subjected to uniform load. Composite Structures, 83, 381–390(2008)
[30] LI, X. Y., DONG, Y. H., LIU, C., LIU, Y., WANG, C. J., and SHI, T. F. Axisymmetric thermo-magneto-electro-elastic field in a heterogeneous circular plate subjected to a uniform thermal load. International Journal of Mechanical Sciences, 88, 71–81(2014)
[31] HEYLIGER, P. R. and PAN, E. Static fields in magnetoelectroelastic laminates. AIAA Journal, 42, 1435–1443(2004)
[32] CHEN, J. Y., HEYLIGER, P. R., and PAN, E. Free vibration of three-dimensional multilayered magneto-electro-elastic plates under combined clamped/free boundary conditions. Journal of Sound and Vibration, 333, 4017–4029(2014)
[33] ZHANG, P., QI, C., FANG, H., MA, C., and HUANG, Y. Semi-analytical analysis of static and dynamic responses for laminated magneto-electro-elastic plates. Composite Structures, 222, 110933(2019)
[34] LAGE, R. G., SOARES, C. M. M., SOARES, C. A. M., and REDDY, J. N. Layerwise partial mixed finite element analysis of magneto-electro-elastic plates. Computers & Structures, 82, 1293–1301(2004)
[35] BHANGALE, R. K. and GANESAN, N. Free vibration studies of simply supported non-homogeneous functionally graded magneto-electro-elastic finite cylindrical shells. Journal of Sound and Vibration, 288, 412–422(2005)
[36] KIRAN, M. C. and KATTIMANI, S. Assessment of vibrational frequencies and static characteristics of multilayered skew magneto-electro-elastic plates: a finite element study. Iranian Journal of Science and Technology, Transactions of Mechanical Engineering, 44, 61–82(2020)
[37] VINYAS, M. and DINESHKUMAR, H. Nonlinear vibration of functionally graded magneto-electro-elastic higher order plates reinforced by CNTs using FEM. Engineering with Computers, 38, 1029–1051(2022)
[38] VINYAS, M. and DINESHKUMAR, H. Large defection analysis of functionally graded magneto-electro-elastic porous fat panels. Engineering with Computers, 38, 1615–1634(2022)
[39] MOITA, J. M. S., SOARES, C. M. M., and SOARES, C. A. M. Analyses of magneto-electro-elastic plates using a higher order finite element model. Composite Structures, 91, 421–426(2009)
[40] BENEDETTI, I. and MILAZZO, A. Advanced models for smart multilayered plates based on Reissner mixed variational theorem. Composites Part B: Engineering, 119, 215–229(2017)
[41] MILAZZO, A. Unified formulation for a family of advanced finite elements for smart multilayered plates. Mechanics of Advanced Materials and Structures, 23, 971–980(2016)
[42] KONDAIAH, P., SHANKAR, K., and GANESAN, N. Studies on magneto-electro-elastic cantilever beam under thermal environment. Coupled Systems Mechanics, 1, 205–217(2012)
[43] KONDAIAH, P., SHANKAR, K., and GANESAN, N. Pyroelectric and pyromagnetic effects on behavior of magneto-electro-elastic plate. Coupled Systems Mechanics, 2, 1–22(2013)
[44] LI, M., LIU, M., and ZHOU, L. The static behaviors study of magneto-electro-elastic materials under hygrothermal environment with multi-physical cell-based smoothed finite element method. Composites Science and Technology, 193, 108130(2020)
[45] BIJU, B., GANESAN, N., and SHANKAR, K. Dynamic response of multiphase magnetoelectroelastic sensors using 3D magnetic vector potential approach. IEEE Sensors Journal, 11, 2169–2176(2011)
[46] YANG, Z. X., DANG, P. F., HAN, Q. K., and JIN, Z. H. Natural characteristics analysis of magneto-electro-elastic multilayered plate using analytical and finite element method. Composite Structures, 185, 411–420(2018)
[47] ZHANG, S. Q., ZHAO, Y. F., WANG, X., CHEN, M., and SCHMIDT, R. Static and dynamic analysis of functionally graded magneto-electro-elastic plates and shells. Composite Structures, 281, 114950(2022)
[48] QUANG, V. D., QUAN, T. Q., and TRAN, P. Static buckling analysis and geometrical optimization of magneto-electro-elastic sandwich plate with auxetic honeycomb core. Thin-Walled Structures, 173, 108935(2022)
[49] PAN, E. Three-dimensional Green’s functions in anisotropic magneto-electro-elastic bimaterials. Journal of Applied Mathematics and Physics, 53, 815–838(2002)
[50] AMMAR, S., HELFEN, A., JOUINI, N., FIÉVET, F., ROSENMAN, I., VILLAIN, F., MOLINIÉ, P., and DANOT, M. Magnetic properties of ultrafine cobalt ferrite particles synthesized by hydrolysis in a polyol medium. Journal of Materials Chemistry, 11, 186–192(2001)