Abstract
This paper is concerned with the exploration of the role of transverse normal and shear deformations on enhancing the magnetoelectric (ME) coefficient of multiferroic bilayer composite beams composed of a piezoelectric layer and a piezomagnetic layer. Analytical models have been derived based on the displacement field which accounts for both the transverse normal and shear deformations, Timoshenko beam theory and Euler Bernoulli beam theory. The induced flexoelectricity in the piezoelectric layer due to axial strain gradient and transverse shear strain gradient has also been taken into consideration for estimating the ME coefficient. It has been found that the contribution of transverse normal strain in the piezoelectric layer for enhancing the ME coefficient is significantly larger than that due to axial strain, transverse shear strain and flexoelectricity. For the particular values of the thicknesses of the piezoelectric layer and the piezomagnetic layer, the ME coefficient remains invariant for both thick and thin multiferroic composite beams.
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Bai, Y., Zhao, H., Chen, J., Sun, Y., Zhao, S.: Strong magnetoelectric coupling effect of BiFeO3/Bi5Ti3FeO15 bilayer composite films. Ceram. Int. 42, 10304–10309 (2016)
Benveniste, Y.: Magnetoelectric effect in fibrous composites with piezoelectric and piezomagnetic phases. Phys. Rev. B 51(22), 16424–16427 (1995)
Chu, B., Salem, D.R.: Flexoelectricity in several thermoplastic and thermosetting polymers. Appl. Phys. Lett. 101, 103905 (2012)
Deng, Q., Liu, L., Sharma, P.: Flexoelectricity in soft materials and biological membranes. J. Mech. Phys. Solids 62, 209–227 (2014)
Fang, F., Zhou, Y.Y., Xu, Y.T., Jing, W.Q., Yang, W.: Magnetoelectric coupling of multiferroic composites under combined magnetic and mechanical loadings. Smart Mater. Struct. 22, 075009 (2013)
Indenbom, V.L., Loginov, E.B., Osipov, M.A.: Flexoelectric effect and the structure of crystals. Kristalografija 26, 1157 (1981)
Jayachandran, K.P., Guedes, J.M., Rodrigues, H.C.: A generic homogenization model for magnetoelectric multiferroics. J. Intell. Mater. Syst. Struct. 25, 1243–1255 (2014)
Jiang, X., Huang, W., Zhang, S.: Flexoelectric nano-generator: materials, structures and devices. Nano Energy 2, 1079–1092 (2013)
Kogan, S.M.: Piezoelectric effect during inhomogeneous deformation and acoustic scattering of carriers in crystals. Sov. Phys. Solid State 5(10), 2069–2070 (1964)
Kuo, H.Y., Wang, Y.L.: Optimization of magnetoelectricity in multiferroic fibrous composites. Mech. Mater. 50, 88–99 (2012)
Lin, Y., Cai, N., Zhai, J., Liu, G., Nan, C.W.: Giant magnetoelectric effect in multiferroic laminated composites. Phys. Rev. B 72, 012405 (2005)
Ma, W., Cross, L.E.: Flexoelectric effect in ceramic lead zirconate titanate ceramics. Appl. Phys. Lett. 86, 072905 (2005)
Ma, W., Cross, L.E.: Flexoelectricity of barium titanate. Appl. Phys. Lett. 88, 232902 (2006)
Ma, W., Eric Cross, L.: Large flexoelectric polarization in ceramic lead magnesium niobate. Appl. Phys. Lett. 79, 4420–4422 (2001)
Ma, W., Eric Cross, L.: Flexoelectric polarization of barium strontium titanate in the paraelectric state. Appl. Phys. Lett. 81, 3440–3442 (2002)
Ma, W., Eric Cross, L.: Strain-gradient-induced electric polarization in lead zirconate titanate ceramics. Appl. Phys. Lett. 82, 3293–3295 (2003)
Majdoub, M.S., Sharma, P., Cagin, T.: Enhanced size dependent piezoelectricity and elasticity in nanostructures due to the flexoelectric effect. Phys. Rev. B 77, 125424 (2008)
Maranganti, R., Sharma, N.D., Sharma, P.: Electromechanical coupling in nonpiezoelectric materials due to nanoscale nonlocal size effects: green’s function solutions and embedded inclusions. Phys. Rev. B 74, 014110 (2006)
Mashkevich, V.S., Tolpygo, K.B.: Electrical, optical and elastic properties of diamond type crystals. I. Sov. Phys. JETP 5(3), 435–439 (1957)
Mindlin, R.D.: Polarization gradient in elastic dielectrics. Int. J. Solids Struct. 4, 637–642 (1968)
Nan, C.W.: Magnetoelectric effect in composites of piezoelectric and piezomagnetic phases. Phys. Rev. B 50(9), 6082–6088 (1994)
Nan, C.W., Bichurin, M.I.: Multiferroic magnetoelectric composites: historical perspective, status, and future directions. J. Appl. Phys. 103, 031101 (2008)
Nan, C.W., Lin, Y., Huang, J.H.: Magnetoelectricity of multiferroic composites. Ferroelectrics 280, 153–163 (2002)
Ortega, N., Kumar, A., Scott, J.F., Katiyar, R.S.: Multifunctional magnetoelectric materials for device applications. J. Phys.: Condens. Matter 27, 504002 (2015)
Pan, E., Wang, X., Wang, R.: Enhancement of magnetoelectric effect in multiferroic fibrous nanocomposites via size-dependent material properties. Appl. Phys. Lett. 95, 181904 (2009)
Ray, M.C., Pradhan, A.K.: The performance of vertically reinforced 1–3 piezoelectric composites in active damping of smart structures. Smart Mater. Struct. 15(2), 631–641 (2006)
Ryu, J., Priya, S., Uchino, K., Kim, H.E.: Magnetoelectric effect in composites of magnetostrictive and piezoelectric materials. J. Electroceram. 8, 107–119 (2002)
Sharma, N.D., Maranganti, R., Sharma, P.: On the possibility of piezoelectric nanocomposites without using piezoelectric materials. J. Mech. Phys. Solids 55, 2328–2350 (2007)
Srinivas, S., Li, J.Y.: The effective magnetoelectric coefficients of polycrystalline multiferroic composites. Acta Mater. 53, 4135–4142 (2005)
Srinivas, S., Li, J.Y., Zhou, Y.C., Soh, A.K.: The effective magnetoelectroelastic moduli of matrix-based multiferroic composites. J. Appl. Phys. 99, 043905 (2006)
Wang, X., Pan, E.: Magnetoelectric effects in multiferroic fibrous composite with imperfect interface. Phys. Rev. B 76, 214107 (2007)
Yan, Z., Jiang, L.: Size-dependent bending and vibration behavior of piezoelectric nanobeams due to flexoelectricity. J. Phys. D Appl. Phys. 46, 355502 (2013)
Yudin, P.V., Tagantsev, A.K.: Fundamentals of flexoelectricity in solids. Nanotechnology 24, 432001 (2013)
Zang, C., Zhang, L., Shen, X., Chen, W.: Enhancing magnetoelectric effect in multiferroic composite bilayers via flexoelectricity. J. Appl. Phys. 119, 134102 (2016)
Zubko, P., Catalan, G., Tagantsev, A.K.: Flexoelectric effect in solids. Annu. Rev. Mater. Res. 43, 387–421 (2013)
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Ray, M.C. Enhanced magnetoelectric effect in multiferroic composite beams due to flexoelectricity and transverse deformations. Int J Mech Mater Des 14, 461–472 (2018). https://doi.org/10.1007/s10999-017-9380-7
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DOI: https://doi.org/10.1007/s10999-017-9380-7