# Analysis of Smart Piezo-Magneto-Thermo-Elastic Composite and Reinforced Plates: Part II – Applications

D. A. Hadjiloizi; A.L. Kalamkarov; Ch. Metti; A. V. Georgiades

Curved and Layered Structures (2014)

- Volume: 1, Issue: 1
- ISSN: 2353-7396

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topD. A. Hadjiloizi, et al. "Analysis of Smart Piezo-Magneto-Thermo-Elastic Composite and Reinforced Plates: Part II – Applications." Curved and Layered Structures 1.1 (2014): null. <http://eudml.org/doc/276958>.

@article{D2014,

abstract = {A comprehensive micromechanical model for the analysis of a smart composite piezo-magneto-thermoelastic thin plate with rapidly varying thickness is developed in Part I of thiswork. The asymptotichomogenization model is developed using static equilibrium equations and the quasi-static approximation of Maxwell’s equations. The work culminates in the derivation of general expressions for effective elastic, piezoelectric, piezomagnetic, dielectric permittivity and other coefficients. Among these coefficients, the so-called product coefficients are determined which are present in the behavior of the macroscopic composite as a result of the interactions between the various phases but can be absent from the constitutive behavior of some individual phases of the composite structure. The model is comprehensive enough to also allow for calculation of the local fields of mechanical stresses, electric displacement and magnetic induction. The present paper determines the effective properties of constant thickness laminates comprised of monoclinic materials or orthotropic materials which are rotated with respect to their principal material coordinate system. A further example illustrates the determination of the effective properties of wafer-type magnetoelectric composite plates reinforced with smart ribs or stiffeners oriented along the tangential directions of the plate. For generality, it is assumed that the ribs and the base plate are made of different orthotropic materials. It is shown in this work that for the purely elastic case the results of the derived model converge exactly to previously established models. However, in the more general case where some or all of the phases exhibit piezoelectric and/or piezomagnetic behavior, the expressions for the derived effective coefficients are shown to be dependent on not only the elastic properties but also on the piezoelectric and piezomagnetic parameters of the constituent materials. Thus, the results presented here represent a significant refinement of previously obtained results.},

author = {D. A. Hadjiloizi, A.L. Kalamkarov, Ch. Metti, A. V. Georgiades},

journal = {Curved and Layered Structures},

keywords = {smart composite piezo-magneto-thermoelastic
thin plate; asymptotic homogenization; effective
properties; product properties},

language = {eng},

number = {1},

pages = {null},

title = {Analysis of Smart Piezo-Magneto-Thermo-Elastic Composite and Reinforced Plates: Part II – Applications},

url = {http://eudml.org/doc/276958},

volume = {1},

year = {2014},

}

TY - JOUR

AU - D. A. Hadjiloizi

AU - A.L. Kalamkarov

AU - Ch. Metti

AU - A. V. Georgiades

TI - Analysis of Smart Piezo-Magneto-Thermo-Elastic Composite and Reinforced Plates: Part II – Applications

JO - Curved and Layered Structures

PY - 2014

VL - 1

IS - 1

SP - null

AB - A comprehensive micromechanical model for the analysis of a smart composite piezo-magneto-thermoelastic thin plate with rapidly varying thickness is developed in Part I of thiswork. The asymptotichomogenization model is developed using static equilibrium equations and the quasi-static approximation of Maxwell’s equations. The work culminates in the derivation of general expressions for effective elastic, piezoelectric, piezomagnetic, dielectric permittivity and other coefficients. Among these coefficients, the so-called product coefficients are determined which are present in the behavior of the macroscopic composite as a result of the interactions between the various phases but can be absent from the constitutive behavior of some individual phases of the composite structure. The model is comprehensive enough to also allow for calculation of the local fields of mechanical stresses, electric displacement and magnetic induction. The present paper determines the effective properties of constant thickness laminates comprised of monoclinic materials or orthotropic materials which are rotated with respect to their principal material coordinate system. A further example illustrates the determination of the effective properties of wafer-type magnetoelectric composite plates reinforced with smart ribs or stiffeners oriented along the tangential directions of the plate. For generality, it is assumed that the ribs and the base plate are made of different orthotropic materials. It is shown in this work that for the purely elastic case the results of the derived model converge exactly to previously established models. However, in the more general case where some or all of the phases exhibit piezoelectric and/or piezomagnetic behavior, the expressions for the derived effective coefficients are shown to be dependent on not only the elastic properties but also on the piezoelectric and piezomagnetic parameters of the constituent materials. Thus, the results presented here represent a significant refinement of previously obtained results.

LA - eng

KW - smart composite piezo-magneto-thermoelastic
thin plate; asymptotic homogenization; effective
properties; product properties

UR - http://eudml.org/doc/276958

ER -

## References

top- [1] Kalamkarov, A.L., Georgiades, A.V., MacDonald, D., and Fitzgerald, S., 2000, Pultruded FRP reinforcements with embedded fiber optic sensors, Canadian Journal of Civil Engineering, 27(5), pp. 972-984.
- [2] A.K. Jain and J.S. Sirkis, Continuum damage mechanics in piezoelectric ceramics. Adaptive Structures and Composite Materials: Analysis and Application, Eds. E. Garcia, H. Cudney and A. Dasgupta, 47-58, (1994).
- [3] Newnham R E, Skinner D P, Cross L E, Connectivity and piezoelectric-pyroelectric composites,Mat. Res. Bull. 13 (1978) 525-536. [Crossref]
- [4] Nan C-W, Bichurin M I, Dong S, Viehland D and Srinivasan G Multiferroic magnetoelectric composites: Historical perspective, status, and future directions J. Appl. Phys 031101(1) – 031101 (2008) (35). [Crossref]
- [5] Srinivasan G Magnetoelectric composites Annual Review of Materials Research, 40 (2010) 153-178.
- [6] Bichurin M, Petrov V, Priya S, Bhalla A, Multiferroic magnetoelectric composites and their applications Advances in Condensed Matter Physics (2012) Article ID 129794.
- [7] Bhatra D, Masud Md, De S K, Chauduri B K Large magnetoelectric effect and low-loss high relative permittivity in 0-3 CuO/PVDF composite films exhibiting unusual ferromagnetism at room temperature J. Phys. D: Appl. Phys. 45 (2012) 485002.
- [8] Chen L, Li P, Wen Y, Zhu Y Analysis of the low-frequency magnetoelectric performance in three-phase laminate composites with Fe-based nanocrystalline ribbon SmartMaterials and Structures 22 (2013) 115031
- [9] Shen Y, Gao J, Hasanyan D, Wang Y, Li M, Li J, Viehland D Investigation of vehicle inducedmagnetic anomaly by triple-axis magnetoelectric sensors Smart Materials and Structures 21 (2012) 115007.
- [10] Ju S, Chae S H, Choi Y, Lee S, Lee HW, Ji C-H A low frequency vibration energy harvester usingmagnetoelectric laminate composite Smart Materials and Structures 22 (2013) 115037.
- [11] Ruy J, Priya S, Uchino K, Kim H-EMagnetoelectric effect in composites ofmagnetostrictive and piezoelectricmaterials Journal of Electroceramics 8 (2002) 107-119.
- [12] Oh S R, Wong T C, Tan, CW, Yao K, Tay F E Fabrication of polymer multilayers on flexible substrates for energy harvesting Smart Materials and Structures 23 (2014) 015013.
- [13] Lottermoser T, Lonkai T, Amann U, Hohlwein D, Ihringer J, FiebigMMagnetic phase control by an electric field Nature 430 (2004) 541-544.
- [14] Shen Y, McLaughlin K L, Gao J, Gray D, Shen L, Wang Y, Li M, Berry D, Li, J, Viehland D AC magnetic dipole localization by a magnetoelectric sensor Smart Materials and Structures 21 (2012) 065007.
- [15] Harshe G, Doherty J P, Newnham RE Theoretical modeling of 3- 0/0-3 magnetoelectric composites International Journal of Applied Electromagnetics in Materials, 4(2) (1993) 145-159
- [16] Harshe G, Doherty J P, Newnham R E Theoretical modeling of multilayermagnetoelectric composites International Journal of Applied Electromagnetics in Materials 4(2) (1993) 161-171 .
- [17] Avellaneda M, Harshé G Magnetoelectric effect in piezoelectric/ magnetostrictive multilayer (2-2) composites J. Intel. Mat. Syst. Str. 5 (1994) 501-513. [Crossref]
- [18] I.A. Osaretin, R.G. Rojas, Theoretical model for the magnetoelectric effect in magnetostrictive/piezoelectric composites, Phys. Rev. B 82 (2010) 174415(1)-174415(8). [Crossref]
- [19] I. Getman, Magnetoelectric composite materials: Theoretical approach to determine their properties, Ferroelectrics 162(1) (1994), 45-50. [Crossref]
- [20] C.W. Nan,Magnetoelectric effect in composites of piezoelectric and piezomagnetic phases, Physical Review B, 50(9), (1994), 6082-6088. [Crossref]
- [21] Huang J H, Kuo W S The analysis of piezoelectric/ piezomagnetic compositematerials containing ellipsoidal inclusions Journal of Applied Physics 81(3) (1997) 1378-1386. [Crossref]
- [22] Eshelby J D The determination of the elastic field of an ellipsoidal inclusion, and related problems Proc. R. Soc. Lond. A 241(1226) (1957) 376-396. Zbl0079.39606
- [23] Huang J H Analytical predictions for the magnetoelectric coupling in piezomagnetic materials reinforced by piezoelectric ellipsoidal inclusions Physical Review B 58(1) (1998) 12-15. [Crossref]
- [24] Huang J H, Liu H K, Dai W L The optimized fiber volume fraction for magnetoelectric coupling effect in piezoelectricpiezomagnetic continuous fiber reinforced composites International Journal of Engineering Science 38(11) (2000) 1207- 1217. [Crossref]
- [25] Hadjiloizi, D.A., Georgiades, A.V, Kalamkarov, A.L, Jothi, S, Micromechanical Model of Piezo-Magneto-Thermo-Elastic Composite Structures: Part I-Theory, European Journal of Mechanics A-Solids, 39, (2013), 298-312.
- [26] Hadjiloizi, D.A., Georgiades, A.V, Kalamkarov, A.L, Jothi, S, Micromechanical Model of Piezo-Magneto-Thermo-Elastic Composite Structures: Part II-Applications, European Journal of Mechanics A-Solids, 39, (2013), 313-326.
- [27] Bravo-Castillero J, Rodrigues-Ramos R, Mechkour H, Otero J, Sabina FJ Homogenization of magneto-electro-elastic multilaminated materials Q J Mechanics Appl Math 61(3) (2008) 311- 332 . Zbl1147.74040
- [28] Ni Y, Priya S and Khachaturyan A G Modeling of magnetoelectric effect in polycrystalline multiferroic laminates influenced by the orientations of applied electric/magnetic fields J Appl Phys 105 (2009) 083914(1)-083914(4). [Crossref]
- [29] C.H. Tsang, K.H. Chau, C.K. Wong, Y.W. Wong, F.G. Shin, Modeling of the magnetoelectric effect of three-phase multiferroic particulate composites, Integrated Ferroelectrics, 100:1, (2008), 177-197.
- [30] D.A. Pan, S.G. Zhang, A.A. Volinsky, L.J. Qiao, Simple model of themagnetoelectric effect in layered cylindrical composites, J. Phys. D: Appl. Phys. 41 (2008) 205008(1)-205008(5). [Crossref]
- [31] Bichurin M I, Petrov V N, Srinivasan G Modeling of magnetoelectric effect in ferromagnetic/piezoelectric multilayer composites Ferroelectrics 280 (2002) 165-175. [Crossref]
- [32] Bichurin M I, Petrov V N, Averkin S V, Liverts E Present status of theoretical modeling the magnetoelectric effect in magnetostrictive-piezoelectric nanostructures. Part I: Low frequency electromechanical resonance ranges J. Appl. Phys. 107(5), (2010) 053904(1)-053904(11). [Crossref]
- [33] Akbarzadeh A H, Babaei M H, Chen Z T The thermoelectromagnetoelastic behavior of a rotating functionally graded piezoelectric cylinder, Smart Mater. Struct. 20 (2011) 065008(1)- 065008(11). [Crossref]
- [34] Soh A K, Liu J X On the constitutive equations of magnetoelectroelastic solids Journal of Intelligent Materials Systems and Structures 16 (2005) 597-602.
- [35] Kirchner H O K, Alshits V I Elastically anisotropic angularly inhomogeneous media II. The Green’s function for piezoelectric, piezomagnetic andmagnetoelectric media PhilosophicalMagazine A 74(4) (1996) 861-885.
- [36] Pan E, Heyliger R P Free vibrations of simply supported and multilayered magneto-electro-elastic plates, Journal of Sound and Vibration 252(3) (2002) 429-442.
- [37] Benveniste Y, Milton G W New exact results for the effective electric, elastic, piezoelectric and other properties of composite ellipsoid assemblages Journal of the Mechanics and Physics of Solids 51(10) (2003) 1773-1813. [Crossref] Zbl1077.74591
- [38] Spyropoulos C P, Sih G C , Song Z FMagnetoelectroelastic composite with poling parallel to plane of line crack under out-ofplane deformation Theoretical and Applied Fracture Mechanics 40(2) (2003) 281-289. [Crossref]
- [39] Tang T, YuWVariational Asymptotic homogenization of heterogeneous electromagnetoelastic materials Int. J. Eng. Sci. 46 (2008) 741-757. [Crossref] Zbl1213.74140
- [40] Tang T, Yu W Micromechanical modeling of the multiphysical behavior of smart materials using the variational asymptotic method Smart Mater. Struct. 18(12) (2009) 125026 (1)-125026 (14). [Crossref]
- [41] Bensoussan A, Lions J L, Papanicolaou G Asymptotic analysis for periodic structures, Amsterdam: North-Holland, 1978. Zbl0404.35001
- [42] Sanchez-Palencia E, Non-Homogeneous media and vibration theory. Lecture Notes in Physics, Berlin: Springer-Verlag, 1980.
- [43] Bakhvalov N, Panasenko G Homogenisation: Averaging processes in periodic media, Amsterdam: Kluwer Academic Publishers, 1984.
- [44] Cioranescu D, Donato P, An Introduction to homogenization ,Oxford: Oxford University Press, 1999. Zbl0939.35001
- [45] Kalamkarov A L, Composite and Reinforced Elements of Construction, New York: Wiley,1992.
- [46] Kalamkarov A L, Kolpakov A G Analysis, design and optimization of composite structures ,New York: Wiley, 1997. Zbl0936.74002
- [47] Guedes J M and Kikuchi N Preprocessing and postprocessing formaterials based on the homogenization method with adaptive finite element methods, Comput. Methods Appl. Mech. Engrg. 83 (1990) 143-198. [Crossref] Zbl0737.73008
- [48] Duvaut G Analyse fonctionnelle et méchanique des milieux continus, Proceedings of the 14th IUTAM Congress (Delft, Holland) (1976) 119-132.
- [49] Duvaut G, Metellus A-M Homogénéisation d’une plaque mince en flexion de structure périodique et symétrique C.R. Acad. Sci., Ser. A. 283 (1976) 947-950. Zbl0368.73058
- [50] Andrianov I V,Manevich L I Shell design using the homogenization method Uspekhi Mekh 6 (1983) 3-29.
- [51] Andrianov I V, Lesnichaya V , Manevich L I Homogenization methods in the statics and dynamics of ribbed shells (Moscow, Nauka) (1985). Zbl0576.73054
- [52] Caillerie D Equations de la diffusion stationnaire dans un domaine comportant une distribution périodique d’inclusions aplaties de grande conductivité C.R. Acad. Sci., Ser. 1 292(1) (1981) 115-118. Zbl0468.73149
- [53] Caillerie D Homogénéisation des equation de la diffusion stationnaire dans les domaines cylindrique aplatis Anal. Numér. 15 (1981) 295-319.
- [54] Kohn R V, Vogelius M A new model for thin plates with rapidly varying thickness, Int. J. of Solids and Struct. 20 (1984) 333- 350. [Crossref] Zbl0532.73055
- [55] Kohn R V, Vogelius M A new model for thin plates with rapidly varying thickness, II: A convergence proof, Quart. J. Appl. Math. 43 (1985) 1-22. Zbl0565.73046
- [56] Kohn R V, Vogelius M A new model for thin plates with rapidly varying thickness, III: Comparison of Different Scalings, Quart. J. Appl. Math. 44 (1986) 35-48. Zbl0605.73048
- [57] Hussain F, Hojjati M, Okamoto M, Gorga R.E., Polymer-matrix nanocomposites, processing, manufacturing and application: An overview, Journal of Composite Materials 40(17) (2006), 1511-1575.
- [58] Challagulla K S, Georgiades A V, Kalamkarov A L Asymptotic homogenization modeling of smart composite generally orthotropic grid-reinforced shells. Part I-Theory European Journal of Mechanics A-Solids 29 (2010) 530-540. [Crossref]
- [59] Georgiades A V, Challagulla K S, Kalamkarov A L Asymptotic homogenization modeling of smart composite generally orthotropic grid-reinforced shells. Part II-Applications European Journal of Mechanics A-Solids 29 (2010) 541-556. [Crossref]
- [60] A.L. Kalamkarov and A.V. Georgiades, Asymptotic homogenization models for smart composite plates with rapidly varying thickness: Part I-Theory, Journal of Multiscale Computational Engineering 2(1) ( 2004) 133-148.
- [61] A.V. Georgiades and A.L. Kalamkarov, Asymptotic homogenization models for smart composite plates with rapidly varying thickness: Part II-Applications, Journal of Multiscale Computational Engineering 2(1) (2004) 149-174.
- [62] G.C. Saha, A.L. Kalamkarov, A.V. Georgiades, Micromechanical analysis of effective piezoelastic properties of smart composite sandwich shells made of generally orthotropic materials, Smart Materials and Structures 16(3) (2007) 866-883.
- [63] HadjiloiziDA, Georgiades A V, Kalamkarov A L. Dynamic modeling and determination of effective properties of smart composite plates with rapidly varying thickness, International Journal of Engineering Science 56 (2012) 63-85. [Crossref]
- [64] Hadjiloizi D A, Kalamkarov A L, Georgiades A V, Quasi-static Analysis of Piezo-Magneto-Thermo-Elastic Composite and Reinforced Plates: Part I – Model Development, Curved and Layered Structures 1 (2014) 11-31.
- [65] Sevostianov I, Kachanov M Effect of interphase layers on the overall elastic and conductive properties of matrix composites. Applications to nanosize inclusion Int. J. Solids Struct. 44 (2007) 1304-1315. [Crossref] Zbl1124.74041
- [66] Gibson R F, Principles of Composite Material Mechanics, McGraw-Hill, New York, 1994.
- [67] Vinson, J R, Sierakowski, R L, The Behavior of Structures Composed of Composite Materials, Kluwer Academic Publishers, Dordrecht, Netherlands, 2002. Zbl1029.74001
- [68] Reddy, J N, Mechanics of laminated composite plates, CRC Press, New York, 1997. Zbl0899.73002
- [69] Li L, Dunn ML, Micromechanics of magnetoelectroelastic composite materials: average fields and effective behaviour, J. Intel. Mat. Syst. Str. 1998; 9: 404–416. [Crossref]
- [70] Yoshihiro O, Tanigawa Y. Transient analysis of multilayered magneto-electro-thermoelastic strip due to nonuniform heat supply, Compos. Struct. 2005; 66: 471-480.
- [71] Cook W R Jr, Berlincourt, D A, Scholz, Thermal Expansion and pyroelectricity in Lead Zirconium Titanate Zirconate and Barium Titanate, Journal of Applied Physics 34 (1963), 1392-1398. [Crossref]
- [72] Verma KC, Gupta V, Kaur J, Kotnala, R K, Raman Spectra, photoluminescence, magnetism and magnetoelectric coupling in pure and Fe doped BaTiO3 nanostructures, Journal of Alloys and Compounds 578 (2013), 5-11.
- [73] Dascalu G, Popescu T, Feder, M, Caltun, O F, Structural, electric and magnetic properties of CoFe1.8RE0.2O4 (RE = Dy, Gd, La) bulk materials, Journal of Magnetism and Magnetic Materials 33 (2013), 69-74.
- [74] Kalamkarov, AL (2014) Asymptotic Homogenization Method and Micromechanical Models for Composite Materials and Thin-Walled Composite Structures, in “Mathematical Methods and Models in Composites,” pp. 1-60, Imperial College Press, London. Zbl1302.74136
- [75] Kalamkarov, AL and Challagulla KS (2013) Effective Properties of CompositeMaterials, Reinforced Structures andSmart Composites. Asymptotic Homogenization Approach, in “Effective Properties of Heterogeneous Materials,” Solid Mechanics and Its Applications, Vol. 193, pp. 283-363. Springer, Dordrecht, New York.
- [76] Challagulla, KS, Georgiades AV. Micromechanical Analysis of Magneto-Electro-Thermo-Elastic CompositeMaterials with Applications to Multilayered Structures. International Journal of Engineering Science 49 (2011) 85-104. [Crossref]

## Citations in EuDML Documents

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