Multilevel Modeling of 1-3 Piezoelectric Energy Harvester Based ‎on Porous Piezoceramics

Document Type : Research Paper


1 Department of Theoretical and Applied Mechanics, Don State Technical University,‎ Gagarin sqr.1, Rostov on Don, 34400, Russia‎

2 Laboratory of Computational Mechanics, Institute of Mathematics, Mechanics and Computer Sciences, Southern Federal University,‎Milchakova str. 8a, Rostov on Don, 344090, Russia‎


The paper presents a computer analysis of the properties of a piezoelectric composite consisting of porous piezoceramic rods regularly arranged in an elastic matrix (piezocomposite with a connectivity of 1-3). The porous piezoceramic PZT-4 is used based on porous piezoceramics as an active material. The calculation of material properties is carried out based on a multilevel approach. First, the effective moduli of porous piezoceramics are determined, and then a 1-3 piezocomposite with rods having the calculated homogeneous properties is analyzed. The simulation uses the homogenization method based on the Hill lemma and the finite element method, as well as approximate analytical models. The effective properties of 1-3 composite are determined for various percentages of porosity of piezoceramic rods, which are a composite of 3-0 connectivity. Calculations were performed in the software package ACELAN-COMPOS. The calculated properties are used in finite element models to evaluate the effectiveness of composite materials in sensors and energy harvesting devices. Two cases of stiffness of an isotropic matrix are considered, which correspond to the stiffness of a porous composite at 50% and 80% porosity. The electromechanical properties, such as electro-mechanical coupling coefficient and output potential, for different transducers models made from the proposed composite are analyzed.


Main Subjects

Publisher’s Note Shahid Chamran University of Ahvaz remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

[1] Ghazanfarian, J., Mohammadi, M.M., Uchino K., Piezoelectric energy harvesting: A systematic review of reviews, Actuators, 10(12), 2021, 312.
[2] Aabid, A., Raheman, M.A., Ibrahim, Y.E., Anjum, A., Hrairi, M., Parveez, B., Parveen, N., Mohammed Zayan, J., A systematic review of piezoelectric materials and energy harvesters for industrial applications, Sensors, 21, 2021, 4145.
[3] Banerjee, S., Bairagi, S., Wazed Ali, S., A critical review on lead-free hybrid materials for next generation piezoelectric energy harvesting and conversion, Ceramics International, 47, 2021, 16402–16421.
[4] Li, T., Lee, P.S., Piezoelectric energy harvesting technology: From materials, structures, to applications, Small Structures, 3, 2022, 2100128.
[5] Liu, Y., Khanbareh, H., Halim, M.A., Feeney, A., Zhang, X., Heidari, H., Ghannam, R., Piezoelectric energy harvesting for self-powered wearable upper limb applications, Nano Select, 2, 2021, 1459-1479.
[6] Mahapatra, S.D., Mohapatra, P.C., Aria, A.I., Christie, G., Mishra, Y.K., Hofmann, S., Thakur, V.K., Piezoelectric materials for energy harvesting and sensing applications: Roadmap for future smart materials, Advanced Science, 8, 2021, 2100864.
‎[7] Parinov, I.A., Cherpakov, A.V., Overview: State-of-the-‎Art in the energy harvesting based on piezoelectric devices for last decade, Symmetry, 14, 2022, 765.‎
[8] Sezer, N., Koç, M., A comprehensive review on the state-of-the-art of piezoelectric energy harvesting, Nano Energy, 80, 2021, 105567,
[9] Chorsi, M.T., Curry, E.J., Chorsi, H.T., Das, R., Baroody, J., Purohit, P.K., Ilies, H., Nguyen, T.D., Piezoelectric biomaterials for sensors and actuators, Advanced Materials, 31, 2019, 1802084.
[10] Wang, Y., Hong, M., Venezuela, J., Liu, T., Dargusch, M., Expedient secondary functions of flexible piezoelectrics for biomedical energy harvesting, Bioactive Materials, 22, 2023, 291-311.
[11] Newnham, R.E., Skinner, D.P., Cross L.E., Connectivity and piezoelectric-pyroelectric composites, Materials Research Bulletin, 13(5), 1978, 525-536.
[12] Avellaneda, M., Swart, P.J., Calculating the performance of 1–3 piezocomposite for hydrophone applications: An effective medium approach, Journal of the Acoustical Society of America, 103, 1998, 1449–1467.
[13] Berger, H., Kari, S., Gabbert, U., Rodriguez-Ramos, R., Guinovart-Diaz, R., Otero, J.A., Bravo-Castillero, J., An analytical and numerical approach for calculating effective material coefficients of piezoelectric fiber composites, International Journal of Solids and Structures, 42, 2005, 5692–5714.
[14] Bravo-Castillero, J., Guinovart-Dı́az, R., Sabina, F.J., Rodrı́guez-Ramos, R., Closed-form expressions for the effective coefficients of a fiber-reinforced composite with transversely isotropic constituents – II. Piezoelectric and square symmetry, Mechanics of Materials, 33, 2001, 237–248.
[15] Castillero, J.B., Diaz, R.G., Hernandez, J.A.O., Ramos R.R., Electromechanical properties of continuous fibre-reinforced piezoelectric composites, Mechanics of Composite Materials, 33, 1997, 475-482.
[16] Gibiansky L.V., Torquato S., On the use of homogenization theory to design optimal piezocomposites for hydrophone applications, Journal of the Mechanics and Physics of Solids, 45(5), 1997, 689-708.
[17] Guinovart-Dıaz, R., Bravo-Castillero, J., Rodrıguez-Ramos, R., Sabina, F.J., Martınez-Rosado, R., Overall properties of piezocomposite materials 1–3, Materials Letters, 48, 2001, 93–98.
[18] Levin, V.M., Sabina, F.J., Bravo-Castillero, J., Guinovart-Díaz, R., Rodríguez-Ramos, R., Valdiviezo-Mijangos, O.C., Analysis of effective properties of electroelastic composites using the self-consistent and asymptotic homogenization methods, International Journal of Engineering Science, 46, 2008, 818–834.
[19] Sevostianov, I., Levin, V., Kachanov, M., On the modeling and design of piezocomposites with prescribed properties, Archive of Applied Mechanics, 71, 2001, 733–747.
[20] Pramanik R., Arockiarajan A., Effective properties and nonlinearities in 1-3 piezocomposites: a comprehensive review, Smart Materials and Structures, 2019, 28, 103001.
[21] Aloui, R., Larbi, W., Chouchane, M., Uncertainty quantification and global sensitivity analysis of piezoelectric energy harvesting using macro fiber composites, Smart Materials and Structures, 29, 2020, 095014.
[22] Shi, Y., Hallett, S.R., Zhu, M., Energy harvesting behaviour for aircraft composites structures using macro-fibre composite: Part I – Integration and experiment, Composite Structures, 160, 2017, 1279-1286.
[23] Song, H.J., Choi, Y.-T., Wereley, N.M., Purekar, A., Comparison of monolithic and composite piezoelectric material–based energy harvesting devices, Journal of Intelligent Material Systems and Structures, 25(14), 2014, 1825-1837.
[24] Swallow, L.M., Luo, J.K., Siores, E., Patel, I., Dodds, D., A piezoelectric fibre composite based energy harvesting device for potential wearable applications, Smart Materials and Structures, 17, 2008, 025017.
[25] Della, C.N., Shu, D. Performance of 1–3 piezoelectric composites with porous piezoelectric matrix, Applied Physics Letters, 103, 2013, 132905.
[26] Della, C.N., Shu, D.W., Della, C.N., Shu, D., The performance of 1–3 piezoelectric composites with a porous non-piezoelectric matrix, Acta Materialia, 56(4), 2008, 754-761.
[27] Gibiansky L.V., Torquato S., On the use of homogenization theory to design optimal piezocomposites for hydrophone applications, Journal of the Mechanics and Physics of Solids, 45(5), 1997, 689-708.
[28] Sigmund, O., Torquato, S., Aksay, I.A. On the design of 1–3 piezocomposites using topology optimization, Journal of Materials Research, 13, 1998, 1038–1048.
[29] Sladek J., Novak P., Bishay P.L., Sladek V., Effective properties of cement-based porous piezoelectric ceramic composites, Construction and Building Materials, 190, 2018, 1208-1214.
[30] Nasedkin, A.V., Oganesyan, P.A., Soloviev, A.N., Analysis of Rosen type energy harvesting devices from porous piezoceramics with great longitudinal piezomodulus, Zeitschrift für Angewandte Mathematik und Mechanik, 101, 2021, e202000129.
[31] Roscow, J.I., Lewis, R.W.C., Taylor, J., Bowen, C.R. Modelling and fabrication of porous sandwich layer barium titanate with improved piezoelectric energy harvesting figures of merit, Acta Materialia, 128, 2017, 207-217.
[32] Rybyanets, A.N., Naumenko, A.A., Lugovaya, M.A., Shvetsova, N.A., Electric power generations from PZT composite and porous ceramics for energy harvesting devices, Ferroelectrics, 484, 2015, 95-100.
[33] Yan, M., Xiao, Z., Ye, J., Yuan, X., Li, Z., Bowen, C., Zhang, Y., Zhang, D., Porous ferroelectric materials for energy technologies: current status and future perspectives, Energy & Environmental Science, 14(12), 2021, 6158-6190.
[34] Gerasimenko, T.E., Kurbatova, N.V., Nadolin, D.K., Nasedkin, A.V., Nasedkina, A.A., Oganesyan, P.A., Skaliukh, A.S., Soloviev, A.N., Homogenization of piezoelectric composites with internal structure and inhomogeneous polarization in ACELAN-COMPOS finite element package. In: Sumbatyan, M.A., (ed) Wave Dynamics, Mechanics and Physics of Microstructured Metamaterials. Advanced Structured Materials, 109, Springer: Singapore, 2019, 113–131.
[35] Kurbatova, N.V., Nadolin, D.K., Nasedkin, A.V., Oganesyan, P.A., Soloviev A.N., Finite element approach for composite magneto-piezoelectric materials modelling in ACELAN-COMPOS Package. In: Altenbach, H., Carrera, E., Kulikov, G., (eds) Analysis and Modelling of Advanced Structures and Smart Systems. Advanced Structured Materials, 81, Singapore: Singapore, 2018, 69-88.
[36] Belokon', A.V., Nasedkin, A.V., Solov'ev, A.N., New schemes for the finite-element dynamic analysis of piezoelectric devices, Journal of Applied Mathematics and Mechanics, 66, 2002, 481–490.
[37] Nasedkin, A.V., Some finite element methods and algorithms for solving acousto-piezoelectric problems. In: Parinov, I.A., (ed) Piezoceramic Materials and Devices, Nova Science Publishers, New York, 2010, 177–218.
[38] Dunn, M.L., Taya, M., Micromechanics predictions of the effective electroelastic moduli of piezoelectric composites, International Journal of Solids and Structures, 30, 1993, 161–175.
[39] Hori, M., Nemat-Nasser, S., Universal bounds for effective piezoelectric moduli, Mechanics of Materials, 30, 1998, 295-308. doi: 10.1016/S0167-6636(98)00029-5
[40] Kar-Gupta, R., Venkatesh, T.A., Electromechanical response of porous piezoelectric materials, Acta Materialia, 54, 2006, 4063–4078.
[41] Martínez-Ayuso, G., Friswell, M.I., Adhikari, S., Khodaparast, H.H., Berger, H., Homogenization of porous piezoelectric materials, International Journal of Solids and Structures, 113–114, 2017, 218–229.
[42] Mawassy, N., Reda, H., Ganghoffer, J.-F., Eremeyev, V.A., Lakiss, H., A variational approach of homogenization of piezoelectric composites towards piezoelectric and flexoelectric effective media, International Journal of Engineering Science, 158, 2021, 103410.
[43] Nasedkin, A.V., Shevtsova, M.S., Improved finite element approaches for modelling of porous piezocomposite materials with different connectivity. In: Parinov, I.A., (ed) Ferroelectrics and Superconductors: Properties and Applications, Nova Science Publishers, New York, 2011, 231–254.
[44] Nasedkin, A.V., Nasedkina, A.A., Nassar, M.E., Homogenization of porous piezocomposites with extreme properties at pore boundaries by effective moduli method, Mechanics of Solids, 55(6), 2020, 827–836.
[45] Odegard, G.M., Constitutive modeling of piezoelectric polymer composites, Acta Materialia, 52, 2004, 5315–5330,
[46] Nasedkin, A., Nassar, M.E., About anomalous properties of porous piezoceramic materials with metalized or rigid surfaces of pores, Mechanics of Materials, 162, 2021, 104040.
[47] Firooz, S., Steinmann, P., and Javili, A., Homogenization of composites with extended general interfaces: Comprehensive review and unified modeling, Applied Mechanics Reviews, 73(4), 2021, 040802.
[48] Kudimova, A.B., Nadolin, D.K., Nasedkin, A.V., Oganesyan, P.A., Soloviev, A.N., Finite element homogenization models of bulk mixed piezocomposites with granular elastic inclusions in ACELAN package, Materials Physics and Mechanics, 37, 2018, 25–33.
[49] Kudimova, A.B., Nadolin, D.K., Nasedkin, A.V., Nasedkina, A.A., Oganesyan, P.A. Soloviev, A.N., Finite element homogenization of piezocomposites with isolated inclusions using improved 3-0 algorithm for generating representative volumes in ACELAN-COMPOS package, Materials Physics and Mechanics, 44, 2020, 392-403. 10.18720/MPM.4432020_10
[50] El Moumen, A., Kanit, T., Imad, A., Numerical evaluation of the representative volume element for random composites, European Journal of Mechanics/A Solids, 86, 2021, 104181.
[51] Kari, S., Berger, H., Rodriguez-Ramos, R., Gabbert, U., Computational evaluation of effective material properties of composites reinforced by randomly distributed spherical particles, Composite Structures, 77, 2007, 223–231.
[52] Segurado, J., Llorca, J., A numerical approximation to the elastic properties of sphere reinforced composites, Journal of the Mechanics and Physics of Solids, 50, 2002, 2107–2121.
[53] Schröder, J., Balzani, D., Brands, D., Approximation of random microstructures by periodic statistically similar representative volume elements based on lineal-path functions, Archive of Applied Mechanics, 81, 2011, 975–997.
[54] COMSOL Multiphysics® v. 5.6. COMSOL AB, Stockholm, Sweden. (License № 9602094)