[1] Ghazanfarian, J., Mohammadi, M.M., Uchino K., Piezoelectric energy harvesting: A systematic review of reviews, Actuators, 10(12), 2021, 312. https://doi.org/10.3390/act10120312
[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. http://doi.org/10.3390/s21124145
[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. http://doi.org/10.1016/j.ceramint.2021.03.054
[4] Li, T., Lee, P.S., Piezoelectric energy harvesting technology: From materials, structures, to applications, Small Structures, 3, 2022, 2100128. https://doi.org/10.1002/sstr.202100128
[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. http://doi.org/10.1002/nano.202000242
[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. https://doi.org/10.1002/advs.202100864
[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. https://doi.org/10.3390/sym14040765
[8] Sezer, N., Koç, M., A comprehensive review on the state-of-the-art of piezoelectric energy harvesting, Nano Energy, 80, 2021, 105567, http://doi.org/10.1016/j.nanoen.2020.105567
[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. https://doi.org/10.1002/adma.201802084
[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. https://doi.org/10.1016/j.bioactmat.2022.10.003
[11] Newnham, R.E., Skinner, D.P., Cross L.E., Connectivity and piezoelectric-pyroelectric composites, Materials Research Bulletin, 13(5), 1978, 525-536. https://doi.org/10.1016/0025-5408(78)90161-7
[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. http://doi.org/10.1121/1.421306
[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. http://doi.org/10.1016/j.ijsolstr.2005.03.016
[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. http://doi.org/10.1016/S0167-6636(00)00060-0
[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. https://doi.org/10.1007/BF02256903
[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. https://doi.org/10.1016/S0022-5096(96)00106-8
[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. http://doi.org/10.1016/S0167-577X(00)00285-8
[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. http://doi.org/10.1016/j.ijengsci.2008.01.017
[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. http://doi.org/10.1007/s004190100181
[20] Pramanik R., Arockiarajan A., Effective properties and nonlinearities in 1-3 piezocomposites: a comprehensive review, Smart Materials and Structures, 2019, 28, 103001. https://doi.org/10.1088/1361-665X/ab350a
[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. http://doi.org/10.1088/1361-665X/ab9f12
[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. https://doi.org/10.1016/j.compstruct.2016.11.037.
[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. http://doi.org/10.1177/1045389X14530592
[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. http://doi.org/10.1088/0964-1726/17/2/025017
[25] Della, C.N., Shu, D. Performance of 1–3 piezoelectric composites with porous piezoelectric matrix, Applied Physics Letters, 103, 2013, 132905. https://doi.org/10.1063/1.4822109
[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. https://doi.org/10.1016/j.actamat.2007.10.022
[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. https://doi.org/10.1016/S0022-5096(96)00106-8
[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. https://doi.org/10.1557/JMR.1998.0145
[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. https://doi.org/10.1016/j.conbuildmat.2018.09.127
[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. http://doi.org/10.1002/zamm.202000129
[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. http://dx.doi.org/10.1016/j.actamat.2017.02.029
[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. https://doi.org/10.1080/00150193.2015.1060065
[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. http://doi.org/10.1039/d1ee03025f
[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. http://doi.org/10.1007/978-3-030-17470-5_8
[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. http://doi.org/10.1007/978-981-10-6895-9_5
[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. http://doi.org/10.1016/S0021-8928(02)00058-8
[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. http://doi.org/10.1016/0020-7683(93)90058-F
[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. http://doi.org/10.1016/j.actamat.2006.04.037
[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. http://doi.org/10.1016/j.ijsolstr.2017.03.003
[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. https://doi.org/10.1016/j.ijengsci.2020.103410
[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. https://doi.org/10.3103/S0025654420050131
[45] Odegard, G.M., Constitutive modeling of piezoelectric polymer composites, Acta Materialia, 52, 2004, 5315–5330, https://doi.org/10.1016/j.actamat.2004.07.037
[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. http://doi.org/10.1016/j.mechmat.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. https://doi.org/10.1115/1.4051481
[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. http://doi.org/10.18720/MPM.3712018_4
[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. http://doi.org/ 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. https://doi.org/10.1016/j.euromechsol.2020.104181
[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. http://doi.org/10.1016/j.compstruct.2005.07.003
[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. http://doi.org/10.1016/S0022-5096(02)00021-2
[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. http://doi.org/10.1007/s00419-010-0462-3
[54] COMSOL Multiphysics® v. 5.6. www.comsol.com. COMSOL AB, Stockholm, Sweden. (License № 9602094)