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A. V. Nasedkin, A. A. Nasedkina, A. N. Rybyanets


DOI: 10.17804/2410-9908.2018.5.038-056

The paper considers computational homogenization problems for porous piezoceramic materials with partially metallized pore surfaces. The investigation is based on a complex approach including the effective moduli method, modeling of representative volumes with closed random porosity and metalized pore surfaces, finite element solution of a set of static piezoelectric problems with special boundary conditions and postprocessing of the computation results. Static problems of the piezoelectricity theory for an inhomogeneous representative volume are solved numerically with the help of the ANSYS finite element package. It is assumed that the thickness of the metal layer at the boundaries of the pores is infinitesimally small; therefore, the pore metallization is taken into account only by the electric boundary conditions of equipotentiality on the pore boundaries. Following the previous research, here we simulate the nonuniform polarization field around the pores. The porosity dependences of the effective moduli are analyzed for homogeneous and inhomogeneous polarization fields. The computation results have shown that microporous piezoceramics with metalized pore surfaces has a range of extreme properties promising for practical use.

Acknowledgments: This research was supported by grant 16-58-48009 from the Russian Foundation for Basic Research and by grant 9.5070.2017/6.7 of the Russian Ministry of Education and Sciences for the first author.

Keywords: piezoelectricity, porous piezoceramics, microstructure, metallized micropore, effective module, representative volume, finite element method


  1. Ringgaard E., Lautzenhiser F., Bierregaard L.M., Zawada T., Molz E. Development of porous piezoceramics for medical and sensor applications. Materials, 2015, vol. 8, no. 12, pp. 8877-8889. DOI: 10.3390/ma8125498
  2. Xiang P.-H., Dong X.-L., Chen H., Zhang Z., Guo J.-K. Mechanical and electrical properties of small amount of oxides reinforced PZT ceramics. Ceramics International, 2003, vol. 29, no. 5, pp. 499-503. DOI: 10.1016/S0272-8842(02)00193-1
  3. Rybyanets A.N., Naumenko A.A. Nanoparticles transport in ceramic matrixes: a novel approach for ceramic matrix composites fabrication. Journal of Modern Physics, 2013, vol. 4, no. 8, pp. 1041–1049. DOI: 10.4236/jmp.2013.48140
  4. Nasedkin A.V., Nasedkina A.A., Rybyanets A.N. Finite element analysis of effective properties of microporous piezoceramics with partial metallization of pore surfaces, taken into account the boundary conditions of free electrodes. Fundamentalnye problemy radioehlektronnogo priborostroeniya, 2017, vol. 17, no. 2, pp. 336–339. (In Russian).
  5. Nasedkin A.V., Nasedkina A.A., Rybyanets A.N. Models of microporous piezoelectric composites produced by the method of transport of metal-containing microparticles. Sovremennye problemy mekhaniki sploshnoj sredy, Proc. XVIII Int. Conf., Rostov-on-Don, 7-10 November 2016, vol. 2, Rostov-on-Don, SFedU Publ, 2016, pp. 122-126. (In Russian).
  6. Nasedkin A.V., Nasedkina A.A., Rybyanets A.N. Numerical study of the stiffness effect of the pore surface metallization on the properties of microporous piezoceramics obtained by the  metal-containing particle transport method. Fundamentalnye problemy radioehlektronnogo priborostroeniya, 2016, vol. 16, no 2, pp. 58–61. (In Russian).
  7. Nasedkin A.V. Models and finite element approximations for interacting nanosized piezoelectric bodies and acoustic medium. AIP Conference Proceedings, 2017, vol. 1798, pp. 020181-1-7. DOI: 10.1063/1.4975643
  8. Nasedkin A., Nasedkina A., Rybyanets A. Finite element simulation of effective properties of microporous piezoceramic material with metallized pore surfaces. Ferroelectrics, 2017, vol. 508, pp. 100-107. DOI: 10.1080/00150193.2017.1289569
  9. Nasedkin A.V., Nasedkina A.A., Rybyanets A.N. Mathematical modeling and computer design of piezoceramic materials with random arrangement of micropores and metallized pore surfaces. In: Proceedings of the 2016 International Conference on "Physics, Mechanics of New Materials and Their Applications". Eds. I.A. Parinov, S.-H. Chang, M.A. Jani. New York, Nova Science Publishers, 2017, ch. 54, pp. 385-392.
  10. Nasedkin A.V., Nasedkina A.A., Rybyanets A.N. Modeling and computer design of piezoceramic materials with stochastic microporous structure and local alloying pore surfaces. In: Poromechanics VI. Proceedings of the Sixth Biot Conference on Poromechanics, July 9–13, 2017, Paris, France. Eds. M. Vandamme, P, Dangla, J.-M. Pereiram, S. Ghabezloo. Publ. ASCE, Reston, Virginia, USA, 2017, pp. 724-731. DOI: 10.1061/9780784480779.089
  11. Nasedkin A.V., Shevtsova M.S. Effective moduli simulation for various types of porous piezoceramic materials. Vestnik of DSTU, 2013, no. 3-4 (72-73), pp. 16-26. (In Russian).
  12. Nasedkin A.V., Shevtsova M.S. Multiscale computer simulation of piezoelectric devices with elements from porous piezoceramics. In: Physics and mechanics of new materials and their applications. Eds. I.A. Parinov and S.-H. Chang. New York, Nova Science Publishers, 2013, ch. 16, pp. 185-202.
  13. Bowen C.R., Kara H. Pore anisotropy in 3–3 piezoelectric composites. Materials Chemistry and Physics, 2002, vol. 75, pp. 45–49. DOI: 10.1016/S0254-0584(02)00028-7
  14. Dunn H.; Taya M. Micromechanics predictions of the effective electroelastic moduli of piezoelectric composites. Int. J. Solids Struct., 1993, vol. 30, no. 2, pp. 161–175. DOI: 10.1016/0020-7683(93)90058-F
  15. Iyer S., Venkatesh T.A. Electromechanical response of (3–0, 3–1) particulate, fibrous, and porous piezoelectric composites with anisotropic constituents: A model based on the homogenization method. Int. J. Solids Struct., 2014, vol. 51, no. 6, pp. 1221–1234. DOI: 10.1016/j.ijsolstr.2013.12.008
  16. Lekhnickij S.G. Teoriya uprugosti anizotropnogo tela, M., Nauka, 1977. 416 p. (In Russian).
  17. Nasedkin A.V., Nasedkina A.A., Rajagopal A. Analysis of cymbal transducer from porous piezoceramics PZT-4 with various material properties based on ANSYS. In: Advanced Materials - Proceedings of the International Conference on “Physics and Mechanics of New Materials and Their Applications”, PHENMA 2017. Springer Proceedings in Physics, vol. 207, Eds. I.A. Parinov, S.-H. Chang, V.K. Gupta. Heidelberg, New York, Dordrecht, London, Springer Cham, 2018. DOI: 10.1007/978-3-319-78919-4_42 (in print)
  18. Wang K.F., Wang B.L., Kitamura T. A review on the application of modified continuum models in modeling and simulation of nanostructures. Acta Mech. Sin., 2016, vol. 32, no 1, pp. 83-100. DOI: 10.1007/s10409-015-0508-4



Article reference

Nasedkin A. V., Nasedkina A. A., Rybyanets A. N. Finite Element Modeling and Analysis of the Effective Properties of Inhomogeneously Polarized Porous Piezoceramic Material with Partial Metallization of Pore Surfaces // Diagnostics, Resource and Mechanics of materials and structures. - 2018. - Iss. 5. - P. 38-56. -
DOI: 10.17804/2410-9908.2018.5.038-056. -
URL: http://eng.dream-journal.org/issues/content/article_181.html
(accessed: 05/22/2024).


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