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Finite Element Study of Ceramic Matrix Piezocomposites with Mechanical Interface Properties by the Effective Moduli Method with Different Types of Boundary Conditions

  • G. Iovane
  • A. V. NasedkinEmail author
Chapter
Part of the Advanced Structured Materials book series (STRUCTMAT, volume 109)

Abstract

The paper deals with the problem of finding the effective moduli of a ceramic matrix composite with surface stresses on the interphase boundaries. The composite consists of a PZT ceramic matrix, elastic inclusions and interface boundaries. It is assumed that the interface stresses depend on the surface strains according to the Gurtin–Murdoch model. This model describes the size effects and contributes to the total stress-strain state only for nanodimensional inclusions. The homogenization problem was set and solved with the help of the effective moduli method for piezoelectric composites with interface boundaries and finite-element technologies used for simulating the representative volumes and solving the resulting boundary-value electroelastic problems. Here in the effective moduli method, different combinations of linear first-kind boundary conditions and constant second-kind boundary conditions for mechanical and electric fields were considered. The representative volume consisted of cubic finite elements with the material properties of the matrix or inclusions and also included the surface elements on the interfaces. Bulk elements were supplied with the material properties of the matrix or inclusions, using a simple random method. In the numerical example, the influence of the fraction of inclusions, the interface stresses and boundary conditions on the effective electroelastic modules were analysed.

Notes

Acknowledgements

This work for second author was supported by the Russian Science Foundation (grant number 15-19-10008-P).

References

  1. 1.
    Bobrov, S.V., Nasedkin, A.V., Rybjanets, A.N.: Finite element modeling of effective moduli of porous and polycrystalline composite piezoceramics. In: Topping, B.H.V., Montero, G., Montenegro, R. (eds.) Proceedings VIII International Conference on Computational Structures Technology, Civil-Comp Press, Stirlingshire, UK, Paper 107 (2006)Google Scholar
  2. 2.
    Chatzigeorgiou, G., Javili, A., Steinmann, P.: Multiscale modelling for composites with energetic interfaces at the micro-or nanoscale. Math. Mech. Solids. 20, 1130–1145 (2015)CrossRefGoogle Scholar
  3. 3.
    Chen, T.: Exact size-dependent connections between effective moduli of fibrous piezoelectric nanocomposites with interface effects. Acta Mech. 196, 205–217 (2008)CrossRefGoogle Scholar
  4. 4.
    Dai, Sh., Gharbi, M., Sharma, P., Park, H.S.: Surface piezoelectricity: size effects in nanostructures and the emergence of piezoelectricity in non-piezoelectric materials. J. Appl. Phys. 110, 104305-1–104305-7 (2011)Google Scholar
  5. 5.
    Duan, H.L., Wang, J., Karihaloo, B.L.: Theory of elasticity at the nanoscale. In: Advances in Applied Mechanics, vol. 42, pp. 1–68. Elsevier (2008)Google Scholar
  6. 6.
    Duan, H.L., Wang, J., Karihaloo, B.L., Huang, Z.P.: Nanoporous materials can be made stiffer than non-porous counterparts by surface modification. Acta Mater. 54, 2983–2990 (2006)CrossRefGoogle Scholar
  7. 7.
    Eremeyev, V.A.: On effective properties of materials at the nano- and microscales considering surface effects. Acta Mech. 227, 29–42 (2016)CrossRefGoogle Scholar
  8. 8.
    Eremeyev, V., Morozov, N.: The effective stiffness of a nanoporous rod. Dokl. Phys. 55(6), 279–282 (2010)CrossRefGoogle Scholar
  9. 9.
    Eremeyev, V.A., Nasedkin, A.V.: Mathematical models and finite element approaches for nanosized piezoelectric bodies with uncoupled and coupled surface effects. In: Sumbatyan, M.A. (ed.) Wave Dynamics and Composite Mechanics for Microstructured Materials and Metamaterials. Ser. Advanced Structured Materials, vol. 59, pp. 1–18. Springer, Singapore (2017)Google Scholar
  10. 10.
    Fang, X.-Q., Zhu, C.-S., Liu, J.-X., Liu, X.-L.: Surface energy effect on free vibration of nano-sized piezoelectric double-shell structures. Phys. B: Condens. Matter. 529, 41–56 (2018)CrossRefGoogle Scholar
  11. 11.
    Gu, S.-T., He, Q.-C.: Interfacial discontinuity relations for coupled multifield phenomena and their application to the modeling of thin interphases as imperfect interfaces. J. Mech. Phys. Solids. 59, 1413–1426 (2011)Google Scholar
  12. 12.
    Gu, S.-T., He, Q.-C., Pensee, V.: Homogenization of fibrous piezoelectric composites with general imperfect interfaces under anti-plane mechanical and in-plane electrical loadings. Mech. Mater. 88, 12–29 (2015)CrossRefGoogle Scholar
  13. 13.
    Gu, S.-T., Liu, J.-T., He. Q.-C.: Piezoelectric composites: Imperfect interface models, weak formulations and benchmark problems. Comp. Mater. Sci. 94, 182–190 (2014)Google Scholar
  14. 14.
    Gu, S.-T., Liu, J.-T., He. Q.-C.: The strong and weak forms of a general imperfect interface model for linear coupled multifield phenomena. Int. J. Eng. Sci. 85, 31–46 (2014)Google Scholar
  15. 15.
    Gu, S.-T., Qin, L.: Variational principles and size-dependent bounds for piezoelectric inhomogeneous materials with piezoelectric coherent imperfect interfaces. Int. J. Eng. Sci. 78, 89–102 (2014)CrossRefGoogle Scholar
  16. 16.
    Huang, G.Y., Yu, S.W.: Effect of surface piezoelectricity on the electromechanical behaviour of a piezoelectric ring. Phys. Status Solidi B. 243(4), R22–R24 (2006)CrossRefGoogle Scholar
  17. 17.
    Javili, A., McBride, A., Mergheima, J., Steinmann, P., Schmidt, U.: Micro-to-macro transitions for continua with surface structure at the microscale. Int. J. Solids Struct. 50, 2561–2572 (2013)CrossRefGoogle Scholar
  18. 18.
    Jeong, J., Cho, M., Choi, J.: Effective mechanical properties of micro/nano-scale porous materials considering surface effects. Interact. Multiscale Mech. 4(2), 107–122 (2011)CrossRefGoogle Scholar
  19. 19.
    Kudimova, A.B., Nadolin, D.K., Nasedkin, A.V., Nasedkina, A.A., Oganesyan, P.A., Soloviev, A.N.: Models of porous piezocomposites with 3–3 connectivity type in ACELAN finite element package. Mater. Phys. Mech. 37(1), 16–24 (2018)Google Scholar
  20. 20.
    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. Mater. Phys. Mech. 37(1), 25–33 (2018)Google Scholar
  21. 21.
    Malakooti, M.H., Sodano, H.A.: Multi-inclusion modeling of multiphase piezoelectric composites. Compos.: Part B. 47, 181–189 (2013)Google Scholar
  22. 22.
    Nasedkin, A.V.: Some homogenization models of nanosized piezoelectric composite materials of types ceramics-pores and ceramics-ceramics with surface effects. In: Guemes, A., Benjeddou, A., Rodellar, J., Leng, J. (eds.) VIII ECCOMAS Thematic Conference on Smart Structures and Materials, VI Int. Conf. on Smart Materials and Nanotechnology in Engineering-SMART 2017, 5–8 June 2017, Madrid, Spain, pp. 1137–1147. CIMNE, Barcelona, Spain (2017)Google Scholar
  23. 23.
    Nasedkin, A.V., Eremeyev, V.A.: Harmonic vibrations of nanosized piezoelectric bodies with surface effects. ZAMM 94(10), 878–892 (2014)CrossRefGoogle Scholar
  24. 24.
    Nasedkin, A.V., Kornievsky, A.S.: Finite element modeling and computer design of anisotropic elastic porous composites with surface stresses. In: Sumbatyan, M.A. (ed.) Wave Dynamics and Composite Mechanics for Microstructured Materials and Metamaterials. Series Advanced Structured Materials, vol. 59, pp. 107–122. Springer, Singapore (2017)Google Scholar
  25. 25.
    Nasedkin, A.V., Kornievsky, A.S.: Finite element modeling of effective properties of elastic materials with random nanosized porosities. ycisl. meh. splos. sred – Comput. Continuum Mech. 10(4), 375–387 (2017)Google Scholar
  26. 26.
    Nasedkin, A.V., Nasedkina, A.A., Remizov, V.V.: Finite element modeling of porous thermoelastic composites with account for their microstructure. Vycisl. meh. splos. sred – Comput. Continuum Mech. 7(1), 100–109 (2014)Google Scholar
  27. 27.
    Nasedkin, A.V., Shevtsova, M.S.: Improved finite element approaches for modeling of porous piezocomposite materials with different connectivity. In: Parinov, I.A. (ed.) Ferroelectrics and Superconductors: Properties and Applications, pp. 231–254. Nova Science Publication, NY (2011)Google Scholar
  28. 28.
    Nasedkin, A.V., Shevtsova, M.S.: Multiscale computer simulation of piezoelectric devices with elements from porous piezoceramics In: Parinov, I.A., Chang, S.-H. (eds.) Physics and Mechanics of New Materials and Their Applications, pp. 185–202. Nova Science Publ., NY (2013)Google Scholar
  29. 29.
    Pan, X.H., Yu, S.W., Feng, X.Q.: A continuum theory of surface piezoelectricity for nanodielectrics. Sci. China: Phys. Mech. Astron. 54(4), 564–573 (2011)Google Scholar
  30. 30.
    Park, H.S., Devel, M., Wang, Z.: A new multiscale formulation for the electromechanical behavior of nanomaterials. Comput. Methods Appl. Mech. Eng. 200, 2447–2457 (2011)CrossRefGoogle Scholar
  31. 31.
    Rybyanets, A.N., Konstantinov, G.M., Naumenko, A.A., Shvetsova, N.A., Makarev, D.I., Lugovaya, M.A.: Elastic, dielectric, and piezoelectric properties of ceramic lead zirconate titanate/\(\alpha \)-Al\(_2\)O\(_3\) composites. Phys. Solid State. 57(3), 527–530 (2015)Google Scholar
  32. 32.
    Rybyanets, A.N., Naumenko, A.A., Konstantinov, G.M., Shvetsova, N.A., Lugovaya, M.A.: Elastic loss and dispersion in ceramic-matrix piezocomposites. Phys. Solid State. 57(3), 558–562 (2015)CrossRefGoogle Scholar
  33. 33.
    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. 32(1), 83–100 (2016)Google Scholar
  34. 34.
    Wang, W., Li, P., Jin, F., Wang, J.: Vibration analysis of piezoelectric ceramic circular nanoplates considering surface and nonlocal effects. Compos. Struct. 140, 758–775 (2016)CrossRefGoogle Scholar
  35. 35.
    Wang, Z., Zhu, J., Jin, X.Y., Chen, W.Q., Zhang, Ch.: Effective moduli of ellipsoidal particle reinforced piezoelectric composites with imperfect interfaces. J. Mech. Phys. Solids. 65, 138–156 (2014)CrossRefGoogle Scholar
  36. 36.
    Xiao, J.H., Xu, Y.L., Zhang, F.C.: Size-dependent effective electroelastic moduli of piezoelectric nanocomposites with interface effect. Acta Mech. 222, 59–67 (2011)CrossRefGoogle Scholar
  37. 37.
    Zhao, D., Liu, J.L., Wang, L.: Nonlinear free vibration of a cantilever nanobeam with surface effects: semi-analytical solutions. Int. J. Mech. Sci. 113, 184–195 (2016)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of SalernoFiscianoItaly
  2. 2.Institute of Mathematics, Mechanics and Computer ScienceSouthern Federal UniversityRostov-on-DonRussia

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