Abstract
The chapter presents the mathematical models for thermopiezomagnetoelectric composite materials of an arbitrary anisotropy classes for computer engineering finite element package ACELAN. These homogenization models are based on the method of effective moduli with different boundary conditions, the approaches for generation of representative volumes with specified properties and the finite element method. Important features of ACELAN package also include the original models of irreversible processes of polarization and repolarization for polycrystalline ferroelectric materials. In this paper the software architecture of ACELAN package and its ability for creation of representative volumes with different structures are also described.
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References
Belokon, A.V., Nasedkin, A.V., Soloviev, A.N.: New schemes for the finite-element dynamic analysis of piezoelectric devices. J. Appl. Math. Mech. (PMM) 66(3), 481–490 (2002)
Belokon, A.V., Skaliuh, A.S.: Mathematical modeling of irreversible processes of polarization. M., FIZMATLIT, 1–328 (2010) (Russian edition)
Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005)
Benzi, M., Wathen, A.J.: Some preconditioning techniques for saddle point problems. In: Schilders, W.H.A., van der Vorst, H.A., Rommes, J. (eds.) Model Order Reduction: Theory, Research Aspects and Applications. Mathematics in Industry, vol. 13, pp. 195–211
Berlincourt, D.A., Curran, D.R., Jaffe, H.: Piezoelectric and piezomagnetic materials. In: Physical Acoustics, Part A, vol. 1. Academic Press, NY, pp. 233–256 (1964)
Challagulla, K.S., Georgiades, A.V.: Micromechanical analysis of magneto-electro-thermo-elastic composite materials with applications to multilayered structures. Int. J. Eng. Sci. 49, 85–104 (2011)
Lee, J., Boyd, J.G., Lagoudas, D.C.: Effective properties of three-phase electro-magneto-elastic composites. Int. J. Eng. Sci. 43, 790–825 (2005)
Li, J.Y.: Magnetoelectroelastic multi-inclusion and inhomogeneity problems and their applications in composite materials. Int. J. Eng. Sci. 38, 1993–2011 (2000)
Hadjiloizi, A.D., Georgiades, A.V., Kalamkarov, A.V., Jothi, S.: Micromechanical modeling of piezo-magneto-thermo-elastic composite structures: part I-Theory. Eur. J. Mech. A-Solids 39, 298–312 (2013)
Hadjiloizi, D.A., Georgiades, A.V., Kalamkarov, A.L., Jothi, S.: Micromechanical modeling of piezo-magneto-thermo-elastic composite structures: Part II–Applications. Eur. J. Mech. A-Solids 39, 313–327 (2013)
Nan, C.-W., Bichurin, M.I., Dong, S., Viehland, D., Srinivasan, G.: Multiferroic magnetoelectric composites: historical perspective, status, and future directions. J. Appl. Phys. 103, 031101–1–35 (2008)
Nasedkin, A.V.: Some finite element methods and algorithms for solving acousto-piezoelectric problems. In: Parinov, I.A. (ed.) Piezoceramic Materials and Devices, pp. 177–218. Nova Science Publishers, New York (2010)
Nasedkin, A.V.: Modeling of magnetoelectric composites by effective moduli and finite element methods. Theoretical approaches. Ferroelectrics. 461(1), 106–112 (2014)
Nasedkin, A.V.: Multiscale computer design of piezomagnetoelectric mixture composite structures. AIP Conf. Proc. 1627, 64–69 (2014)
Nasedkin, A.V.: Finite element design of piezoelectric and magnetoelectric composites by using symmetric saddle algorithms. In: Parinov, I.A., Chang, S.-H., Theerakulpisut, S. (eds.) Advanced Materials-Studies and Applications, pp. 109–124. Nova Science Publishers, New York (2015)
Nasedkin, A.V., Eremeyev, V.A.: Modeling of nanosized piezoelectric and magnetoelectric bodies with surface effects. AIP Conf. Proc. 1627, 70–75 (2014)
Nasedkin, A.V., Eremeyev, V.A.: Some models for nanosized magnetoelectric bodies with surface effects. In: Parinov, I.A., Chang, S.-H., Topolov, V.Y. (eds.) Advanced Materials-Manufacturing, Physics, Mechanics and Applications, Series “Springer Proceedings in Physics, vol. 175, pp. 373–391. Springer, Heidelberg, New York, Dordrecht, London (2016)
Nasedkin, A.V., Nasedkina, A.A.: Finite element modeling and computer design of porous composites. In: Hellmich, C., Pichler, B., Adam, D. (eds.) Poromechanics V. Proceedings of the Fifth Biot Conference on Poromechanics, pp. 608–617, 10–12 July 2013, Vienna, Austria. Publ. ASCE (2013)
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 Publishers, New York (2011)
Nasedkin, A., Skaliukh, A., Soloviev, A.: New models of coupled active materials for finite element package ACELAN. AIP Conf. Proc. 1637, 714–723 (2014)
Rybyanets, A.N.: Ceramic piezocomposites: modeling, technology, characterization. In: Parinov, I.A. (ed.) Piezoceramic Materials and Devices, pp. 115–174. Nova Science Publishers, New York (2010)
Rybyanets, A.N.: Porous piezoeramics: theory, technology, and properties. IEEE Trans. UFFC. 58, 1492–1507 (2011)
Skaliukh, A.S.: Modeling of polarisation of the polycrystilline ferroelectrics. In: Parinov, I.A. (ed.) Piezoelectric materials and devices, pp. 50–102. Nova Science Publishers, New York (2012)
Skaliukh, A.S., Soloviev, A.N., Oganesyan, P.A.: Modeling of piezoelectric elements with inhomogeneous polarization in ACELAN. Ferroelectrics 483(1), 95–101 (2015)
Soloviev, A.N., Oganesyan, P.A., Skaliukh, A.S.: Modeling of piezoelectric elements with inhomogeneous polarization by using ACELAN. In: Parinov, I.A., Chang, S.-H., Theerakulpisut, S. (eds.) Advanced Materials-Studies and Applications, pp. 169–192. Nova Science Publishers, New York (2015)
Tang, T., Yu, W.: Variational asymptotic homogenization of heterogeneous electromagnetoelastic materials. Int. J. Eng. Sci. 46, 741–757 (2008)
Topolov, V.Yu., Bowen, C.R.: Electromechanical Properties in Composites Based on Ferroelectrics, pp. 1–202. Springer, London (2009)
Vanderbei, R.J.: Symmetric quasidefinite matrices. SIAM J. Optim. 5, 100–113 (1995)
Zhang, Z.K., Soh, A.K.: Micromechanics predictions of the effective moduli of magnetoelectroelastic composite materials. Eur. J. Mech. A-Solids 24, 1054–1067 (2005)
Acknowledgements
The investigations on the development of homogenization models for active composite materials have been carried by A. Nasedkin with the support of the Russian Scientific Foundation (RSCF) by Project 15-19-10008.
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Kurbatova, N.V. et al. (2017). Models of Active Bulk Composites and New Opportunities of the ACELAN Finite Element Package. In: Sumbatyan, M. (eds) Wave Dynamics and Composite Mechanics for Microstructured Materials and Metamaterials . Advanced Structured Materials, vol 59. Springer, Singapore. https://doi.org/10.1007/978-981-10-3797-9_8
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DOI: https://doi.org/10.1007/978-981-10-3797-9_8
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