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http://dx.doi.org/10.12989/csm.2018.7.1.005

Linear elastic mechanical system interacting with coupled thermo-electro-magnetic fields  

Moreno-Navarro, Pablo (Sorbonne Universites-Universite de Technologie Compiegne, Laboratoire Roberval de Mecanique)
Ibrahimbegovic, Adnan (Sorbonne Universites-Universite de Technologie Compiegne, Laboratoire Roberval de Mecanique)
Perez-Aparicio, Jose L. (Department of Continuum Mechanics & Theory of Structures, Universitat Politecnica de Valencia)
Publication Information
Coupled systems mechanics / v.7, no.1, 2018 , pp. 5-25 More about this Journal
Abstract
A fully-coupled thermodynamic-based transient finite element formulation is proposed in this article for electric, magnetic, thermal and mechanic fields interactions limited to the linear case. The governing equations are obtained from conservation principles for both electric and magnetic flux, momentum and energy. A full-interaction among different fields is defined through Helmholtz free-energy potential, which provides that the constitutive equations for corresponding dual variables can be derived consistently. Although the behavior of the material is linear, the coupled interactions with the other fields are not considered limited to the linear case. The implementation is carried out in a research version of the research computer code FEAP by using 8-node isoparametric 3D solid elements. A range of numerical examples are run with the proposed element, from the relatively simple cases of piezoelectric, piezomagnetic, thermoelastic to more complicated combined coupled cases such as piezo-pyro-electric, or piezo-electro-magnetic. In this paper, some of those interactions are illustrated and discussed for a simple geometry.
Keywords
electromagnetic-thermomechanical coupling; elasticity; thermodynamics; finite element formulation;
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1 Aboudi, J. (2001), "Micromechanical analysis of fully coupled electro-magneto-thermo-elastic multiphase composites", Smart Mater. Struct., 10(5), 867.   DOI
2 Allik, H. and Hughes, T. (1970), "Finite element method for piezoelectric vibration", J. Numer. Meth. Eng., 2(2), 151-157.   DOI
3 Babuska, I., Szabo, B.A. and Katz, I. (1981), "The p-version of the finite element method", SIAM J. Numer. Analy., 18(3), 515-545.   DOI
4 Balanis, C. (1989), Advanced Engineering Electromagnetics, John Wiley & Sons.
5 Chen, W., Lee, K. and Ding, H. (2004), "General solution for transversely isotropic magneto-electrothermoelasticity and the potential theory method", J. Eng. Sci., 42(13), 1361-1379.   DOI
6 De Groot, S. and Mazur, P. (1984), Non-Equilibrium Thermodynamics, Dover.
7 Duczek, S. and Gabbert, U. (2013), "Anisotropic hierarchic finite elements for the simulation of piezoelectric smart structures", Eng. Comput., 30(5), 682-706.   DOI
8 Ferrari, A. and Mittica, A. (2013), "Thermodynamic formulation of the constitutive equations for solids and fluids", Energy Convers. Manage., 66, 77-86.   DOI
9 Fung, R.F., Huang, J.S. and Jan, S.C. (2000), "Dynamic analysis of a piezothermoelastic resonator with various shapes", J. Vibr. Acoust., 122(3), 244-253.   DOI
10 Gornandt, A. and Gabbert, U. (2002), "Finite element analysis of thermopiezoelectric smart structures", Acta Mech., 154(1), 129-140.   DOI
11 Hou, P., Ding, H. and Leung, A. (2006), "The transient responses of a special non-homogeneous magnetoelectro- elastic hollow cylinder for axisymmetric plane strain problem", J. Sound Vibr., 291(1), 19-47.   DOI
12 Ibrahimbegovic, A. (2009), Nonlinear Solid Mechanics: Theoretical Formulations and Finite Element Solution Methods, Springer Science & Business Media.
13 Jiang, J.P. and Li, D.X. (2007), "A new finite element model for piezothermoelastic composite beam", J. Sound Vibr., 306(3), 849-864.   DOI
14 Lezgy-Nazargah, M., Vidal, P. and Polit, O. (2013), "An efficient finite element model for static and dynamic analyses of functionally graded piezoelectric beams", Compos. Struct., 104, 71-84.   DOI
15 Li, J. (2000), "Magnetoelectroelastic multi-inclusion and inhomogeneity problems and their applications in composite materials", J. Eng. Sci., 38(18), 1993-2011.   DOI
16 Moreno-Navarro, P., Ibrahimbegovic, A. and Perez-Aparicio, J. (2017), "Plasticity coupled with thermoelectric fields: Thermodynamics framework and finite element method computations", Comput. Meth. Appl. Mech. Eng., 315, 50-72.   DOI
17 Pan, E. (2001), "Exact solution for simply supported and multilayered magneto-electro-elastic plates", J. Appl. Mech., 68(4), 608-618.   DOI
18 Perez-Aparicio, J.L., Palma, R. and Taylor, R.L. (2016), "Multiphysics and thermodynamic formulations for equilibrium and non-equilibrium interactions: Non-linear finite elements applied to multi-coupled active materials", Archiv. Comput. Meth. Eng., 23(3), 535-583.   DOI
19 Ramirez, F., Heyliger, P.R. and Pan, E. (2006), "Free vibration response of two-dimensional magnetoelectroelastic laminated plates", J. Sound Vibr., 292(3), 626-644.   DOI
20 Rao, S. and Sunar, M. (1993), "Analysis of distributed thermopiezoelectric sensors and actuators inadvanced intelligent structures", AIAA J., 31(7), 1280-1286.   DOI
21 Wang, X. and Zhong, Z. (2003), "A finitely long circular cylindrical shell of piezoelectric/piezomagnetic composite under pressuring and temperature change", J. Eng. Sci., 41(20), 2429-2445.   DOI
22 Ryu, J., Carazo, A., Uchino, K. and Kim, H. (2001), "Magnetoelectric properties in piezoelectric and magnetostrictive laminate composites", Jap. J. Appl. Phys., 40(8R), 4948.   DOI
23 Safari, A. and Akdogan, E. (2008), Piezoelectric and Acoustic Materials for Transducer Applications, Springer Science & Business Media.
24 Smith, R. (2005), Smart Material Systems: Model Development, Siam.
25 Zienkiewicz, O. and Taylor, R. (2005), The Finite Element Method, Elsevier.