Browse > Article
http://dx.doi.org/10.12989/csm.2021.10.6.521

Multi-scale model for coupled piezoelectric-inelastic behavior  

Moreno-Navarro, Pablo (Department of Continuum Mechanics & Theory of Structures, UPV-Universitat Politecnica de Valencia)
Ibrahimbegovic, Adnan (UTC-Universite de Technologie de Compiegne-Alliance Sorbonne Universite, Lab. Roberval, UTC & IUF)
Damjanovic, Dragan (EPFL-Ecole Polytechnique Federale de Lausanne, Group for Ferroelectrics and Functional Oxides)
Publication Information
Coupled systems mechanics / v.10, no.6, 2021 , pp. 521-544 More about this Journal
Abstract
In this work, we present the development of a 3D lattice-type model at microscale based upon the Voronoi-cell representation of material microstructure. This model can capture the coupling between mechanic and electric fields with non-linear constitutive behavior for both. More precisely, for electric part we consider the ferroelectric constitutive behavior with the possibility of domain switching polarization, which can be handled in the same fashion as deformation theory of plasticity. For mechanics part, we introduce the constitutive model of plasticity with the Armstrong-Frederick kinematic hardening. This model is used to simulate a complete coupling of the chosen electric and mechanics behavior with a multiscale approach implemented within the same computational architecture.
Keywords
finite element method; lattice model; multi-scale model; piezoelectricity; Voronoi-cell microstructure representation;
Citations & Related Records
연도 인용수 순위
  • Reference
1 Zienkiewicz, O.C. and Taylor, R.L. (2005), The Finite Element Method, Vols. I, II, III, Elsevier.
2 Schlangen, E. and Garboczi, E.J. (1997), "Fracture simulations of concrete using lattice models: computational aspects", Eng. Fract. Mech., 57(2-3), 319-332. https://doi.org/10.1016/S0013-7944(97)00010-6.   DOI
3 Ibrahimbegovic, A. (1997), "Theorie geometriquement exacte des coques en rotations finies et son implantation elements finis", Revue Europeenne des Elements Finis, 6(3), 263-335. https://doi.org/10.1080/12506559.1997.10511273.   DOI
4 Keip, M.A. and Schroder, J. (2011), "A ferroelectric and ferroelastic microscopic switching criterion for tetragonal ferroelectrics", PAMM, 11(1), 475-476. https://doi.org/10.1002/pamm.201110229.   DOI
5 Abdollahi, A. and Arias, I. (2015), "Phase-field modeling of fracture in ferroelectric materials", Arch. Comput. Meth. Eng., 22(2), 153-181. https://doi.org/10.1007/s11831-014-9118-8.   DOI
6 Armero, F. and Garikipati, K. (1996), "An analysis of strong discontinuities in multiplicative finite strain plasticity and their relation with the numerical simulation of strain localization in solids", Int. J. Solid. Struct., 33(20-22), 2863-2885. https://doi.org/10.1016/0020-7683(95)00257-X.   DOI
7 Balanis, C.A. (1999), Advanced Engineering Electromagnetics, John Wiley & Sons.
8 Nikolic, M. and Ibrahimbegovic, A. (2015), "Rock mechanics model capable of representing initial heterogeneities and full set of 3D failure mechanisms", Comput. Meth. Appl. Mech. Eng., 290, 209-227. https://doi.org/10.1016/j.cma.2015.02.024.   DOI
9 Taylor, R.L. (2012), FEAP-A Finite Element Analysis Program, Version 8.4 Theory Manual.
10 White Jr. B.E. (2008), "Energy-harvesting devices: Beyond the battery", Nat. Nanotechnol., 3(2), 71.   DOI
11 Ibrahimbegovic, A., Gharzeddine, F. and Chorfi, L. (1998), "Classical plasticity and viscoplasticity models reformulated: theoretical basis and numerical implementation", Int. J. Numer. Meth. Eng., 42(8), 1499-1535. https://doi.org/10.1002/(SICI)1097-0207(19980830)42:8<1499::AID-NME443>3.0.CO;2-X.   DOI
12 McMeeking, R.M. and Hwang, S.C. (1997), "On the potential energy of a piezoelectric inclusion and the criterion for ferroelectric switching", Ferroelec., 200(1), 151-173. https://doi.org/10.1080/00150199708008603.   DOI
13 McMeeking, R.M. and Landis, C.M. (2002), "A phenomenological multi-axial constitutive law for switching in polycrystalline ferroelectric ceramics", Int. J. Eng. Sci., 40(14), 1553-1577. https://doi.org/10.1016/S0020-7225(02)00033-2.   DOI
14 Miehe, C., Rosato, D. and Kiefer, B. (2011), "Variational principles in dissipative electro-magneto-mechanics: A framework for the macro-modeling of functional materials", Int. J. Numer. Meth. Eng., 86(10), 1225-1276. https://doi.org/10.1002/nme.3127.   DOI
15 Moreno-Navarro, P., Ibrahimbegovich, A. and Perez-Aparicio, J.L. (2018), "Linear elastic mechanical system interacting with coupled thermo-electro-magnetic fields", Couple. Syst. Mech., 7(1), 5-25. https://doi.org/10.12989/csm.2018.7.1.005   DOI
16 Nikolic, M., Ibrahimbegovic, A. and Miscevic, P. (2016), "Discrete element model for the analysis of fluid-saturated fractured poro-plastic medium based on sharp crack representation with embedded strong discontinuities", Comput. Meth. Appl. Mech. Eng., 298, 407-427. https://doi.org/10.1016/j.cma.2015.10.009.   DOI
17 Brancherie, D. and Ibrahimbegovic, A. (2009), "Novel anisotropic continuum-discrete damage model capable of representing localized failure of massive structures: Part I: Theoretical formulation and numerical implementation", Eng. Comput., 26(1/2), 100-127. https://doi.org/10.1108/02644400910924825.   DOI
18 Ngo, V.M., Ibrahimbegovic, A. and Brancherie, D. (2013), "Model for localized failure with thermo-plastic coupling: theoretical formulation and ED-FEM implementation", Comput. Struct., 127, 2-18. https://doi.org/10.1016/j.compstruc.2012.12.013.   DOI
19 Ibrahimbegovic, A. and Delaplace, A. (2003), "Microscale and mesoscale discrete models for dynamic fracture of structures built of brittle material", Comput. Struct., 81(12), 1255-1265. https://doi.org/10.1016/S0045-7949(03)00040-3.   DOI
20 Ibrahimbegovic, A. and Wilson, E.L. (1991), "A modified method of incompatible modes", Commun. Appl. Numer. Meth., 7(3), 187-194. https://doi.org/10.1002/cnm.1630070303.   DOI
21 Karavelic, E., Ibrahimbegovic, A. and Dolarevic, S. (2019), "Multi-surface plasticity model for concrete with 3D hardening/softening failure modes for tension, compression and shear", Comput. Struct., 221, 74-90. https://doi.org/10.1016/j.compstruc.2019.05.009.   DOI
22 Ibrahimbegovic, A., Matthies, H.G. and Karavelic, E. (2020), "Reduced model of macro-scale stochastic plasticity identification by Bayesian inference: Application to quasi-brittle failure of concrete", Comput. Meth. Appl. Mech. Eng., 372, 113428. https://doi.org/10.1016/j.cma.2020.113428.   DOI
23 Ostoja-Starzewski, M. (2002), "Lattice models in micromechanics", Appl. Mech. Rev., 55(1), 35-60. https://doi.org/10.1115/1.1432990.   DOI
24 Palma, R., Perez-Aparicio, J.L. and Taylor, R.L. (2018), "Dissipative finite-element formulation applied to piezoelectric materials with the Debye memory", IEEE/ASME Tran. Mechatron., 23(2), 856-863. https://doi.org/10.1109/TMECH.2018.2792308.   DOI
25 Bui, N.N., Ngo, M., Nikolic, M., Brancherie, D. and Ibrahimbegovic, A. (2014), "Enriched Timoshenko beam finite element for modeling bending and shear failure of reinforced concrete frames", Comput. Struct., 143, 9-18. https://doi.org/10.1016/j.compstruc.2014.06.004.   DOI
26 Rowe, D.M. (2018), Thermoelectrics Handbook: Macro to Nano, CRC Press.
27 Huber, J.E., Fleck, N.A. and McMeeking, R.M. (1999), "A crystal plasticity model for ferroelectrics", Ferroelec., 228(1), 39-52. https://doi.org/10.1080/00150199908226124.   DOI
28 Ibrahimbegovic, A. (2009), Nonlinear Solid Mechanics: Theoretical Formulations and Finite Element Solution Methods, Vol. 160, Springer Science & Business Media.
29 Ibrahimbegovic, A. and Melnyk, S. (2007), "Embedded discontinuity finite element method for modeling of localized failure in heterogeneous materials with structured mesh: an alternative to extended finite element method", Comput. Mech., 40(1), 149-155. https://doi.org/10.1007/s00466-006-0091-4.   DOI
30 Labusch, M., Keip, M.A., Shvartsman, V.V., Lupascu, D.C. and Schroder, J. (2016), "On the influence of ferroelectric polarization states on the Magneto-electric coupling in two-phase composites", Technische Mechanik-Eur. J. Eng. Mech., 36(1-2), 73-87. https://doi.org/10.24352/UB.OVGU-2017-011.   DOI
31 Medic, S., Dolarevic, S. and Ibrahimbegovic, A. (2013), "Beam model refinement and reduction", Eng. Struct., 50, 158-169. https://doi.org/10.1016/j.engstruct.2012.10.004.   DOI
32 Hwang, S.C., Lynch, C.S. and McMeeking, R.M. (1995), "Ferroelectric/ferroelastic interactions and a polarization switching model", Acta Metallurgica et Materialia, 43(5), 2073-2084. https://doi.org/10.1016/0956-7151(94)00379-V.   DOI
33 Chen, W. and Lynch, C.S. (1998), "A micro-electro-mechanical model for polarization switching of ferroelectric materials", Acta Materialia, 46(15), 5303-5311. https://doi.org/10.1016/S1359-6454(98)00207-9.   DOI
34 Damjanovic, D. (2006), Hysteresis in Piezoelectric and Ferroelectric Materials, No. BOOK_CHAP, Academic Press.
35 Nikolic, M., Karavelic, E., Ibrahimbegovic, A. and Miscevic, P. (2018), "Lattice element models and their peculiarities", Arch. Comput. Meth. Eng., 25(3), 753-784. https://doi.org/10.1007/s11831-017-9210-y.   DOI
36 Hadzalic, E., Ibrahimbegovic, A. and Dolarevic. S. (2019), "Theoretical formulation and seamless discrete approximation for localized failure of saturated poro-plastic structure interacting with reservoir", Comput. Struct., 214, 73-93. https://doi.org/10.1016/j.compstruc.2019.01.003.   DOI
37 Daniel, L., Hubert, O. and Billardon, R. (2004), "Homogenisation of magneto-elastic behaviour: from the grain to the macro scale", Comput. Appl. Math., 23, 285-308.
38 Daniel, L., Rekik, M. and Hubert, O. (2014), "A multiscale model for magneto-elastic behaviour including hysteresis effects", Arch. Appl. Mech., 84(9), 1307-1323. https://doi.org/10.1007/s00419-014-0863-9.   DOI
39 De Jong, M., Chen, W., Geerlings, H., Asta, M. and Persson, K.A. (2015), "A database to enable discovery and design of piezoelectric materials", Scientif. Data, 2(1), 1-13. https://doi.org/10.1038/sdata.2015.53.   DOI
40 Do, X.N., Ibrahimbegovic, A. and Brancherie, D. (2017), "Dynamics framework for 2D anisotropic continuum-discrete damage model for progressive localized failure of massive structures", Comput. Struct., 183, 14-26. https://doi.org/10.1016/j.compstruc.2017.01.011.   DOI
41 Daniel, L., Hubert, O., Buiron, N. and Billardon, R. (2008), "Reversible magneto-elastic behavior: A multiscale approach", J. Mech. Phys. Solid., 56(3), 1018-1042. https://doi.org/10.1016/j.jmps.2007.06.003.   DOI
42 Schroder, J. and Romanowski, H. (2005), "A thermodynamically consistent mesoscopic model for transversely isotropic ferroelectric ceramics in a coordinate-invariant setting", Arch. Appl Mech., 74(11), 863-877. https://doi.org/10.1007/s00419-005-0412-7.   DOI
43 Rukavina, I., Ibrahimbegovic, A., Do, X.N. and Markovic, D. (2019), "ED-FEM multi-scale computation procedure for localized failure", Couple. Syst. Mech., 8(2), 111-127. https://doi.org/10.12989/csm.2019.8.2.111.   DOI
44 Said, S.M., Sabri, M.F.M. and Salleh, F. (2017), Ferroelectrics and their Applications, Reference Module in Materials Science and Materials Engineering, Elsevier.
45 Saksala, T., Brancherie, D., Harari, I. and Ibrahimbegovic, A. (2015), "Combined continuum damage-embedded discontinuity model for explicit dynamic fracture analyses of quasi-brittle materials", Int. J. Numer. Meth. Eng., 101(3), 230-250. https://doi.org/10.1002/nme.4814.   DOI
46 Belytschko, T., Fish, J. and Engelmann, B. E. (1988), "A finite element with embedded localization zones", Comput. Meth. Appl. Mech. Eng., 70(1), 59-89. https://doi.org/10.1016/0045-7825(88)90180-6.   DOI
47 Simo, J.C., Oliver, J.A.V.I.E.R. and Armero, F. (1993), "An analysis of strong discontinuities induced by strain-softening in rate-independent inelastic solids", Comput. Mech., 12(5), 277-296. https://doi.org/10.1007/BF00372173.   DOI
48 Ibrahimbegovic, A. and Brancherie, D. (2003), "Combined hardening and softening constitutive model of plasticity: precursor to shear slip line failure", Comput. Mech., 31(1), 88-100. https://doi.org/10.1007/s00466-002-0396-x.   DOI