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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)
  • Received : 2021.10.27
  • Accepted : 2021.11.02
  • Published : 2021.12.25

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

Acknowledgement

This article was supported jointly by Hauts-de-France Region (CR Picardie) (120-2015RDISTRUCT-000010 and RDISTRUCT-000010) and EU funding (FEDER) for Chair of Mechanics (120-2015-RDISTRUCTF-000010 and RDISTRUCTI-000004), IUF-Institut Universitaire de France and by Germaine de Stael Collaborative Program between France and Switzerland. All this support is gratefully acknowledged.

References

  1. 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.
  2. 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.
  3. Balanis, C.A. (1999), Advanced Engineering Electromagnetics, John Wiley & Sons.
  4. 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.
  5. 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.
  6. 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.
  7. 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.
  8. Damjanovic, D. (2006), Hysteresis in Piezoelectric and Ferroelectric Materials, No. BOOK_CHAP, Academic Press.
  9. 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.
  10. 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.
  11. 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.
  12. 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.
  13. 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.
  14. 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.
  15. 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.
  16. 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.
  17. 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.
  18. Ibrahimbegovic, A. (2009), Nonlinear Solid Mechanics: Theoretical Formulations and Finite Element Solution Methods, Vol. 160, Springer Science & Business Media.
  19. 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.
  20. 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.
  21. 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.
  22. 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.
  23. 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.
  24. 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.
  25. 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.
  26. 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.
  27. 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.
  28. 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.
  29. 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.
  30. 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.
  31. 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.
  32. 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
  33. 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.
  34. 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.
  35. 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.
  36. 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.
  37. Ostoja-Starzewski, M. (2002), "Lattice models in micromechanics", Appl. Mech. Rev., 55(1), 35-60. https://doi.org/10.1115/1.1432990.
  38. 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.
  39. Rowe, D.M. (2018), Thermoelectrics Handbook: Macro to Nano, CRC Press.
  40. 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.
  41. Said, S.M., Sabri, M.F.M. and Salleh, F. (2017), Ferroelectrics and their Applications, Reference Module in Materials Science and Materials Engineering, Elsevier.
  42. 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.
  43. 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.
  44. 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.
  45. 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.
  46. Taylor, R.L. (2012), FEAP-A Finite Element Analysis Program, Version 8.4 Theory Manual.
  47. White Jr. B.E. (2008), "Energy-harvesting devices: Beyond the battery", Nat. Nanotechnol., 3(2), 71. https://doi.org/10.1038/nnano.2008.19
  48. Zienkiewicz, O.C. and Taylor, R.L. (2005), The Finite Element Method, Vols. I, II, III, Elsevier.