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Finite element elastoplastic homogenization model of a corrugated-core sandwich structure

  • Luong, Viet D. (MATIM, University of Reims Champagne-Ardenne, UFR SEN, Campus Moulin de la Housse) ;
  • Abbes, Fazilay (MATIM, University of Reims Champagne-Ardenne, UFR SEN, Campus Moulin de la Housse) ;
  • Hoang, Minh P. (Thai Nguyen University of Technology) ;
  • Duong, Pham T.M. (Thai Nguyen University of Technology) ;
  • Abbes, Boussad (MATIM, University of Reims Champagne-Ardenne, UFR SEN, Campus Moulin de la Housse)
  • Received : 2020.05.16
  • Accepted : 2021.09.24
  • Published : 2021.11.10

Abstract

This study aimed to develop an elastoplastic homogenization model to accurately predict the elastoplastic static behavior of a corrugated-core sandwich structure. A panel composed of two planar layers and one corrugated layer is modeled by a homogeneous orthotropic single-layer plate. A plane stress elastoplastic model is adopted to describe the behavior of each layer. Homogenization is achieved by local integration across the thickness of each layer. The proposed homogenization model is implemented in the ABAQUS finite element software using UGENS user subroutine. The results obtained by our model are compared to those obtained by full 3D simulations under different loading conditions. The comparisons show the efficiency and the accuracy of the proposed elastoplastic homogenization model.

Keywords

References

  1. ABAQUS Inc. (2019), https://www.3ds.com/productsservices/simulia/products/abaqus/.
  2. Abbes, B. and Guo, Y.Q. (2010), "Analytic homogenization for torsion of orthotropic sandwich plates: application to corrugated cardboard", Compos. Struct., 92(3), 699-706. https://doi.org/10.1016/j.compstruct.2009.09.020.
  3. Aboura, Z., Talbi, N., Allaoui, S. and Benzeggagh, M.L. (2004), "Elastic behavior of corrugated cardboard: experiments and modeling", Compos. Struct., 63(1), 53-62. https://doi.org/10.1016/S0263-8223(03)00131-4.
  4. Adim, B., Daouadji, T.H. and Rabahi, A. (2016), "A simple higher order shear deformation theory for mechanical behavior of laminated composite plates", Int. J. Adv. Struct. Eng., 8, 103-117. https://doi.org/10.1007/s40091-016-0109-x.
  5. Adim, B. and Hassaine Daouadji, T. (2016), "Effects of thickness stretching in FGM plates using a quasi-3D higher order shear deformation theory", Adv. Mater. Res., 5(4), 223-244. https://doi.org/10.12989/amr.2016.5.4.223.
  6. Adim, B., Hassaine Daouadji, T., Rabahi, A., Benhenni, M.A., Zidour, M. and Abbes, B. (2018), "Mechanical buckling analysis of hybrid laminated composite plates under different boundary conditions", Struct. Eng. Mech., 66(6), 761-769. https://doi.org/10.12989/sem.2018.66.6.761.
  7. Biancolini, M.E. (2005), "Evaluation of equivalent stiffness properties of corrugated board", Compos. Struct., 69(3), 322-328. https://doi.org/10.1016/j.compstruct.2004.07.014.
  8. Benhenni, M.A., Adim, B., Hassaine Daouadji, T., Abbes, B., Abbes, F., Li, Y. and Bouzidane, A. (2019), "A comparison of closed form and finite element solutions for the free vibration of hybrid cross ply laminated plates", Mech. Compos. Mater., 55(2). https://doi.org/10.1007/s11029-019-09803-2.
  9. Buannic, N., Cartraud, P. and Quesnel, T. (2003), "Homogenization of corrugated core sandwich panels", Compos. Struct., 59(3), 299-312. https://doi.org/10.1016/S0263-8223(02)00246-5.
  10. Carlsson, L.A., Nordstrand, T. and Westerlind, B. (2001), "On the elastic stiffnesses of corrugated core sandwich", J. Sandw. Struct. Mater., 3(4), 253-267. https://doi.org/10.1106/BKJFN2TF-AQ97-H72.
  11. Chang, W.S., Krauthammer, T. and Ventsel, E. (2006), "Elastoplastic analysis of corrugated-core sandwich plates", Mech. Adv. Mater. Struct., 13, 151-160. https://doi.org/10.1080/15376490500451767.
  12. Cong, Y., Nezamabadi, S., Zahrouni, H. and Yvonnet, J. (2015), "Multiscale computational homogenization of heterogeneous shells at small strains with extensions to finite displacements and buckling", Int. J. Numer. Method. Eng., 104(4), 235-259. https://doi.org/10.1002/nme.4927.
  13. Dayyani, I., Friswell, M.I., Ziaei-Rad, S. and Saavedra Flores, E.I. (2013), "Equivalent models of composite corrugated cores with elastomeric coatings for morphing structures", Compos. Struct., 104, 281-292. https://doi.org/10.1016/j.compstruct.2013.04.034.
  14. Duong, P.T.M., Abbes, B., Li, Y.M., Hammou, A.D., Makhlouf, M. and Guo, Y.Q. (2013), "An analytic homogenization model for shear-torsion coupling problems of double corrugated core sandwich plates", J. Compos. Mater., 47(11), 1327-1341. https://doi.org/10.1177/0021998312447206.
  15. Haj-Ali, R., Choi, J., Wei, B.S., Popil, R. and Schaepe, M. (2009), "Refined nonlinear finite element models for corrugated fiberboards", Compos. Struct., 87(4): 321-333. https://doi.org/10.1016/j.compstruct.2008.02.001.
  16. Hammou, A.D., Duong, P.T.M., Abbes, B., Makhlouf, M and Guo, Y.Q. (2012), "Finite element simulation with a homogenization model and experimental study of free drop tests of corrugated cardboard packaging", Mech. Ind., 13(3), 175-184. https://doi.org/10.1051/meca/2012013.
  17. Harrysson, A. and Ristinmaa, M. (2008), "Large strain elastoplastic model of paper and corrugated board", Int. J. Solids Struct., 45(11-12), 3334-3352. https://doi.org/10.1016/j.ijsolstr.2008.01.031.
  18. Hassaine Daouadji, T., Abbes, B., Rabahi, A., Benferhat, R., Abbes, F. and Adim, B. (2019), "Flexural behaviour of steel beams reinforced by carbon fibre reinforced polymer: Experimental and numerical study", Struct. Eng. Mech., 72(4), 409-419. http://doi.org/10.12989/sem.2019.72.4.409.
  19. Hill, R. (1948), "A theory of the yielding and plastic flow in anisotropic metals", Proceedings of the Royal Society A, 193, 111-128. https://doi.org/10.1098/rspa.1948.0045.
  20. Hoffman, O. (1967), "The brittle strength of orthotropic materials", J. Compos. Mater., 1(2), 200-206. https://doi.org/10.1177/002199836700100210.
  21. Karafillis, A.P. and Boyce, M.C. (1993), "A general anisotropic yield criterion using bounds and a transformation weighting tensor", J. Mech. Phys. Solids, 41(12), 1859-1886. https://doi.org/10.1016/0022-5096(93)90073-O.
  22. Khalkhali, A., Sarmadi, M., Khakshournia, S. and Jafari, N. (2016), "Probabilistic multi-objective optimization of a corrugated-core sandwich structure", Geomech. Eng., 10(6), 709-726. https://doi.org/10.12989/gae.2016.10.6.709.
  23. Kiymaz, G., Coskun, E., Cosgun, C. and Seckin, E. (2010), "Transverse load carrying capacity of sinusoidally corrugated steel web beams with web openings", Steel Compos. Struct., 10(1), 69-85. https://doi.org/10.12989/scs.2010.10.1.069.
  24. Li, Y.M., Abbes, B. and Guo, Y.Q. (2007), "Two efficient algorithms of plastic integration for sheet forming modeling", J. Manufact. Sci. Eng. T. ASME, 129(4), 698-704. https://doi.org/10.1115/1.2738125.
  25. Luong, V.D., Bonnin, A.-S., Abbes, F., Nolot, J.B., Erre, D. and Abbes, A. (2020), "Finite element and experimental investigation on the effect of repetitive shock in corrugated cardboard packaging", J. Appl. Comput. Mech., 7(2), 8 https://doi.org/10.22055/JACM.2020.35968.2771.
  26. Makela, P. and Ostlund, S. (2003), "Orthotropic elastic-plastic material model for paper materials", Int. J. Solids Struct., 40(21), 5599-5620. https://doi.org/10.1016/S0020-7683(03)00318-4.
  27. Moon, J., Ko, H.J., Sung, I.H. and Lee, H.E. (2015), "Natural frequency of a composite girder with corrugated steel web", Steel Compos. Struct., 18(1), 255-271. http://dx.doi.org/10.12989/scs.2015.18.1.255.
  28. Nezamabadi, S., Yvonnet, J., Zahrouni, H. and Potier-Ferry, M. (2009), "A multilevel computational strategy for microscopic and macroscopic instabilities", Comput. Method. Appl. M., 198(27-29), 2099-2110. https://doi.org/10.1016/j.cma.2009.02.026.
  29. Nordstrand, T.M., Carlsson, L.A. and Allen, H.G. (1994), "Transverse shear stiffness of structural core sandwich", Compos. Struct., 27(3), 317-329. https://doi.org/10.1016/0263-8223(94)90091-4.
  30. Nordstrand, T.M. (1995), "Parametric study of the post-buckling strength of structural core sandwich panels", Compos. Struct., 30(4), 441-451. https://doi.org/10.1016/0263-8223(94)00066-2.
  31. Nordstrand, T.M. (2004a), "Analysis and testing of corrugated board panels into the post-buckling regime", Compos. Struct., 63(2), 189-199. https://doi.org/10.1016/S0263-8223(03)00155-7.
  32. Nordstrand, T.M. (2004b), "On buckling loads for edge-loaded orthotropic plates including transverse shear", Compos. Struct., 65(1), 1-6. https://doi.org/10.1016/S0263-8223(03)00154-5.
  33. Rabczuk, T., Kim, J.Y., Samaniego, E. and Belytschko, T. (2004), "Homogenization of sandwich structures", Int. J. Numer. Method. Eng., 61, 1009-1027. https://doi.org/10.1002/nme.1100.
  34. Reany, J. and Grenestedt, J.L. (2009), "Corrugated skin in a foam core sandwich panel", Compos. Struct., 89(3), 345-355. https://doi.org/10.1016/j.compstruct.2008.08.008.
  35. Rabahi, A. Benferhat, R., Hassaine Daouadji, T., Abbes, B., Adim, B. and Abbes, F. (2018), "Elastic analysis of interfacial stresses in prestressed PFGM-RC hybrid beams", Adv. Mater. Res., 7(2), 83-103. https://doi.org/10.12989/amr.2018.7.2.083
  36. Reddy, J.N. (2003), Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, (2nd Edition), CRC Press, Boca Raton, FL, USA.
  37. Shokrollahi, H., Fallah, F. and Kargarnovin, M.H. (2017), "An approach in deformation and stress analysis of elasto-plastic sandwich cylindrical shell panels based on harmonic differential quadrature method", J. Sandw. Struct. Mater., 19(2), 167-191. https://doi.org/10.1177/1099636215604553.
  38. Stenberg, N. (2003), "A model for the through-thickness elastic-plastic behaviour of paper", Int. J. Solid. Struct., 40(26), 7483- 7498. https://doi.org/10.1016/j.ijsolstr.2003.09.003.
  39. Stenberg, N., Fellers, C. and Ostlund, S. (2001), "Plasticity in the thickness direction of paperboard under combined shear and normal loading", J. Eng. Mater. Technol., 123(2), 184-190. https://doi.org/10.1115/1.1352747.
  40. Talbi, N., Batti, A., Ayad, R. and Guo, Y.Q. (2009), "An analytical homogenization model for finite element modelling of corrugated cardboard", Compos. Struct., 88(2): 280-289. https://doi.org/10.1016/j.compstruct.2008.04.008.
  41. Tsai, S.W. and Wu, E.M. (1971), "A general theory of strength for anisotropic materials", J. Compos. Mater., 5(1), 58-80. https://doi.org/10.1177/002199837100500106.
  42. Xia, Q.S., Boyce, M.C. and Parks, D.M. (2002), "A constitutive model for the anisotropic elastic-plastic deformation of paper and paper board", Int. J. Solids Struct., 39(15), 4053-4071. https://doi.org/10.1016/S0020-7683(02)00238-X.