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An efficient ABAQUS solid shell element implementation for low velocity impact analysis of FGM plates

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Abstract

The main objective of this paper is to develop a numerical model susceptible to solve the numerical locking problems that may appear when applying the conventional solid and shell finite elements of ABAQUS. This model is based on a hexahedral solid shell element. The formulation of this element relays on the combination of the enhanced assumed strain (EAS) and assumed natural strain (ANS) methods with modified First Shear Deformation Theory (FSDT). The developed element is implemented into the ABAQUS user element (UEL) interface. The performance of this element is demonstrated by different benchmark tests from the literature. Our contribution consists on applying a single solid shell element through the thickness direction to predict the low velocity impact behavior on functionally graded material (FGM) circular plates.

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References

  1. Hou-Cheng H (1987) Membrane locking and assumed strain shell elements. Comput Struct 27:671–677. https://doi.org/10.1016/0045-7949(87)90083-6

    Article  MATH  Google Scholar 

  2. Kui LX, Liu GQ, Zienkiewicz OC (1985) A generalized displacement method for the finite element analysis of thin shells. Int J Numer Methods Eng 21:2145–2155. https://doi.org/10.1002/nme.1620211203

    Article  MathSciNet  Google Scholar 

  3. Petchsasithon A, Gosling PD (2005) A locking-free hexahedral element for the geometrically non-linear analysis of arbitrary shells. Comput Mech 35:94–114. https://doi.org/10.1007/s00466-004-0604-y

    Article  MATH  Google Scholar 

  4. Puso MA, Solberg J (2006) A stabilized nodally integrated tetrahedral. Int J Numer Methods Eng 67:841–867. https://doi.org/10.1002/nme.1651

    Article  MathSciNet  MATH  Google Scholar 

  5. Klinkel S, Gruttmann F, Wagner W (2006) A robust non-linear solid shell element based on a mixed variational formulation. Comput Methods Appl Mech Eng 195:179–201. https://doi.org/10.1016/j.cma.2005.01.013

    Article  MATH  Google Scholar 

  6. Tan XG, Vu-Quoc L (2005) Efficient and accurate multilayer solid-shell element: non-linear materials at finite strain. Int J Numer Methodsss Eng 63:2124–2170. https://doi.org/10.1002/nme.1360

    Article  MATH  Google Scholar 

  7. Bathe K, Dvorkin EN (1984) A continuum mechanics based four-node shell element for general non-linear analysis. Eng Comput 1:77–88. https://doi.org/10.1108/eb023562

    Article  Google Scholar 

  8. Simo JC, Rifai MS (1990) A class of mixed assumed strain methods and the method of incompatible modes. Int J Numer Methods Eng 29:1595–1638. https://doi.org/10.1002/nme.1620290802

    Article  MathSciNet  MATH  Google Scholar 

  9. Flores FG (2016) A simple reduced integration hexahedral solid-shell element for large strains. Comput Methods Appl Mech Eng 303:260–287. https://doi.org/10.1016/j.cma.2016.01.013

    Article  MathSciNet  MATH  Google Scholar 

  10. Hajlaoui A, Jarraya A, Kallel-Kamoun I, Dammak F (2012) Buckling analysis of a laminated composite plate with delaminations using the enhanced assumed strain solid shell element. J Mech Sci Technol 26:3213–3221. https://doi.org/10.1007/s12206-012-0829-1

    Article  Google Scholar 

  11. Rah K, Paepegem WV, Habraken AM, Degrieck J (2012) A mixed solid-shell element for the analysis of laminated composites. Int J Numer Methods Eng 89:805–828. https://doi.org/10.1002/nme.3263

    Article  MathSciNet  MATH  Google Scholar 

  12. Vu-Quoc L, Tan XG (2003) Optimal solid shells for non-linear analyses of multilayer composites. I. Statics. Comput Methods Appl Mech Eng 192:975–1016. https://doi.org/10.1016/S0045-7825(02)00435-8

    Article  MATH  Google Scholar 

  13. Vu-Quoc L, Tan XG (2003) Optimal solid shells for nonlinear analyses of multilayer composites: Part II: dynamics. Comput Methods Appl Mech Eng 192:1017–1059

    Article  Google Scholar 

  14. Vu-Quoc L, Tan X (2013) Efficient Hybrid-EAS solid element for accurate stress prediction in thick laminated beams, plates, and shells. Comput Methods Appl Mech Eng 253:337–355. https://doi.org/10.1016/j.cma.2012.07.025

    Article  MathSciNet  MATH  Google Scholar 

  15. Li LM, Peng YH, Li DY (2011) A stabilized underintegrated enhanced assumed strain solid-shell element for geometrically nonlinear plate/shell analysis. Finite Elem Anal Des 47:511–518. https://doi.org/10.1016/j.finel.2011.01.001

    Article  Google Scholar 

  16. Hajlaoui A, Triki E, Frikha A et al (2017) Nonlinear dynamics analysis of FGM shell structures with a higher order shear strain enhanced solid-shell element. Latin Am J Solids Struct 14:72–91. https://doi.org/10.1590/1679-78253323

    Article  Google Scholar 

  17. Jrad H, Mars J, Wali M, Dammak F (2018) An extended finite element method for modeling elastoplastic FGM plate-shell type structures. Struct Eng Mech 68:299–312

    Google Scholar 

  18. Jrad H, Mars J, Wali M, Dammak F (2018) Geometrically nonlinear analysis of elastoplastic behavior of functionally graded shells. Eng Comput. https://doi.org/10.1007/s00366-018-0633-3

    Article  Google Scholar 

  19. Mallek H, Jrad H, Wali M, Dammak F (2019) Piezoelastic response of smart functionally graded structure with integrated piezoelectric layers using discrete double directors shell element. Compos Struct 210:354–366. https://doi.org/10.1016/j.compstruct.2018.11.062

    Article  Google Scholar 

  20. Mars J, Koubaa S, Wali M et al (2017) Numerical analysis of geometrically non-linear behavior of functionally graded shells. Latin Am J Solids Struct 14:1952–1978. https://doi.org/10.1590/1679-78253914

    Article  Google Scholar 

  21. Mellouli H, Jrad H, Wali M, Dammak F (2019) Meshfree implementation of the double director shell model for FGM shell structures analysis. Eng Anal Bound Elem 99:111–121. https://doi.org/10.1016/j.enganabound.2018.10.013

    Article  MathSciNet  MATH  Google Scholar 

  22. Wali M, Hentati T, Jarraya A, Dammak F (2015) Free vibration analysis of FGM shell structures with a discrete double directors shell element. Compos Struct 125:295–303. https://doi.org/10.1016/j.compstruct.2015.02.032

    Article  Google Scholar 

  23. Hajlaoui A, Chebbi E, Wali M, Dammak F (2019) Geometrically nonlinear analysis of FGM shells using solid-shell element with parabolic shear strain distribution. Int J Mech Mater Des. https://doi.org/10.1007/s10999-019-09465-x

    Article  Google Scholar 

  24. Hajlaoui A, Jarraya A, El Bikri K, Dammak F (2015) Buckling analysis of functionally graded materials structures with enhanced solid-shell elements and transverse shear correction. Compos Struct 132:87–97. https://doi.org/10.1016/j.compstruct.2015.04.059

    Article  Google Scholar 

  25. Reinoso J, Blázquez A (2016) Geometrically nonlinear analysis of functionally graded power-based and carbon nanotubes reinforced composites using a fully integrated solid shell element. Compos Struct 152:277–294. https://doi.org/10.1016/j.compstruct.2016.05.036

    Article  Google Scholar 

  26. Chalal H, Abed-Meraim F (2018) Quadratic solid-shell finite elements for geometrically nonlinear analysis of functionally graded material plates. Materials 11:1046. https://doi.org/10.3390/ma11061046

    Article  Google Scholar 

  27. Dhatt G (1969) Numerical analysis of thin shells by curved triangular elements based on discrete kirchhoff hypothesis. In: Proceedings ASCE, symposium on applications of fem in civil engineering, Vanderbilt University, Nashville, TN, 1969, pp 13–14

  28. Mindlin RD (1951) Influence of rotatory inertia and shear on flexural motions of isotropic, elastic plates. J Appl Mech 18:31–38

    Article  Google Scholar 

  29. Murthy MVV (1981) An improved transverse shear deformation theory for laminated antisotropic plates

  30. Mellouli H, Jrad H, Wali M, Dammak F (2019) Meshless implementation of arbitrary 3D-shell structures based on a modified first order shear deformation theory. Comput Math Appl 77:34–49. https://doi.org/10.1016/j.camwa.2018.09.010

    Article  MathSciNet  MATH  Google Scholar 

  31. Trabelsi S, Frikha A, Zghal S, Dammak F (2018) Thermal post-buckling analysis of functionally graded material structures using a modified FSDT. Int J Mech Sci 144:74–89. https://doi.org/10.1016/j.ijmecsci.2018.05.033

    Article  Google Scholar 

  32. Hajlaoui A, Chebbi E, Dammak F (2019) Buckling analysis of carbon nanotube reinforced FG shells using an efficient solid-shell element based on a modified FSDT. Thin-Walled Struct 144:106254. https://doi.org/10.1016/j.tws.2019.106254

    Article  Google Scholar 

  33. Hajlaoui A, Chebbi E, Wali M, Dammak F (2019) Static analysis of carbon nanotube-reinforced FG shells using an efficient solid-shell element with parabolic transverse shear strain. EC. https://doi.org/10.1108/EC-02-2019-0075(ahead-of-print)

    Article  Google Scholar 

  34. BeikMohammadlou H, EkhteraeiToussi H (2017) Parametric studies on elastoplastic buckling of rectangular FGM thin plates. Aerosp Sci Technol 69:513–525. https://doi.org/10.1016/j.ast.2017.07.015

    Article  Google Scholar 

  35. Huang H, Zhang Y, Han Q (2017) Inelastic buckling of FGM cylindrical shells subjected to combined axial and torsional loads. Int J Struct Stab Dyn 17:1771010. https://doi.org/10.1142/S0219455417710109

    Article  MathSciNet  Google Scholar 

  36. Vaghefi R, Hematiyan MR, Nayebi A (2016) Three-dimensional thermo-elastoplastic analysis of thick functionally graded plates using the meshless local Petrov–Galerkin method. Eng Anal Bound Elem 71:34–49. https://doi.org/10.1016/j.enganabound.2016.07.001

    Article  MathSciNet  MATH  Google Scholar 

  37. Zhang J, Qi D, Zhou L et al (2015) A progressive failure analysis model for composite structures in hygrothermal environments. Compos Struct 133:331–342. https://doi.org/10.1016/j.compstruct.2015.07.063

    Article  Google Scholar 

  38. Doghri I, Ouaar A (2003) Homogenization of two-phase elasto-plastic composite materials and structures: study of tangent operators, cyclic plasticity and numerical algorithms. Int J Solids Struct 40:1681–1712. https://doi.org/10.1016/S0020-7683(03)00013-1

    Article  MATH  Google Scholar 

  39. Ponte Castañeda P (2002) Second-order homogenization estimates for nonlinear composites incorporating field fluctuations: I—theory. J Mech Phys Solids 50:737–757. https://doi.org/10.1016/S0022-5096(01)00099-0

    Article  MathSciNet  MATH  Google Scholar 

  40. Suquet P (1997) Effective properties of nonlinear composites. In: Suquet P (ed) Continuum micromechanics. Springer Vienna, Vienna, pp 197–264

    Chapter  Google Scholar 

  41. Mori T, Tanaka K (1973) Average stress in matrix and average elastic energy of materials with misfitting inclusions. Acta Metall 21:571–574. https://doi.org/10.1016/0001-6160(73)90064-3

    Article  Google Scholar 

  42. Bao G, Wang L (1995) Multiple cracking in functionally graded ceramic/metal coatings. Int J Solids Struct 32:2853–2871. https://doi.org/10.1016/0020-7683(94)00267-Z

    Article  MATH  Google Scholar 

  43. Abida M, Mars J, Gehring F, Vivet A, Fakhreddine-Dammak A (2018) Anisotropic visco-elastoplastic modeling of quasi-unidirectional flax fiber reinforced epoxy behavior: an investigation on low-velocity impact response. J Renew Mater 6:464–476. https://doi.org/10.3204/JRM.2018.01897

    Article  Google Scholar 

  44. Koubaa S, Mars J, Wali M, Dammak F (2017) Numerical study of anisotropic behavior of aluminum alloy subjected to dynamic perforation. Int J Impact Eng 101:105–114. https://doi.org/10.1016/j.ijimpeng.2016.11.017

    Article  Google Scholar 

  45. Mars J, Wali M, Jarraya A, Dammak F, Dhiab A (2015) Finite element implementation of an orthotropic plasticity model for sheet metal in low velocity impact simulations. Thin-Walled Struct 89:93–100. https://doi.org/10.1016/j.tws.2014.12.019

    Article  Google Scholar 

  46. Mars J, Chebbi E, Wali M, Dammak F (2018) Numerical and experimental investigations of low velocity impact on glass fiber-reinforced polyamide. Compos B Eng 146:116–123. https://doi.org/10.1016/j.compositesb.2018.04.012

    Article  Google Scholar 

  47. Mars J, Said LB, Wali M, Dammak F (2018) Elasto-plastic modeling of low-velocity impact on functionally graded circular plates. Int J Appl Mech 10:1850038. https://doi.org/10.1142/S1758825118500382

    Article  Google Scholar 

  48. Gunes R, Aydin M, Kemal Apalak M, Reddy JN (2014) Experimental and numerical investigations of low velocity impact on functionally graded circular plates. Compos B Eng 59:21–32. https://doi.org/10.1016/j.compositesb.2013.11.022

    Article  Google Scholar 

  49. Chi S-H, Chung Y-L (2006) Mechanical behavior of functionally graded material plates under transverse load—part I: analysis. Int J Solids Struct 43:3657–3674. https://doi.org/10.1016/j.ijsolstr.2005.04.011

    Article  MATH  Google Scholar 

  50. Belhassen L, Koubaa S, Wali M, Dammak F (2017) Anisotropic effects in the compression beading of aluminum thin-walled tubes with rubber. Thin-Walled Struct 119:902–910. https://doi.org/10.1016/j.tws.2017.08.010

    Article  Google Scholar 

  51. Bouhamed A, Jrad H, Said LB et al (2019) A non-associated anisotropic plasticity model with mixed isotropic–kinematic hardening for finite element simulation of incremental sheet metal forming process. Int J Adv Manuf Technol 100:929–940. https://doi.org/10.1007/s00170-018-2782-3

    Article  Google Scholar 

  52. Klinkel S, Gruttmann F, Wagner W (1999) A continuum based three-dimensional shell element for laminated structures. Comput Struct 71:43–62. https://doi.org/10.1016/S0045-7949(98)00222-3

    Article  Google Scholar 

  53. Timoshenko SP, Woinosky-Krieger S (1959) Theory of plates and shells, 2nd edn. McGraw-Hill, New York

    Google Scholar 

  54. Duarte Filho LA, Awruch AM (2004) Geometrically nonlinear static and dynamic analysis of shells and plates using the eight-node hexahedral element with one-point quadrature. Finite Elem Anal Des 40:1297–1315. https://doi.org/10.1016/j.finel.2003.08.012

    Article  Google Scholar 

  55. Chen LB, Xi F, Yang JL (2007) Elastic–plastic contact force history and response characteristics of circular plate subjected to impact by a projectile. Acta Mech Sin 23:415–425. https://doi.org/10.1007/s10409-007-0084-3

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Electro-Mechanical System’s Laboratory (LASEM), National Engineering School of Sfax, University of Sfax, BP 1173-3038, Sfax, Tunisia

    A. Chaker, S. Koubaa, J. Mars & F. Dammak

  2. Normandie University, ENSICAEN, UNICAEN, CEA, CNRS, CIMAP, 14000, Caen, France

    A. Chaker & A. Vivet

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  1. A. Chaker
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  2. S. Koubaa
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  3. J. Mars
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Chaker, A., Koubaa, S., Mars, J. et al. An efficient ABAQUS solid shell element implementation for low velocity impact analysis of FGM plates. Engineering with Computers 37, 2145–2157 (2021). https://doi.org/10.1007/s00366-020-00954-8

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