Modelling of Large Elasto-plastic Deformations by EFGM

Open Access

Year : 2024 | Volume : | : | Page : –
By

Azher Jameel

G. A. Harmain

Mohammad Junaid Mir

  1. Assistant Professor Department of Mechanical Engineering, National Institute of Technology Srinagar Jammu and Kashmir India
  2. Professor Department of Mechanical Engineering, National Institute of Technology Srinagar Jammu and Kashmir India
  3. Assistant Professor Department of Mechanical Engineering, Islamic University of Science and Technology, Awantipora, Jammu and Kashmir India

Abstract

Current work reports modelling and simulation of geometric and material nonlinearities arising due large elasto-plastic displacements in structural specimens by invoking enriched element free Galerkin method (EFGM). The displacement approximations are constructed by using moving least square approach. Standard displacement based approximations are modified by incorporating suitable enrichment functions depending on the nature of interfaces present in the components. Large deformations give rise to geometric nonlinearities which have been modelled by invoking total Lagrangian approach in which the initial unloaded state is chosen as the reference state for investigation. One of the main advantages of total Lagrangian approach lies in the selection of reference configuration which remains same throughout the simulation. Elastic-predictor-plastic-corrector algorithm has been used for the estimation of stresses during simulation. Mathematical foundations on EFGM are programmed in MATLAB to solve different engineering problems. Finally, various nonlinear problems are reported to establish the potential of enriched EFGM in modelling geometric and material nonlinearities in bi-material structural components. The results obtained in the current work are compared with finite element and coupled FE-EFG solutions so that the potential and accuracy of the proposed approach are established.

Keywords: EFGM, Bi-material interfaces, Elasto-plasticity, Large Deformation, Enrichment Functions

How to cite this article: Azher Jameel, G. A. Harmain, Mohammad Junaid Mir. Modelling of Large Elasto-plastic Deformations by EFGM. Journal of Polymer and Composites. 2024; ():-.
How to cite this URL: Azher Jameel, G. A. Harmain, Mohammad Junaid Mir. Modelling of Large Elasto-plastic Deformations by EFGM. Journal of Polymer and Composites. 2024; ():-. Available from: https://journals.stmjournals.com/jopc/article=2024/view=146112

Full Text PDF Download

References

  1. Portela A, Aliabadi MH, Rooke DP. The dual boundary element method: Effective implementation for crack problems. International Journal for Numerical Methods in Engineering. 1992;33(6):1269–87.
  2. Yan AM, Nguyen-Dang H. Multiple-cracked fatigue crack growth by BEM. Computational Mechanics. 1995;16(5):273–80.
  3. Xiangqiao Yan. A boundary element modeling of fatigue crack growth in a plane elastic plate. Mechanics Research Communications. 2006;33:470–81.
  4. Cheung S, A.R. Luxmoore. A finite element analysis of stable crack growth in an aluminium alloy. Engineering Fracture Mechanics. 2003;70(9):1153–69.
  5. Belytschko T, Lu YY, Gu L. Crack propagation by element-free Galerkin methods. Engineering Fracture Mechanics. 1995;51(2):295–315.
  6. Jha A, Sarkar S, Singh IV, Mishra BK, Singh R, Singh RN. A study on the effect of residual stresses on hydride assisted crack in Zr-2.5Nb pressure tube material using XFEM. Theoretical and Applied Fracture Mechanics. 2022 Oct;121:103536.
  7. Duflot M, Nguyen-Dang H. A meshless method with enriched weight functions for fatigue crack growth. International Journal for Numerical Methods in Engineering. 2004;59(14):1945–61.
  8. Duflot M, Nguyen-Dang H. Fatigue crack growth analysis by an enriched meshless method. Journal of Computational and Applied Mathematics. 2004;168(1-2):155–64.
  9. Belytschko T, Black T. Elastic crack growth in finite elements with minimal remeshing. International Journal for Numerical Methods in Engineering. 1999;45(5):601–20.
  10. Daux C, Moes N, Dolbow J, Sukumar N, Belytschko T. Arbitrary branched and intersecting cracks with the extended finite element method. International Journal for Numerical Methods in Engineering. 2000;48(12):1741–60..
  11. Jena J, Singh IV, Gaur V. XFEM for semipermeable crack in piezoelectric material with Maxwell stress. Engineering Fracture Mechanics. 2023 Jun 1;285:109281–1.
  12. Sukumar N, Prevost JH. Modeling quasi-static crack growth with the extended finite element method Part I: Computer implementation. International Journal of Solids and Structures. 2003;40(26):7513–37.
  13. Zi G, Belytschko T. New crack-tip elements for XFEM and applications to cohesive cracks. International Journal for Numerical Methods in Engineering. 2003;57(15):2221–40.
  14. Unger JF, Eckardt S, Könke C. Modelling of cohesive crack growth in concrete structures with the extended finite element method. Computer Methods in Applied Mechanics and Engineering. 2007;196(41-44):4087–100.
  15. Asferg JL, Peter Noe Poulsen, Leif Otto Nielsen. A consistent partly cracked XFEM element for cohesive crack growth. International Journal for Numerical Methods in Engineering. 2007;72(4):464–85.
  16. Qian J, Fatemi A. Mixed mode fatigue crack growth: A literature survey. Engineering Fracture Mechanics. 1996;55(6):969–90.
  17. Chopp DL, Sukumar N. Fatigue crack propagation of multiple coplanar cracks with the coupled extended finite element/fast marching method. 2003;41(8):845–69.
  18. Stolarska M, Chopp DL. Modeling thermal fatigue cracking in integrated circuits by level sets and the extended finite element method. International Journal of Engineering Science. 2003;41(20):2381–410.
  19. Ventura G, Élisa Budyn, Belytschko T. Vector level sets for description of propagating cracks in finite elements. International Journal for Numerical Methods in Engineering. 2003;58(10):1571–92.
  20. Areias PMA, Belytschko T. Analysis of three-dimensional crack initiation and propagation using the extended finite element method. International Journal for Numerical Methods in Engineering. 2005;63(5):760–88.
  21. Sukumar N, Moes N, Moran B, Belytschko T. Extended finite element method for three-dimensional crack modelling. International Journal for Numerical Methods in Engineering. 2000;48(11):1549–70..
  22. Giner E, Sukumar N, Denia FD, Fuenmayor FJ. Extended finite element method for fretting fatigue crack propagation. 2008;45(22-23):5675–87.
  23. Budyn É, Zi G, Moës N, Belytschko T. A method for multiple crack growth in brittle materials without remeshing. International Journal for Numerical Methods in Engineering. 2004;61(10):1741–70.
  24. Jameel A, Harmain GA. Modeling and Numerical Simulation of Fatigue Crack Growth in Cracked Specimens Containing Material Discontinuities. Strength of Materials. 2016;48(2):294–307.
  25. Bellec J, Dolbow JE. A note on enrichment functions for modelling crack nucleation. Communications in Numerical Methods in Engineering. 2003;19(12):921–32.
  26. Kanth SA, Harmain GA, Jameel A. Modeling of Nonlinear Crack Growth in Steel and Aluminum Alloys by the Element Free Galerkin Method. Materials Today: Proceedings. 2018;5(9):18805–14.
  27. Duhan N, Mishra BK, Singh IV. XFEM for multiphysics analysis of edge dislocations with nonuniform misfit strain: A novel enrichment implementation. Computer Methods in Applied Mechanics and Engineering. 2023;413:116079–9..
  28. Belytschko T, Parimi C, Moës N, Sukumar N, Usui S. Structured extended finite element methods for solids defined by implicit surfaces. International Journal for Numerical Methods in Engineering. 2002;56(4):609–35.
  29. Singh AK, Jameel A, Harmain GA. Investigations on crack tip plastic zones by the extended iso-geometric analysis. Materials Today: Proceedings. 2018;5(9):19284–93.
  30. Hettich T, Ramm E. Interface material failure modeled by the extended finite-element method and level sets. Computer Methods in Applied Mechanics and Engineering. 2006;195(37-40):4753–67.
  31. Asadpoure A, Mohammadi S, Vafai A. Crack analysis in orthotropic media using the extended finite element method. Thin-Walled Structures. 2006;44(9):1031–8.
  32. Kanth SA, Lone AS, Harmain GA, Jameel A. Elasto Plastic Crack Growth by XFEM: A Review. Materials Today: Proceedings. 2019;18:3472–81.
  33. Jameel A, Harmain GA. Fatigue crack growth analysis of cracked specimens by the coupled finite element-element free Galerkin method. Mechanics of Advanced Materials and Structures. 2018;26(16):1343–56.
  34. Vitali E, Benson DJ. An extended finite element formulation for contact in multi-material arbitrary Lagrangian–Eulerian calculations. International Journal for Numerical Methods in Engineering. 2006;67(10):1420–44.
  35. Jameel A, Harmain GA. Extended iso-geometric analysis for modeling three-dimensional cracks. Mechanics of Advanced Materials and Structures. 2018;26(11):915–23.
  36. Lone AS, Kanth SA, Jameel A, Harmain GA. A state of art review on the modeling of Contact type Nonlinearities by Extended Finite Element method. Materials Today: Proceedings. 2019;18:3462–71..
  37. Lone AS, Jameel A, G.A. Harmain. A coupled finite element-element free Galerkin approach for modeling frictional contact in engineering components. Materials Today: Proceedings. 2018;5(9):18745–54.
  38. Jameel A, G.A. Harmain. A coupled FE-IGA technique for modeling fatigue crack growth in engineering materials. 2019;26(21):1764–75.
  39. Belytschko T, Chen H, Xu J, Zi G. Dynamic crack propagation based on loss of hyperbolicity and a new discontinuous enrichment. International Journal for Numerical Methods in Engineering. 2003;58(12):1873–905.
  40. Julien Réthoré, Gravouil A, Alain Combescure. An energy-conserving scheme for dynamic crack growth using the eXtended finite element method. International Journal for Numerical Methods in Engineering. 2005;63(5):631–59.
  41. Sheikh UA, Jameel A. Elasto-plastic large deformation analysis of bi-material components by FEM. Materials Today: Proceedings. 2020;26:1795–802.
  42. Rozycki P, Moes N, Bechet E, Dubois C. X-FEM explicit dynamics for constant strain elements to alleviate mesh constraints on internal or external boundaries. Computer Methods in Applied Mechanics and Engineering. 2008;197(5):349–63.
  43. Kanth SA, Lone AS, Harmain GA, Jameel A. Modeling of embedded and edge cracks in steel alloys by XFEM. Materials Today: Proceedings. 2020;26:814–8.
  44. Hutchinson JW. Singular behaviour at the end of a tensile crack in a hardening material. Journal of The Mechanics and Physics of Solids. 1968;16(1):13–31.
  45. Rice JR, Rosengren GF. Plane strain deformation near a crack tip in a power-law hardening material. Journal of The Mechanics and Physics of Solids. 1967;16(1):1–12.
  46. Wagner GJ, Moës N, Liu WK, Belytschko T. The extended finite element method for rigid particles in Stokes flow. International Journal for Numerical Methods in Engineering. 2001;51(3):293–313.
  47. Chessa J, Belytschko T. An Extended Finite Element Method for Two-Phase Fluids. Journal of Applied Mechanics. 2003;70(1):10–7.
  48. Lone AS, Kanth SA, Harmain GA, Jameel A. XFEM modeling of frictional contact between elliptical inclusions and solid bodies. Materials Today: Proceedings. 2020;26:819–24.
  49. Sven Groí, Reusken A. An extended pressure finite element space for two-phase incompressible flows with surface tension. 2007;224(1):40–58.
  50. Jameel A, Harmain GA. Effect of material irregularities on fatigue crack growth by enriched techniques. International Journal for Computational Methods in Engineering Science and Mechanics. 2020;21(3):109–33.
  51. Sharma D, Singh IV, Kumar J. A computational framework based on 3D microstructure modelling to predict the mechanical behaviour of polycrystalline materials. International Journal of Mechanical Sciences. 2023;258:108565–5.
  52. Kanth SA, Harmain GA, Jameel A. Investigation of fatigue crack growth in engineering components containing different types of material irregularities by XFEM. Mechanics of Advanced Materials and Structures. 2021;1–39.
  53. Ji H, Chopp DL, Dolbow JE. A hybrid extended finite element/level set method for modeling phase transformations. International Journal for Numerical Methods in Engineering. 2002;54(8):1209–33.
  54. Jameel A, Harmain GA. Large deformation in bi-material components by XIGA and coupled FE-IGA techniques. Mechanics of Advanced Materials and Structures. 2020;1–23.
  55. Éric Béchet, Scherzer M, Kuna M. Application of the X‐FEM to the fracture of piezoelectric materials. International Journal for Numerical Methods in Engineering. 2008;77(11):1535–65.
  56. Bordas S, Moran B. Enriched finite elements and level sets for damage tolerance assessment of complex structures. Engineering Fracture Mechanics. 2006;73(9):1176–201.
  57. Lone AS, Harmain GA, Jameel A. Modeling of contact interfaces by penalty based enriched finite element method. Mechanics of Advanced Materials and Structures. 2022;30(7):1485–503.

Ahead of Print Open Access Original Research
Volume
Received March 21, 2024
Accepted April 6, 2024
Published May 14, 2024