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RETRACTED ARTICLE: Fracture analysis using an enriched meshless method

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Abstract

Crack propagation and fatigue fracture is studied with an enriched meshless method. This method uses an intrinsic enrichment of the meshless weighting functions such that the correct crack kinematics can be described. The major advantage of the method is its simplicity, especially with respect to implementation. The method is applied to problems in elastostatics where analytical and experimental data is available. We show the higher accuracy of our method in comparison to standard methods for two problems with analytical solutions. Finally, we show the accuracy of the method for interacting flaws.

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References

  1. Kobelev V (2006) Micropolar model of fracture for composite material. Meccanica 41:653–660

    Article  MATH  Google Scholar 

  2. Uddin FAKM, Shigeishiand M, Ohtsu M (2006) Fracture mechanics of corrosion cracking in concrete by acoustic emission. Meccanica 41:425–442

    Article  MATH  Google Scholar 

  3. Carloni C, Piva A, Viola E (2004) Biaxial load effect on crack initiation for orthotropic materials. Meccanica 39:331–344

    Article  MATH  Google Scholar 

  4. Zhou ZG, Chen YC, Wang B (2000) Analysis of two collinear cracks in a piezoelectric layer bonded to two half spaces subjected to anti-plane shear. Meccanica 35:443–456

    Article  MATH  Google Scholar 

  5. Tong P, Pian THH (1973) On the convergence of the finite element method for problems with singularity. Int J Solids Struct 9:313–321

    Article  MATH  Google Scholar 

  6. Gallagher RH (1978) A review of finite element techniques in fracture mechanics. In: Luxmoore AR, Owen DRJ (eds) Proceedings of the 1st international conference on numerical methods in fracture mechanics, Swansea, Pineridge, pp 1–25

    Google Scholar 

  7. Fawkes AJ, Owen DRJ, Luxmoore AR (1979) An assessment of crack tip singularity models for use with isoparametric elements. Eng Fract Mech 11:143–159

    Article  Google Scholar 

  8. Fawkes AJ, Owen DRJ (1983). Engineering fracture mechanics: numerical methods and applications

  9. Liebowitz H, Moyer ET (1989) Finite element methods in fracture mechanics. Comput Struct 31:1–9

    Article  Google Scholar 

  10. Belytschko T, Lu YY (1995) Element-free Galerkin methods for static and dynamic fracture. Int J Solids Struct 32:2547–2570

    Article  MATH  Google Scholar 

  11. Belytschko T, Tabbara M (1996) Dynamic fracture using element-free Galerkin methods. Int J Numer Methods Eng 39(6):923–938

    Article  MATH  Google Scholar 

  12. Liu WK, Hao S, Belytschko T (1999) Multiple scale meshfree methods for damage fracture and localization. Comput Mater Sci 16(1–4):197–205

    Article  Google Scholar 

  13. Rabczuk T, Belytschko T (2006) Application of particle methods to static fracture of reinforced concrete structures. Int J Fract 137:19–49

    Article  MATH  Google Scholar 

  14. Li S, Hao W, Liu WK (2000) Mesh-free simulations of shear banding in large deformation. Int J Solids Struct 37:7185–7206

    Article  MATH  Google Scholar 

  15. Hao S, Liu WK, Qian D (2000) Localization-induced band and cohesive model. J Appl Mech Trans ASME 67(4):803–812

    Article  MATH  Google Scholar 

  16. Hao S, Liu WK, Klein PA, Rosakis AJ (2004) Modeling and simulation of intersonic crack growth. Int J Solids Struct 41(7):1773–1799

    Article  MATH  Google Scholar 

  17. Li S, Liu WK, Rosakis A, Belytschko T, Hao W (2002) Mesh free Galerkin simulations of dynamic shear band propagation and failure mode transition. Int J Solids Struct 39:1213–1240

    Article  MATH  Google Scholar 

  18. Randles PW, Libersky LD (1997) Recent improvements in sph modeling of hypervelocity impact. Int J Impact Eng 20:525–532

    Article  Google Scholar 

  19. Hao S, Liu WK, Chang CT (2000) Computer implementation of damage models by finite element and meshfree methods. Comput Methods Appl Mech Eng 187(3–4):401–440

    Article  MATH  Google Scholar 

  20. Randles PW, Libersky L (2000) Normalized sph with stress points. Int J Numer Methods Eng 48:1445–1461

    Article  MATH  Google Scholar 

  21. Han ZD, Liu HT, Rajendran AM, Atluri SN (2007) The applications of meshless local Petrov-Galerkin (mlpg) approaches in high-speed impact, penetration and perforation problems. Comput Model Eng Sci 14:119–128

    MathSciNet  Google Scholar 

  22. Rabczuk T, Belytschko T, Xiao SP (2004) Stable particle methods based on Lagrangian kernels. Comput Methods Appl Mech Eng 193:1035–1063

    Article  MATH  MathSciNet  Google Scholar 

  23. Rabczuk T, Eibl J (2003) Simulation of high velocity concrete fragmentation using sph/mlsph. Int J Numer Methods Eng 56:1421–1444

    Article  MATH  Google Scholar 

  24. Hao S, Liu WK (2006) Moving particle finite element method with superconvergence: Nodal integration formulation and applications. Comput Methods Appl Mech Eng 195(44–47):6059–6072

    Article  MATH  Google Scholar 

  25. Belytschko T, Lu YY, Gu L (1995) Crack propagation by element-free Galerkin methods. Eng Fract Mech 51(2):295–315

    Article  ADS  Google Scholar 

  26. Organ D, Fleming M, Terry T, Belytschko T (1996) Continuous meshless approximations for nonconvex bodies by diffraction and transparency. Comput Mech 18:225–235

    Article  MATH  Google Scholar 

  27. Liu HT, Han ZD, Rajendran AM, Atluri SN (2006) Computational modeling of impact response with the rg damage model and the meshless local Petrov-Galerkin (mlpg) approaches. Comput Mater Contin 4:43–53

    Google Scholar 

  28. Rabczuk T, Belytschko T (2004) Cracking particles: a simplified meshfree method for arbitrary evolving cracks. Int J Numer Methods Eng 61(13):2316–2343

    Article  MATH  Google Scholar 

  29. Rabczuk T, Belytschko T (2005) Adaptivity for structured meshfree particle methods in 2d and 3d. Int J Numer Methods Eng 63(11):1559–1582

    Article  MATH  MathSciNet  Google Scholar 

  30. Rabczuk T, Belytschko T (2007) A three-dimensional large deformation meshfree method for arbitrary evolving cracks. Comput Methods Appl Mech Eng 196(29–30):2777–2799

    Article  MATH  MathSciNet  Google Scholar 

  31. Rabczuk T, Areias PMA, Belytschko T (2007) A meshfree thin shell method for non-linear dynamic fracture. Int J Numer Methods Eng 72(5):524–548

    Article  MATH  MathSciNet  Google Scholar 

  32. Rabczuk T, Areias P (2006) A meshfree thin shell for arbitrary evolving cracks based on an extrinsic basis. Comput Model Eng Sci 16(2):115–130

    Google Scholar 

  33. Fleming M, Chu YA, Moran B, Belytschko T (1997) Enriched element-free Galerkin methods for crack tip fields. Int J Numer Methods Eng 40:1483–1504

    Article  MathSciNet  Google Scholar 

  34. Ventura G, Xu J, Belytschko T (2002) A vector level set method and new discontinuity approximation for crack growth by efg. Int J Numer Methods Eng 54(6):923–944

    Article  MATH  Google Scholar 

  35. Rabczuk T, Zi G (2007) A meshfree method based on the local partition of unity for cohesive cracks. Comput Mech 39(6):743–760

    Article  MATH  Google Scholar 

  36. Rabczuk T, Areias PMA, Belytschko T (2007) A simplified mesh-free method for shear bands with cohesive surfaces. Int J Numer Methods Eng 69:993–1021

    Article  MATH  MathSciNet  Google Scholar 

  37. Zi G, Rabczuk T, Wall W (2007) Extended meshfree methods without branch enrichment for cohesive cracks. Comput Mech 40:367–382

    Article  MATH  Google Scholar 

  38. Belytschko T, Lu YY, Gu L (1994) Element-free Galerkin methods. Int J Numer Methods Eng 37:229–256

    Article  MATH  MathSciNet  Google Scholar 

  39. Melenk JM, Babuska I (1996) The partition of unity finite element method: basic theory and applications. Comput Methods Appl Mech Eng 139:289–314

    Article  MATH  MathSciNet  Google Scholar 

  40. Strouboulis T, Copps K, Babuska I (2000) The generalized finite element method: an example ofits implementation and illustration of its performance. Int J Numer Methods Eng 47:1401–1417

    Article  MATH  MathSciNet  Google Scholar 

  41. Moran B, Shih CF (1987) Crack tip and associated domain integrals from momentum and energy balance. Eng Fract Mech 27(6):615–641

    Article  Google Scholar 

  42. Yau JF, Wang SS, Corten HT (1980) A mixed mode crack analysis of isotropic solids using conservation laws of elasticity. J Appl Mech 47:335–341

    Article  MATH  Google Scholar 

  43. Murakami Y (1987) Stress intensity factors handbook. Pergamon, Oxford

    Google Scholar 

  44. Hasegawa K, Miyazaki K (2007) Crack propagation in the presence of shot-peening residual-stresses. Key Eng Mater 345–346:411–416

    Article  Google Scholar 

  45. Tu ST, Cai RY (1988) A coupling of boundary elements and singular integral equation for the solution of the fatigue cracked body. In: Brebbia CA (ed) Boundary elements X. Stress analysis, vol 3. Springer, Berlin, pp 239–247

    Google Scholar 

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Authors and Affiliations

  1. University of Padderborn, Institute for Advanced Studies in Computer Science and Engineering, Paderborn, Germany

    G. Hildebrand

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  1. G. Hildebrand
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Correspondence to G. Hildebrand.

Additional information

Because of the regrettable behavior of the author (Professor Gunter Hildebrand) the paper “Fracture analysis using an enriched meshless method” DOI 10.1007/s11012-008-9189-4 has been withdrawn, since the paper is a fraud and its content and results are copied from another manuscript. Apologies are due to Dr Duflot who emphasized the plagiarism of the Hildebrand paper with his paper: A meshless method with enriched weight functions for fatigue crack growth Marc Duflot and Hung Nguyen-Dang (2004) International Journal for Numerical Methods in Engineering 59:1945-1961. We have tried to obtain an explanation from Professor Hildebrand on this matter, but did not receive any reply from him. Since we have not received a proper note from Professor Hildebrand, and considering the communications of Dr Duflot, Meccanica preferred to withdraw the paper in order to prevent an illicit spread of the paper itself.

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Hildebrand, G. RETRACTED ARTICLE: Fracture analysis using an enriched meshless method. Meccanica 44, 535–545 (2009). https://doi.org/10.1007/s11012-008-9189-4

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  • DOI: https://doi.org/10.1007/s11012-008-9189-4

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