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Continuum damage growth analysis using element free Galerkin method

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Abstract

This paper presents an elasto-plastic element free Galerkin formulation based on Newton-Raphson algorithm for damage growth analysis. Isotropic ductile damage evolution law is used. A study has been carried out in this paper using the proposed element free Galerkin method to understand the effect of initial damage and its growth on structural response of single and bi-material problems. Asimple method is adopted for enforcing EBCs by scaling the function approximation using a scaling matrix, when non-singular weight functions are used over the entire domain of the problem definition. Numerical examples comprising of oneand two-dimensional problems are presented to illustrate the effectiveness of the proposed method in analysis of uniform and non-uniform damage evolution problems. Effect of material discontinuity on damage growth analysis is also presented.

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References

  • Alves M K, Rossi R 2003 Amodified element-free Galerkin method with essential boundary conditions enforced by an extended partition of unity finite element weight function. Int. J. Numerical Methods in Eng. 57: 1523–1552

    Article  MATH  Google Scholar 

  • Arun C O, Rao B N, Sivakumar S M 2007 A new material discontinuity treatment in element free Galerkin method. In: Proceedings of ICTACEM, 27–29 December, India

  • Arun C O, Rao B, Sivakumar S M 2009 On material discontinuity modeling in element free Galerkin method. J. Struct. Eng., SERC 36(3): 182–194

    Google Scholar 

  • Belytschko T, Lu Y Y, Gu L 1994 Element-free Galerkin methods. Int. J. Numerical Methods in Eng. 37: 229–256

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

  • Benallal A Rene B, Doghri I 1988 An integration algorithm and the corresponding consistent tangent operator for fully coupled elasto plastic and damage equations. Communications in Applied Numerical Methods 4: 731–740

    Article  MATH  Google Scholar 

  • Bhatti A M 2006 Advanced topics in finite element analsyis of structures (Hoboken, NJ: John Wiley and Sons)

    Google Scholar 

  • Chaboche J L 1988 Continuum damage mechanics: Part I — General concepts. J. Applied Mech. 55:59–64

    Article  Google Scholar 

  • Chaboche J L 1988 Continuum damage mechanics: Part II — Damage growth, Crack initiation, and Crack growth. J. Applied Mech. 55: 59–64

    Article  Google Scholar 

  • Chen J S, Wang H P 2000 New Boundary Condition Treatments in Mesh-free Computation of Contact Problems. Computer Methods in Applied Mech. and Eng. 187: 441–468

    Article  MATH  Google Scholar 

  • Chen W F, Han D J 1988 Plasticity for Structural Engineers (New York, USA: Springer-Verlag)

    MATH  Google Scholar 

  • Dolbow J, Belytschko T 1998 An introduction to programming the meshless element free Galerkin method. Archives of Computational Mechanics 15(3): 207–241

    Article  MathSciNet  Google Scholar 

  • Duarte C A M, Oden J T 1996 H - p Clouds - An h - p meshless method. Numerical Methods for Partial Differential Equations 12(6): 673–705

    Article  MATH  MathSciNet  Google Scholar 

  • Kachanov L M 1958 Time of the rupture process under creep conditions. IVZ Akad Nauk, S. S. R. Otd Tecg Bayj, 8: 26–31

    Google Scholar 

  • Kattan P I, Voyiadjis G Z 2002 Damage mechanics with finite elements practical applications with computer tools (Berlin, Heidelberg, Germany: Springer-Verlag)

    Google Scholar 

  • Krongauz Y, Belytschko T 1996 Enforcement of essential boundary conditions in meshless approximation using finite elements. Computer Methods in Applied Mechanics and Eng. 131: 1335–1345

    MathSciNet  Google Scholar 

  • Lancaster P, Salkauskas K 1981 Surfaces generated by moving least squares methods. Mathematics of Computation 37: 141–158

    MATH  MathSciNet  Google Scholar 

  • Lemaitre J 1971 Evaluation and dissipation of damage in metals submitted to dynamic loading. In: Proceedings I.C.M.I. Kyoto, Japan

  • Lemaitre J 1985 A continuous damage mechanics model for ductile fracture. J. Eng. Materials and Technol. 107: 83–89

    Article  Google Scholar 

  • Lemaitre J 1992 A course on damage mechanics (Berlin, Heidelberg, Germany: Springer-Verlag)

    MATH  Google Scholar 

  • Lemaitre J, Desmorat R 2005 Engineering damage mechanics (Berlin, Heidelberg, Germany: Springer-Verlag)

    Google Scholar 

  • Liu W K, Jun S, Zhang Y F 1995 Reproducing kernel particle methods. Int. J. Numerical Methods in Fluids 20: 1081–1106

    Article  MATH  MathSciNet  Google Scholar 

  • Liu W K, Li S, Belytschko T 1997 Moving least square kernel Galerkin method — Part I: Methodology and convergence. Computer Methods in Applied Mechanics and Eng. 143: 422–433

    MathSciNet  Google Scholar 

  • Liu G R 2002 Mesh free methods: Moving beyond the finite element method (LLC, Boca Raton FL, USA: CRC Press)

    Book  Google Scholar 

  • Li G, Belytschko T 2001 Element-free Galerkin methods for contact problems in metal forming analysis. Eng. Computations 18: 62–78

    Article  MATH  Google Scholar 

  • Lucy L 1977 A numerical approach to testing the fission hypothesis. Astron. J. 82: 1013–1024

    Article  Google Scholar 

  • Lu Y Y, Belytschko T, Gu L 1994 A new implementation of the element free Galerkin method. Computer Methods in Applied Mechanics and Eng. 113: 397–414

    Article  MATH  MathSciNet  Google Scholar 

  • Lu Y Y, Belytschko T, Tabbara M 1995 Element-free Galerkin methods for wave propagation and dynamic fracture. Computer Methods in Applied Mechanics and Eng. 126: 131–153

    Article  MATH  MathSciNet  Google Scholar 

  • Melenk J M, Babuska I 1996 The partition of unity finite element method: Basic theory and applications. Computer Methods in Applied Mechanics and Eng. 139: 280–314

    MathSciNet  Google Scholar 

  • Monaghan J J 1988 An introduction to SPH. Computer Physics Communications 48: 89–96

    Article  MATH  Google Scholar 

  • Nagashima T 1999 Node-by-Node meshless approach and its applications to structural analyses. Int. J. Numerical Methods in Eng. 46: 341–385

    Article  MATH  Google Scholar 

  • Nayroles B, Touzot G, Villon P 1992 Generalizing the finite element method: Diffuse approximation and diffuse elements. Computational Mechanics 10: 307–318

    Article  MATH  Google Scholar 

  • Ponthot J P, Belytschko T 1998 Arbitrary lagrangian-eulerian formulation for element-free Galerkin method. Computer Methods in Applied Mechanics and Eng. 152: 19–46

    Article  MATH  Google Scholar 

  • Rabotnov Y N 1969 Creep Problems of Structural Members. (North Holland, Amsterdam)

    Google Scholar 

  • Rao B N, Rahman S 2000 An efficient meshless method for fracture analysis of cracks. Computational Mechanics 26(4): 398–408

    Article  MATH  Google Scholar 

  • Sivakumar M S, Voyiadjis G Z 1997 A simple implicit scheme for stress response computation in plasticity models. Computational Mechanics 20: 520–529

    Article  MATH  Google Scholar 

  • Timoshenko S P, Goodier J N 1970 Theory of Elasticity. (New York, USA: McGraw-Hill)

    Google Scholar 

  • Voyiadjis GZ, Kattan P I 1990 Acoupled theory of dmage mechanics and finite strain elasto-plasticity-II. Damage and Finite Strain Plasticity. Int. J. Eng. Sci. 28(6): 505–524

    Article  MATH  Google Scholar 

  • Voyiadjis G Z, Kattan P I 2005 Damage mechanics (LLC, Boca Raton FL, USA: CRC Press)

    MATH  Google Scholar 

Download references

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Authors and Affiliations

  1. Structural Engineering Division, Department of Civil Engineering, Indian Institute of Technology Madras, Chennai, 600 036, India

    C. O. Arun, B. N. Rao & S. M. Srinivasan

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  1. C. O. Arun
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  2. B. N. Rao
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  3. S. M. Srinivasan
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Correspondence to B. N. Rao.

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Arun, C.O., Rao, B.N. & Srinivasan, S.M. Continuum damage growth analysis using element free Galerkin method. Sadhana 35, 279–301 (2010). https://doi.org/10.1007/s12046-010-0010-4

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  • DOI: https://doi.org/10.1007/s12046-010-0010-4

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