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Extracting stress intensity factors for isotropic cracked domains having stochastic material properties

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Abstract

Material properties are inevitably stochastic due to the manufacturing process and the measurement procedure. In case of a cracked domain, the stochasticity of material properties (as stochastic variables) may manifest in the stress intensity factors (SIFs). Having the stochastic representation of the material properties, Young modulus and Poisson ratio (isotropic material), we approximate the SIFs for 2D cracked domains using the generalized polynomial chaos (gPC). The approximated SIF consists of two families of orthogonal polynomials, selected by the probability distribution function of the material properties. The polynomials are multiplied by a deterministic coefficient, consisting of deterministic SIFs, extracted from a finite element model according to the stochastic properties of both Young modulus and Poisson ratio. Numerical example problems are provided where the stochastic approximation of the SIF is computed. The obtained approximation of the SIF is compared with results obtained using the Monte Carlo method. The results demonstrate the efficiency and accuracy of the proposed method.

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References

  1. Hill, R.: On constitutive macro-variables for heterogeneous solids at finite strain. Proc. R. Soc. A Math. Phys. Eng. Sci. 326, 131–147 (1972)

    MATH  Google Scholar 

  2. Desceliers, C., Soize, C., Ghanem, R.: Identification of chaos representations of elastic properties of random media using experimental vibration tests. Comput. Mech. 39, 831–838 (2007)

    Article  Google Scholar 

  3. Zohdi, T.I., Wriggers, P.: An Introduction to Computational Micromechanics. Springer, New-York (2005)

    Book  Google Scholar 

  4. Ghanem, R., Soize, C.: Remarks on stochastic properties of materials through finite deformations. Int. J. Multiscale Comput. Eng. 13, 367–374 (2015)

    Article  Google Scholar 

  5. Ghanem, R., Spanos, P.: Stochastic Finite Elements: A Spectral Approach. Springer, Berlin (1991)

    Book  Google Scholar 

  6. Xiu, D.: Numerical Methods for Stochastic Computations: A Spectral Method approach. Princeton University Press, Cambridge (2010)

    Book  Google Scholar 

  7. Rahman, S.: Probabilistic fracture mechanics: \(j\)-estimation and finite element methods. Eng. Fract. Mech. 68, 107–125 (2001)

    Article  Google Scholar 

  8. Rao, B.N., Rahman, S.: Probabilistic fracture mechanics by galerkin meshless methods part I: rates of stress intensity factors. Comput. Mech. 28, 351–364 (2002)

    Article  Google Scholar 

  9. Reddy, R.M., Rao, B.N.: Stochastic fracture mechanics by fractal finite element method. Comp. Meth. Appl. Mech. Eng. 198, 459–474 (2008)

    Article  MathSciNet  Google Scholar 

  10. Chowdhury, M.S., Song, C., Gao, W.: Probabilistic fracture mechanics by using monte carlo simulation and the scaled boundary finite element method. Eng. Fract. Mech 78, 2369–2389 (2011)

    Article  Google Scholar 

  11. Su, C., Zheng, C.: Probabilistic fracture mechanics analysis of linear-elastic cracked structures by spline fictitious boundary element method. Eng. Anal. Bound. Elements 36, 1828–1837 (2012)

    Article  MathSciNet  Google Scholar 

  12. Beck, Andre Teofilo, de Santana Gomes, Wellison Jose: Stochastic fracture mechanics using polynomial chaos. Prob. Eng. Mech. 34, 26–39 (2013)

    Article  Google Scholar 

  13. Silberschmidt, V.V.: Effect of material?s randomness on scaling of crack propagation in ceramics. Int. J. Fract. 140, 73–85 (2006)

    Article  Google Scholar 

  14. Keleş, Ö., García, R.E., Bowman, K.J.: Stochastic failure of isotropic, brittle materials with uniform porosity. Acta Materialia 61, 2853–2862 (2013)

    Article  Google Scholar 

  15. Omer, N., Yosibash, Z.: Extracting stochastic stress intensity factors using generalized polynomial chaos. Eng. Fract. Mech. 206, 357–391 (2019)

    Article  Google Scholar 

  16. Omer, N.: Direct extraction of stochastic stress intensity factors using generalized polynomial chaos. Int. J. Fract. 219, 123–134 (2019)

    Article  Google Scholar 

  17. Wiener, N.: The homogeneous chaos. Am. J. Math. 60, 897–936 (1938)

    Article  MathSciNet  Google Scholar 

  18. Xiu, D.: Fast numerical methods for stochastic computations: a review. Commun. Comp. Phys. 5(2–4), 242–272 (2009)

    MathSciNet  MATH  Google Scholar 

  19. Gautschi, Walter: Orthogonal Polynomials. Oxford University Press, Oxford (2004)

    Book  Google Scholar 

  20. Milovanović, Gradimir V.: Numerical quadratures and orthogonal polynomials. Studia Universitatis Babes-Bolyai, Mathematica, 56(2) (2011)

  21. Stern, M., Soni, M.L.: On the computation of stress intensities at fixed-free corners. Int. J. Solids Struct. 12, 331–337 (1976)

    Article  Google Scholar 

  22. Sinclair, G.B., Okajima, M., Griffin, J.H.: Path independent integrals for computing stress intensity factors at sharp notches in elastic plates. J. Numer. Methods Eng. 20(6) (1984)

  23. Wen, P.H., Aliabadi, M.H., Rooke, D.P.: A contour integral for the evaluation of stress intensity factors. Appl. Math. Modell. 19(8), 450–455 (1995)

    Article  Google Scholar 

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  1. Department of Mechanical Engineering, Afeka College of Engineering, Tel-Aviv, Israel

    Netta Omer

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Omer, N. Extracting stress intensity factors for isotropic cracked domains having stochastic material properties. Acta Mech 232, 2165–2182 (2021). https://doi.org/10.1007/s00707-020-02928-9

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  • DOI: https://doi.org/10.1007/s00707-020-02928-9

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