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Multiscale modeling of failure in composites under model parameter uncertainty

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Abstract

This manuscript presents a multiscale stochastic failure modeling approach for fiber reinforced composites. A homogenization based reduced-order multiscale computational model is employed to predict the progressive damage accumulation and failure in the composite. Uncertainty in the composite response is modeled at the scale of the microstructure by considering the constituent material (i.e., matrix and fiber) parameters governing the evolution of damage as random variables. Through the use of the multiscale model, randomness at the constituent scale is propagated to the scale of the composite laminate. The probability distributions of the underlying material parameters are calibrated from unidirectional composite experiments using a Bayesian statistical approach. The calibrated multiscale model is exercised to predict the ultimate tensile strength of quasi-isotropic open-hole composite specimens at various loading rates. The effect of random spatial distribution of constituent material properties on the composite response is investigated.

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References

  1. ASTM Standard D3039 (2008) Standard test method for tensile properties of polymer matrix composite materials. ASTM International, West Conshohocken

  2. ASTM Standard D5766 (2011) Standard test method for open-hole tensile strength of polymer matrix composite laminates. ASTM International, West Conshohocken

  3. ASTM Standard D790 (2010) Standard test methods for flexural properties of unreinforced and reinforced plastics and electrical insulating materials. ASTM International, West Conshohocken

  4. Bogdanor MJ, Mahadevan S, Oskay C (2013) Uncertainty quantification in damage modeling of heterogeneous materials. Int J Multiscale Comput Eng 11:287–307

    Article  Google Scholar 

  5. Chamis CC (2004) Probabilistic simulation of multi-scale composite behavior. Theor Appl Fract Mech 41:51–61

    Article  Google Scholar 

  6. Chen NZ, Soares CG (2008) Spectral stochastic finite element analysis for laminated composite plates. Comput Methods Appl Mech Eng 197:4830–4839

    Article  MATH  Google Scholar 

  7. Clement A, Soize C, Yvonnet J (2013) Uncertainty quantification in computational stochastic multiscale analysis of nonlinear elastic materials. Comput Methods Appl Mech Eng 254:61–82

    Article  MathSciNet  MATH  Google Scholar 

  8. Crouch R, Oskay C (2010) Symmetric mesomechanical model for failure analysis of heterogeneous materials. Int J Multiscale Comput Eng 8:447–461

    Article  Google Scholar 

  9. Crouch R, Oskay C (2013) Experimental and computational investigation of progressive damage accumulation in CFRP composites. Compos Part B 48:59–67

    Article  Google Scholar 

  10. Crouch R, Oskay C, Clay S (2012) Multiscale modeling of damage accumulation in carbon fiber reinforced polymers subjected to fatigue. Proceedings of the 53rd AIAA Structures, Structural Dynamics, and Materials Conference

  11. Crouch R, Oskay C, Clay S (2013) Multiple spatio-temporal scale modeling of composites subjected to cyclic loading. Comput Mech 51:93–107

    Article  MathSciNet  MATH  Google Scholar 

  12. Dwaikat MMS, Spitas C, Spitas V (2012) Effect of the stochastic nature of the constituents parameters on the predictability of the elastic properties of fibrous nano-composites. Compos Sci Technol 72(15):1882–1891

    Article  Google Scholar 

  13. Fish J, Wu W (2011) A nonintrusive stochastic multiscale solver. Int J Numer Methods Eng 88:862–879

    Article  MathSciNet  MATH  Google Scholar 

  14. Fish J, Yu Q (2001) Multiscale damage modelling for composite materials: theory and computational framework. Int J Numer Methods Eng 52:161–191

    Article  Google Scholar 

  15. Gerstner T, Griebel M (1998) Numerical integration using sparse grids. Numer Algorithms 18:209–232

    Article  MathSciNet  MATH  Google Scholar 

  16. Greene MS, Xu H, Tang S, Chen W, Liu WK (2013) A generalized uncertainty propagation criterion from benchmark studies of microstructured material systems. Comput Methods Appl Mech Eng 254:271–291

    Article  MathSciNet  MATH  Google Scholar 

  17. Guedes JM, Kikuchi N (1990) Preprocessing and postprocessing for materials based on the homogenization method with adaptive finite element methods. Comput Methods Appl Mech Eng 83:143–198

    Article  MathSciNet  MATH  Google Scholar 

  18. Hombal V, Mahadevan S (2011) Bias minimization in gaussian process surrogate modeling for uncertainty quantification. Int J Uncertain Quantif 1:321–349

    Article  MathSciNet  MATH  Google Scholar 

  19. Hui T, Oskay C (2012) Computational modeling of polyurea-coated composites subjected to blast loads. J Compos Mater 46:2167–2178

    Article  Google Scholar 

  20. Kamiński M, Kleiber M (2000) Perturbation based stochastic finite element method for homogenization of two-phase elastic composites. Comput Struct 78:811–826

    Article  Google Scholar 

  21. Lekou DJ, Philippidis TP (2008) Mechanical property variability in FRP laminates and its effect on failure prediction. Compos Part B 39:1247–1256

    Article  Google Scholar 

  22. Lin SC (2000) Reliability predictions of laminated composite plates with random system parameters. Probab Eng Mech 15:327–338

    Article  Google Scholar 

  23. Lopes PAM, Gomes HM, Awruch AM (2010) Reliability analysis of laminated composite structures using finite elements and neural networks. Compos Struct 92:1603–1613

    Article  Google Scholar 

  24. Oskay C, Fish J (2007) Eigendeformation-based reduced order homogenization for failure analysis of heterogeneous materials. Comput Method Appl Mech Eng 196:1216–1243

    Article  MathSciNet  MATH  Google Scholar 

  25. Parzen E (1962) On estimation of a probability density function and mode. Ann Math Stat 33:1065–1076

    Article  MathSciNet  MATH  Google Scholar 

  26. Rasmussen C, Williams C (2006) Gaussian processes for machine learning. Springer, New York

    MATH  Google Scholar 

  27. Rosenblatt M (1956) Remarks on some nonparametric estimates of a density function. Ann Math Stat 27:832–837

    Article  MathSciNet  MATH  Google Scholar 

  28. Sakata S, Ashida F, Enya K (2010) Stochastic analysis of microscopic stress in fiber reinforced composites considering uncertainty in a microscopic elastic property. J Solid Mech Mater Eng 4:568–577

    Article  Google Scholar 

  29. Sakata S, Ashida F, Kojima T, Zako M (2008) Three-dimensional stochastic analysis using a perturbation-based homogenization method for elastic properties of composite material considering microscopic uncertainty. Int J Solids Struct 45(3):894–907

    Article  MATH  Google Scholar 

  30. Sakata S, Ashida F, Zako M (2008) Kriging-based approximate stochastic homogenization analysis for composite materials. Comput Method Appl Mech Eng 197:1953–1964

    Article  MATH  Google Scholar 

  31. Sankararaman S, Ling Y, Mahadevan S (2011) Uncertainty quantification and model validation of fatigue crack growth prediction. Eng Fract Mech 78:1487–1504

    Article  Google Scholar 

  32. Shaw A, Sriramula S, Gosling PD, Chryssanthopoulos MK (2010) A critical reliability evaluation of fibre reinforced composite materials based on probabilistic micro and macro-mechanical analysis. Compos Part B 41:446–453

    Article  Google Scholar 

  33. Shiao MC, Chamis CC (1999) Probabilistic evaluation of fuselage-type composite structures. Probab Eng Mech 14:179–187

    Article  Google Scholar 

  34. Silverman BW (1986) Density estimation for statistics and data analysis, vol 26. CRC Press, New York

    Book  MATH  Google Scholar 

  35. Simo JC, Ju JW (1987) Strain- and stress-based continuum damage models - I. Formulation. Int J Solids Struct 23:821–840

    Article  MATH  Google Scholar 

  36. Song K, Li Y, Rose CA (2011) Continuum damage mechanics models for the analysis of progressive failure in open-hole tension laminates. Proceedings of the 52nd AIAA structures, structural dynamics, and Materials Conference 1861

  37. Sriramula S, Chryssanthopoulos MK (2009) Quantification of uncertainty modelling in stochastic analysis of FRP composites. Compos Part A 40:1673–1684

    Article  Google Scholar 

  38. Tootkaboni M, Graham-Brady L (2010) A multi-scale spectral stochastic method for homogenization of multi-phase periodic composites with random material properties. Int J Numer Meth Eng 83:59–90

    MathSciNet  MATH  Google Scholar 

  39. Xiu D, Karniadakis GE (2002) The Wiener–Askey polynomial chaos for stochastic differential equations. SIAM J Sci Comput 24:619–644

    Article  MathSciNet  MATH  Google Scholar 

  40. Yan H, Oskay C, Krishnan A, Xu LR (2010) Compression after impact response of woven fiber reinforced composites. Compos Sci Technol 70:2128–2136

    Article  Google Scholar 

  41. Yvonnet J, Monteiro E, He Q-C (2013) Computational homogenization method and reduced database model for hyperelastic heterogeneous structures. Int J Multiscale Comput Eng 11:201–225

    Article  Google Scholar 

Download references

Acknowledgments

The authors gratefully acknowledge the financial support provided by the Aerospace Systems Directorate of the Air Force Research Laboratory (Contract No: GS04T09DBC0017 through Engility Corporation) and the Department of Defense (DoD) through the National Defense Science & Engineering Graduate Fellowship (NDSEG) Program.

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Authors and Affiliations

  1. Department of Civil and Environmental Engineering, Vanderbilt University, VU Station B#351831, 2301 Vanderbilt Place, Nashville, TN, 37235, USA

    Michael J. Bogdanor & Caglar Oskay

  2. Aerospace Systems Directorate, Air Force Research Laboratory, Wright-Patterson Air Force Base, OH, 45433, USA

    Stephen B. Clay

Authors
  1. Michael J. Bogdanor
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  2. Caglar Oskay
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  3. Stephen B. Clay
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Correspondence to Caglar Oskay.

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Bogdanor, M.J., Oskay, C. & Clay, S.B. Multiscale modeling of failure in composites under model parameter uncertainty. Comput Mech 56, 389–404 (2015). https://doi.org/10.1007/s00466-015-1177-7

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  • DOI: https://doi.org/10.1007/s00466-015-1177-7

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