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Statistical Two-Scale Method for Strength Prediction of Composites with Random Distribution and Its Applications

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Computational Mechanics

Abstract

A Statistical two-order and Two-Scale computational Method (STSM) based on two-scale homogenization approach is developed and successfully applied to predicting the strength parameters of random particle reinforced composites. Firstly, the probability distribution model of composites with random distribution of a great number of particles in any ε - size statistic screen, as ε- size cell, is described. And then, the stochastic two-order and two-scale computational expressions for the strain tensor in the structure, which is made from the composites with random distribution model of ε - size cell, are formulated in detail. And the effective expected strength and the minimum strength for the composites with random distribution are expressed, and the computational formulas of them and the algorithm procedure for strength parameter prediction are shown. Finally, some numerical results of its application to the random particle reinforced composites, the concrete with random distribution of a great number of particles in any ε- size statistic screen, are demonstrated, and the comparisons with physical experimental data are given. They show that STSM is validated and efficient for predicting the strength of random particle reinforced composites.

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References

  1. Christensen RM. Mechanics of Composite Materials. Wiley, New York, USA, 1979.

    Google Scholar 

  2. Biwa S, Ito N, Ohno N. Elastic properties of rubber particles in toughened PMMA: ultrasonic and micromechanical evaluation. Mech. Mater., 2001; 3: 717–728.

    Article  Google Scholar 

  3. Sohn MS, Kim KS, Hong SH, Kim JK. Dynamic mechanical properties of particle-reinforced EPDM composites. J. Appl. Polym. Sci., 2003; 87: 1595–1601.

    Article  Google Scholar 

  4. Voigt W. Lehrbuch der Kristallphysik. Teubner-Verlag, Leipzig, Germany, 1928 (in German).

    MATH  Google Scholar 

  5. Reuss A. Berechnung der Fliessgrenze von Mischkristallen auf Grunder Plastizitätsbedingung für Einkristalle. Z. Angew. Math. Mech., 1929; 9: 49–58 (in German).

    Article  MATH  Google Scholar 

  6. Hashin Z, Shtrikman S. A variational approach to the theory of the elastic behavior of multiphase materials. J. Mech. Phys. Solids, 1963; 11: 127–140.

    Article  MATH  MathSciNet  Google Scholar 

  7. Hill R. A self consistent mechanics of composite materials. J. Mech. Phys. Solids, 1965; 13: 213–222.

    Article  Google Scholar 

  8. Budiansky B. On the elastic moduli of some heterogeneous materials. J. Mech. Phys. Solids, 1965; 13: 223–227.

    Article  Google Scholar 

  9. Christensen RM. A critical evaluation for a class of micromechanics models. J. Mech. Phys. Solids, 1990; 38: 379–404.

    Article  Google Scholar 

  10. Eshelby JD. The elastic field outside an ellipsoidal inclusion. Proc. Roy. Soc, 1959; A252: 561–569.

    MathSciNet  Google Scholar 

  11. Baxter WJ. The strength of metal matrix composites reinforced with randomly oriented discontinuous fibers. Metal Trans., 1992; 23A(9): 3045–3053.

    Google Scholar 

  12. Kang CG, Lee JH, Youn SW, Oh JK. An estimation of three-dimensional finite element crystal geometry model for the strength prediction of particle-reinforced metal matrix composites. Journal of Materials Processing Technology, 2005; 166(2): 173–182.

    Article  Google Scholar 

  13. Yang CC, Huang R. A two-phase model for predicting the compressive strength of concrete. Cement and Concrete Research, 1996; 26(10): 1567–1577.

    Article  Google Scholar 

  14. Karihaloo BL, Shao PF, Xiao QZ. Lattice modeling of the failure of particle composites. Engineering Fracture Mechanics, 2003; 70: 2385–2406.

    Article  Google Scholar 

  15. Lee SC. Prediction of concrete strength using artificial neural networks, Engineering Structures, 2003; 25: 849–857.

    Article  Google Scholar 

  16. Bobic I, Jovanović MT, Ilić N. Microstructure and strength of ZA-27-based composites reinforced with A12O3 particles. Materials Letters, 2003; 57: 1683–1688.

    Article  Google Scholar 

  17. Yi ST, Yang El, Choi JC. Effect of specimen sizes, specimen shapes, and placement directions on compressive strength of concrete. Nuclear Engineering and Design, 2006; 236(2): 115–127.

    Article  Google Scholar 

  18. Gesoglu Mehmet, Güneyisi Erhan, Özturan Turan. Effects of end conditions on compressive strength and static elastic modulus of very high strength concrete. Cement and Concrete Research, 2002; 32: 1545–1550.

    Article  Google Scholar 

  19. Cui JZ, Yang HY. A dual coupled method of boundary value problems of PDE with coefficients of small period. Int. J. Comp. Math., 1996; 14: 159–174.

    MATH  MathSciNet  Google Scholar 

  20. Hou TY, Wu XH. A multiscale finite element method for elliptic problems in composite materials and porous media. J. Comput. Phys., 1997; 134: 169–189.

    Article  MATH  MathSciNet  Google Scholar 

  21. Cui JZ, Shin TM, Wang YL. The two-scale analysis method for the bodies with small periodic configurations. Struct. Eng. Mech., 1999; 7(6): 601–614.

    Google Scholar 

  22. Oleinik OA, Shamaev AS, Yosifian GA. Mathematical Problems in Elasticity and Homogenization. North-Holland, Amsterdam, The Netherlands, 1992.

    Google Scholar 

  23. Jikov W, Kozlov SM, Oleinik OA. Homogenization of Differential Operators and Integral Functions. Springer, Berlin, Germany, 1994.

    Google Scholar 

  24. Li YY, Cui JZ. Two-scale analysis method for predicting heat transfer performance of composite materials with random grain distribution. Science in China Ser. A Mathematics, 2004; 47(Supp): 101–110.

    MATH  MathSciNet  Google Scholar 

  25. Li YY, Cui JZ. The multi-scale computational method for mechanics parameters of composite materials with random grain distribution. Journal of Composites Science & Technology, 2005; 65: 1447–1458.

    Article  Google Scholar 

  26. Yu Yan, Cui Junzhi, Han Fei. An effective computer generation method for the materials with random distribution of large numbers of heterogeneous grains. In: Computational Methods in Engineering and Science, Proceeding of the EPMESC X, Sanya, China, 2006, pp. 273.

    Google Scholar 

  27. Wittmann FH, Roelfstra PE, Sadouki H. Simulation and analysis of composite structures. Mater. Sci. Engng, 1984; 68(2): 239–248.

    Google Scholar 

  28. Wriggers P, Moftah SO. Mesoscale models for concrete: homogenisation and damage behaviour. Finite Elements in Analysis and Design, 2006; 42(7): 623–636.

    Article  Google Scholar 

  29. Bazant ZP, Tabbara MR, Kazemi MT, Pijaudier-Cabot G. Random particle model for fracture of aggregate or fiber composites. J. Engng. Mech., 1990; 116(8): 1686–1705.

    Article  Google Scholar 

  30. Schlangen E, van Mier JGM. Simple lattice model for numerical simulation of fracture of concrete materials and structures. Mater. Struct, 1992; 25(153): 534–542.

    Article  Google Scholar 

  31. Wang ZM, Kwan AKH, Chan HC. Mesoscopic study of concrete I: generation of random aggregate structure and finite element mesh. Comput. Struct., 1999; 70(5): 533–544.

    Article  MATH  Google Scholar 

  32. De Schutter G, Taerwe L. Random particle model for concrete based on Delaunay triangulation. Mater. Struct, 1993; 26(156): 67–73.

    Article  Google Scholar 

  33. van Mier JGM, van Vliet MRA. Influence of microstructure of concrete on size/scale effects in tensile fracture. Eng. Fract. Mech., 2003; 70(16): 2281–2306.

    Article  Google Scholar 

  34. George PL. Automatic Mesh Generation: Application to Finite Element Methods. Wiley, London, UK, 1991.

    MATH  Google Scholar 

  35. Cheung YK, Lo SH, Leung AYT. Finite Element Implementation. Blackwell, Oxford, UK, 1996.

    Google Scholar 

  36. Schorn H, Rode U. Numerical simulation of crack propagation from microcracking to fracture. Cem. Concr. Compos., 1991; 13(2): 87–94.

    Article  Google Scholar 

  37. Schlangen E, van Mier JGM. Simple lattice model for numerical simulation of fracture of concrete materials and structures. Mater. Struct, 1992; 25(153): 534–542.

    Article  Google Scholar 

  38. Baalbaki W, Benmokrane B, Chaallal O, Aitcin PC. Influence of coarse aggregate on elastic properties of high performance concrete. ACI Materials Journal, 1991; 88(5): 499–503.

    Google Scholar 

  39. Yang CC, Huang R. A two-phase model for predicting the compressive strength of concrete. Cement and Concrete Research, 1996; 26(10): 1567–1577.

    Article  Google Scholar 

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Authors and Affiliations

  1. Academy of Mathematics and System Sciences, CAS, Beijing, 100080, China

    Junzhi Cui & X. G. Yu

  2. School of Science, Northwestern Polytechnical University, Xi’an, 710072, China

    Yan Yu

Authors
  1. Junzhi Cui
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  2. X. G. Yu
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  3. Fei Han
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  4. Yan Yu
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© 2007 Tsinghua University Press & Springer

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Cui, J., Yu, X.G., Han, F., Yu, Y. (2007). Statistical Two-Scale Method for Strength Prediction of Composites with Random Distribution and Its Applications. In: Computational Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75999-7_6

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