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Abstract

An alternate approach to Aboudi's Method of Cells [1], for a unified treatment of the micromechanical analysis of composite materials is presented. This approach retains the philosophy of Aboudi's Method of Cells but is indeed a finite element (FE) based approach. The equations of equilibrium are applied to a representative volume model (RVM) and a unified method of homogenization (UMH) of micromechanical effects is presented. The method as developed here can be applied to find the homogenized properties of any representative volume model that meets the requirements discussed. In this paper, we first apply it to the analysis of grinding wheels, a "three" constituent isotropic material, wherein the void is treated as a material having volume property only. The equations, which are derived for an orthotropic material, are then specialized to fiber reinforced composites and the results are compared to Aboudi's and others. Several interesting points arise regarding the FE "load vector" for specialists that typically work in developing FE methods and codes.

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References

1. Aboudi, J. 1991. Mechanics of Composite Materials: A Unified Micromechanical Approach, Amsterdam: Elsevier Science.

2. Addessio, F. L. and J. B. Aidun . 1995. "Analysis of Shock-Induced Damage in Fiber-Reinforced Composites," to appear in High Pressure Shock Compression of Solids, Vol. 3.

3. Aidun, J. B. and F. L. Addessio . 1995. "An Enhancement Cell Model with Nonlinear Elasticity," Journal of Composite Materials, in press.

4. Aboudi, J. , M.-J. Pindera and S. M. Arnold . 1993. "Thermoelastic Response of Metal Matrix Composites with Large-Diameter Fibers Subjected to Thermal Gradients," NASA report, NASA-TM-106344.

5. Aboudi, J. 1995. A seminar given at the Los Alamos National Laboratory on his approach to modeling composite materials including microstructure, July 27, 1995.

6. Teply, J. L. and J. N. Reddy . 1991. "A Unified Formulation of Micromechanical Models of Fiber-Reinforced Composites." in Inelastic Deformation of Composite Materials, IUTAM Symposium, Troy, New York, May 29-June 1, 1990, George J. Dvorak , ed., New York: Springer-Verlag.

7. Voigt, W. 1889. Wied. Ann., p. 573.

8. Reuss, von A. 1929. Ztschr.f.angew. Math. Mech., p. 49.

9. Hill, R. 1964. "Theory of Mechanical Properties of Fibre-Strengthened Materials: I. Elastic Behaviour," J. Mech. Phys. Solids, 12:199-212.

10.

10. Hashin, Z. 1979. "Analysis of Properties of Fiber Comosites with Anisotropic Constituents," J. App. Mech., 46:543.

11.

11. Hill, R. 1965. "A Self-Consistent Mechanics of Composite Materials," J. Mech. Phys. Solids, 13:213-222.

12.

12. Budiansky, B. J. 1965. "On the Elastic Moduli of Some Heterogeneous Materials," Mech. Phys. Solids, 13:223.

13.

13. Mori, T. and K. Tanaka . 1973. "Average Stress in Matrix and Average Elastic Energy of Materials with Misfitting Inclusions'" Acta Metallurgica, 21:571-574.

14.

14. Benveniste, Y. 1987. "A New Approach to the Application of Mori-Tanaka's Theory in Composite Materials," Mech. Mater. 36:147.

15.

15. Dvorak, G. J. 1991. Metal Matrix Composites: Mechanisms and Properties, Everett & Arsenault , eds., Academic Press.

16.

16. Lissenden, C. J. and C. T. Herakovich . 1993. "Comparison of Micromechanical Models for Elastic Properties," Space Engineering/Construction/Operations, p. 1309.

17.

17. Teply, J. L. and G. J. Dvorak . 1988. "Bounds on Overall Instantaneous Properties of Elastic-Plastic Composites," J. Mech. Phys. Solids, 36(1):29.

18.

18. Brockenbrough, J. R. , S. Suresh and H. A. Wienecke . 1991. "Deformation of Metal-Matrix Composites with Continuous Fibers: Geometrical Effects of Fiber Distribution and Shape," Acta Metall. Mater., 39(5):735.

19.

19. Allen, D. H. , R. H. Jones and J. G. Boyd . 1994. "Micromechanical Analysis of a Continuous Fiber Metal Matrix Composite Including the Effects of Matrix Viscoplasticity and Evolving Damage," J. Mech. Phys. Solids, 42(3):505.

20.

20. Luciano, R. and E. J. Barbero . 1994. "Formulas for the Stiffness of Composites with Periodic Microstructure," Int. J. Solids Structures, 31(21):P2933.

21.

21. Bathe, K.-J. 1982. Finite Element Procedures in Engineering Analysis, Englewood Cliffs, N.J.: Prentice-Hall Inc.

22.

22. Kriz, R. D. and W. W. Stinchcomb . 1979. "Elastic Moduli of Transversely Isotropic Graphite Fibers and Their Composites," Exp. Mech., 19:41.

23.

23. Tsai, S. W. and H. T. Hahn . 1989. Introduction to Composite Materials, Lancaster, PA: Technomic Publishing Co., Inc.

24.

24. ABAQUS Standard User's Manual, Vers. 5.4, Hibbitt, Karlsson, Sorensen, Inc. 1994.

An Alternate Unified Approach to the Micromechanical Analysis of Composite Materials

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