An algorithm for computing the effective linear elastic properties of heterogeneous materials: three-dimensional results for composites with equal phase Poisson ratios. (English) Zbl 0881.73094


74E30 Composite and mixture properties
74S05 Finite element methods applied to problems in solid mechanics
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[1] Bergman, D. J.; Kantor, Y., Critical properties of an elastic fractal, Phys. Rev. Letts., 53, 511-514 (1984)
[2] Berryman, J. G., Long-wavelength propagation in composite elastic media II. Ellipsoidal inclusions, J. Acoust. Soc. Am., 68, 1820-1831 (1980) · Zbl 0455.73014
[3] Blumenfeld, R.; Torquato, S., Coarse-graining procedure to generate and analyze heterogeneous materials: Theory, Phys. Rev. E, 48, 4492-4500 (1993)
[4] Budiansky, B., On the elastic moduli of some heterogeneous materials, J. Mech. Phys. Solids, 13, 223-227 (1965)
[5] Bullard, J. W.; Garboczi, E. J.; Carter, W. C.; Fuller, E. R., Effect of applied stresses on void growth during sintering (1995), Unpublished
[6] Cook, R. D.; Malkus, D. S.; Plesha, M. E., Concepts and Applications of Finite Element Analysis (1989), Wiley: Wiley New York · Zbl 0696.73039
[7] Day, A. R.; Garboczi, E. J., Elastic moduli and electrical conductivity of a model interpenetrating-phase composite, J. Am. Ceram. Soc. (1995), To be submitted to · Zbl 0881.73094
[8] Day, A. R.; Snyder, K. A.; Garboczi, E. J.; Thorpe, M. F., Elastic moduli of a sheet containing circular holes, J. Mech. Phys. Solids, 40, 1031-1051 (1992)
[9] Day, A. R.; Jha, P.; Yang, Y., Elastic moduli of a two-dimensional isotropic elastic sheet with elliptical holes: Computer simulations and effective medium theory, J. Mech. Phys. Solids. (1996), To be submitted to
[10] Douglas, J. F.; Garboczi, E. J., Intrinsic viscosity and the polarizability of particles having a wide range of shapes, Adv. Chem. Phys. (1995), (in press)
[11] Garboczi, E. J.; Bentz, D. P., Computational materials science of cement-based materials, Mat. Res. Soc. Bull., 18, 50-54 (1993)
[12] Hashin, Z., Analysis of composite materials: A survey, J. Appl. Mech., 50, 481-505 (1983) · Zbl 0542.73092
[13] Hill, R., Elastic properties of reinforced solids: Some theoretical principles, J. Mech. Phys. Solids, 11, 357-372 (1963) · Zbl 0114.15804
[14] Pimienta, P.; Carter, W. C.; Garboczi, E. J., Cellular automaton algorithm for surface mass transport due to curvature gradients: Simulations of sintering, Comp. Mater. Sci., 1, 63-77 (1992)
[15] Polak, E., Computational Methods in Optimization (1971), Academic Press: Academic Press New York · Zbl 0257.90055
[16] Schwartz, L. M.; Crossley, P. A.; Banavar, J. R., Image-based models of porous media: Application to Vycor glass and carbonate rocks, Appl. Phys. Lett., 59, 3553-3555 (1991)
[17] Schwartz, L. M.; Auzerais, F.; Dunsmuir, J.; Martys, N. S.; Bentz, D. P.; Torquato, S., Transport and diffusion in three dimensional composite media, Physica A, 207, 28-36 (1993)
[18] Snyder, K. A.; Garboczi, E. J.; Day, A. R., The elastic moduli of simple two-dimensional isotropic composites: Computer simulation and effective medium theory, J. Appl. Phys., 72, 5948-5955 (1992)
[19] Thorpe, M. F.; Jasiuk, I., New results in the theory of elasticity for two-dimensional composites, (Proc. Roy. Soc. Lond. A, 438 (1994)), 531-544 · Zbl 0806.73042
[20] Thorpe, M. F.; Sen, P. N., Elastic moduli of two dimensional composite continua with elliptical inclusions, J. Acoust. Soc. Am., 77, 1674 (1985) · Zbl 0591.73003
[21] Torquato, S., Random heterogeneous media: Microstructure and improved bounds on effective properties, Appl. Mech. Rev., 44, 37-76 (1991)
[22] Watt, J. P.; Davies, G. F.; O’Connell, R. J., The elastic properties of composite materials, Rev. Geophys. Space Phys., 14, 541-563 (1976)
[23] Zallen, R.; Scher, H., Percolation on a continuum and the localization-delocalization transition in amorphous semiconductors, Phys. Rev. B, 4, 4471-4478 (1971)
[24] Zimmerman, R. W., Behavior of the Poisson ratio of a two-phase composite material in the high-concentration limit, Appl. Mech. Rev. (1995), (in press)
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