zbMATH — the first resource for mathematics

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
Full Text: DOI
[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J.W.; Garboczi, E.J.; Carter, W.C.; Fuller, E.R., Effect of applied stresses on void growth during sintering, (1995), Unpublished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 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 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, (), 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)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.