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References

Published online by Cambridge University Press:  05 February 2013

Leonid Berlyand
Affiliation:
Pennsylvania State University
Alexander G. Kolpakov
Affiliation:
Università degli Studi di Cassino e del Lazio Meridionale
Alexei Novikov
Affiliation:
Pennsylvania State University
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Print publication year: 2012

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References

Abbot, J.R., Tetlow, N., Graham, A.L., Altobell, S.A., Fukushima, E., Mondy, L.A. and Stephens, T.A.. (1991). Experimental observations of particle migration in concentrated suspensions: Couette flow. J. Rheol., 35:773–795.Google Scholar
Aboudi, J. (1991). Mechanics of Composite Material: A Unified Micromechanics Approach. Elsevier Science, Amsterdam.Google Scholar
Acrivos, A. and Chang, E.. (1986). A model for estimating transport quantities in two-phase materials. Phys. Fluids, 29(3):3–4.CrossRefGoogle Scholar
Adams, R.A. (1975). Sobolev Spaces. Academic Press, New York.Google Scholar
Ahlfors, L. (1979). Complex Analysis, 3rd ed. McGraw-Hill, New York.Google Scholar
Akhiezer, N.I. (1990). Elements of the Theory of Elliptic Functions.American Mathematical Society, Providence, RI.CrossRefGoogle Scholar
Almgren, R.F. (1985). An isotropic three-dimensional structure with Poisson's ratio = −1. J. Elasticity, 15:427–430.Google Scholar
Ambegaokar, V., Halperin, B.I. and Langer, J.S.. (1971). Hopping conductivity in disordered systems. Phys. Rev., B, 4(8):2612–2620.CrossRefGoogle Scholar
Andrianov, I.V., Danishevs'kyy, V.V. and Kalamkarov, A.L.. (2002). Asymptotic analysis of effective conductivity of composite materials with large rhombic fibres. Composite Struct., 56(33):229–234.CrossRefGoogle Scholar
Andrianov, I.V., Danishevs'kyy, V.V. and Tokarzewski, S.. (1996). Two-point quasifractional approximants for effective conductivity of a simple cubic lattice of spheres. Int. J. Heat Mass Transfer, 39(11):2349–2352.CrossRefGoogle Scholar
Andrianov, I.V., Starushenko, G.A., Danishevskiy, V.V. and Tokarzewski, S.. (1999). Homogenization procedure and Padé approximants for effective heat conductivity of a composite material with cylindrical inclusions having square cross-section. Proc. R. Soc. London, A, 455:3401–3413.CrossRefGoogle Scholar
Annin, B.D., Kalamkarov, A.L., Kolpakov, A.G. and Parton, V.Z.. (1993). Computation and Design of Composite Material and Structural Elements (in Russian).Nauka, Novosibirsk.Google Scholar
Aurenhammer, F. and Klein, R.. (1999). Voronoi diagrams. In: Handbook of Computational Geometry (Sack, J.R. and Urrutia, J., eds.), North Holland, Amsterdam, pp. 201–291.Google Scholar
Avellaneda, M. (1987). Optimal bounds and microgeometries for an elastic two-phase composite. SIAM J. Appl. Math., 47(6):1216–1228.CrossRefGoogle Scholar
Babǔshka, I., Anderson, B., Smith, P. and Levin, K.. (1999). Damage analysis of fiber composites. Part I. Statistical analysis on fiber scale. Comput. Methods Appl. Mech. Engng., 172:27–77.CrossRefGoogle Scholar
Bakhvalov, N.S. and Panasenko, G.P.. (1989). Homogenization: Averaging Processes in Periodic Media.Kluwer Academic Publishers, Dordrecht.CrossRefGoogle Scholar
Balberg, I. (1987). Recent developments in continuum percolation. Phil. Mag., B 30:991–1003.CrossRefGoogle Scholar
Batchelor, G.K. and O'Brien, R.W.. (1977). Thermal or electrical conduction through a granular material. Proc. R. Soc. London, A, 335:313–333.CrossRefGoogle Scholar
Batchelor, G.K. and Wen, C.S.. (1972). Sedimentation in a dilute dispersion of spheres. J. Fluid Mech., 52:245–268.CrossRefGoogle Scholar
Bendsøe, M.P. and Kikuchi, N.. (1988). Generating optimal topologies in structural design using a homogenization method. Comp. Meth. Appl. Mech. Engng, 71:95–112.CrossRefGoogle Scholar
Bendsøe, M.P. and Sigmund, O.. (2004). Topology Optimization.Springer-Verlag, Berlin.CrossRefGoogle Scholar
Bensoussan, A., Lions, J.-L. and Papanicolaou, G.. (1975). Sur quelques phénomènes asymptotiques d'évolution. Compt. Rend. Acad. Set Paris, Ser. A-B, 281(10):A317–A322.Google Scholar
Bensoussan, A., Lions, J.-L. and Papanicolaou, G.. (1978). Asymptotic Analysis for Periodic Structures.North Holland, Amsterdam.Google Scholar
Beran, M.J. (1968). Statistical Continuum Theories.John Wiley, New York.Google Scholar
Beran, M.J. and Molyneux, J.. (1966). Use of classical variational principles to determine bounds for the effective bulk modulus in heterogeneous media. Quart. Appl. Math., 24:107–118.CrossRefGoogle Scholar
Berdichevsky, V.L. (2009). Variational Principles of Continuum Mechanics.Springer-Verlag, Berlin.Google Scholar
Bergman, D.J. (1983). The dielectric constant of a composite material – a problem in classical physics. Phys. Reports, C43:378–407.Google Scholar
Bergman, D.J., Duering, E. and Murat, M.. (1990). Discrete network models for the low-field Hall effect near a percolation threshold: Theory and simulation. J. Stat. Phys., 1(58):1–43.CrossRefGoogle Scholar
Bergman, D.J. and Dunn, K.J.. (1992). Bulk effective dielectric constant of a composite with periodic micro-geometry. Phys. Rev. B, 45:13262–13271.CrossRefGoogle Scholar
Berlyand, L., Borcea, L. and Panchenko, A.. (2005). Network approximation for effective viscosity of concentrated suspensions with complex geometries. SIAM J. Math. Anal., 36(5):1580–1628.CrossRefGoogle Scholar
Berlyand, L., Gorb, Y. and Novikov, A.. (2005). Discrete network approximation for highly-packed composites with irregular geometry in three dimensions. In: Multiscale Methods in Science and Engineering (Engquist, B., Lotstedt, P. and Runborg, O., eds.), Springer-Verlag, Berlin, pp. 21–58.CrossRefGoogle Scholar
Berlyand, L., Gorb, Y. and Novikov, A.. (2009). Fictitious fluid approach and anomalous blow-up of the dissipation rate in a two-dimensional model of concentrated suspensions. Arch. Rational Mech. Anal., 193(3):585–622.CrossRefGoogle Scholar
Berlyand, L. and Kolpakov, A.. (2001). Network approximation in the limit of small interparticle distance of the effective properties of a high-contrast random dispersed composite. Arch. RationalMech. Anal., 159(3):179–227.CrossRefGoogle Scholar
Berlyand, L. and Kozlov, S.. (1992). Asymptotics of the homogenized moduli for the elastic chess-board composite. Arch. Rational Mech. Anal., 118(2):95–112.CrossRefGoogle Scholar
Berlyand, L. and Mityushev, V.. (2001). Generalized Clausius–Mossotti formula for random composite with circular fibers. J. Stat. Phys., 102(1/2):115–145.CrossRefGoogle Scholar
Berlyand, L. and Mityushev, V.. (2005). Increase and decrease of the effective conductivity of a two phase composite due to polydispersity. J. Stat. Phys., 118(3/4):479–507.CrossRefGoogle Scholar
Berlyand, L. and Novikov, A.. (2002). Error of the network approximation for densely packed composites with irregular geometry. SIAM J. Math. Anal., 34(2):385–408.CrossRefGoogle Scholar
Berlyand, L. and Promislow, K.. (1995). Effective elastic moduli of a soft medium with hard polygonal inclusions and extremal behavior of effective Poisson's ratio. J. Elasticity, 40(1):45–73.CrossRefGoogle Scholar
Berlyand, L.V. and Panchenko, A.. (2007). Strong and weak blow up of the viscous dissipation rates for concentrated suspensions. J. Fluid Mech., 578:1–34.CrossRefGoogle Scholar
Bhattacharya, K., Kohn, R.V. and Kozlov, S.. (1999). Some examples of nonlinear homogenization involving nearly degenerate energies. Proc. R. Soc. London, A, 455:567–583.CrossRefGoogle Scholar
Bollobás, B. (1998). Modern Graph Theory.Springer-Verlag, New York.CrossRefGoogle Scholar
Bonnecaze, R.T. and Brady, J.F.. (1991). The effective conductivity of random suspensions of spherical particles. Proc. R. Soc. London, Ser. A, 432:445–465.CrossRefGoogle Scholar
Borcea, L. (1998). Asymptotic analysis of quasi-static transport in high contrast conductive media. SIAM J. Appl. Math., 2(59):597–635.CrossRefGoogle Scholar
Borcea, L., Berryman, J.G. and Papanicolaou, G.. (1999). Matching pursuit for imaging high-contrast conductivity. Inverse Problems, 15:811–849.CrossRefGoogle Scholar
Borcea, L. and Papanicolaou, G.. (1998). Network approximation for transport properties of high contrast conductivity. Inverse Problems, 4(15):501–539.Google Scholar
Born, M. and Huang, K.. (1954). Dynamical Theory of Crystal Lattices.Oxford University Press, Oxford.Google Scholar
Bourgeat, A., Mikelic, A. and Wright, S.. (1994). Stochastic two-scale convergence in the mean and applications. J. Reine Angew. Math., 456:19–51.Google Scholar
Bourgeat, A. and Piatnitski, A.. (2004). Approximations of effective coefficients in stochastic homogenization. Ann. Inst. H. Poincaré, 40:153–165.CrossRefGoogle Scholar
Brady, J.F. (1993). The rheo logical behavior of concentrated colloidal suspensions. J. Chem. Phys., 99:567–581.CrossRefGoogle Scholar
Brady, J.F. and Bossis, G.. (1985). The rheology of concentrated suspensions of spheres in simple shear flow by numerical simulation. J. Fluid Mech., 155:105–129.CrossRefGoogle Scholar
Brodbent, S.R. and Hammerslay, J.M.. (1957). Percolation processes I. Crystals and mazes. Math. Proc. Cambridge Phil. Soc., 53:629–641.CrossRefGoogle Scholar
Broutman, L.J. and Krock, R.H., eds. (1974). Composite Materials. Vol. 1-8. Academic Press, New York.
Brown, W.F. (1956). Dielectrics.Springer-Verlag, Berlin.CrossRefGoogle Scholar
Bruno, O. (1991). The effective conductivity of strongly heterogeneous composites. Proc. R. Soc. London, A, 433:353–381.CrossRefGoogle Scholar
B¨rger, R. and Wendland, W.L.. (2001). Sedimentation and suspension flows: historical perspective and some recent developments. J. Engng. Math., 41(2/3):101–1 16.CrossRefGoogle Scholar
Burkill, J.C. (2004). The Lebesgue Integral.Cambridge University Press, Cambridge.Google Scholar
Caillerie, D. (1978). Sur la comportement limite d'une inclusion mince de grande rigidité dans un corps élastique. Compt. Rend. Acad. Set Paris, Ser. A., 287:675–678.Google Scholar
Carreau, P.J. and Cotton, F.. (2002). Rheological properties of concentrated suspensions. In: Transport Processes in Bubbles, Drops and Particles (De Kee, D. and Chhabra, R.P., eds.), Taylor & Francis, London.Google Scholar
Chang, Ch. and Powell, R.L.. (1994). Effect of particle size distribution on the rheology of a concentrated bimodal suspension. J. Rheol., 38:85–98.CrossRefGoogle Scholar
Chen, H.-S. and Acrivos, A.. (1978). The effective elastic moduli materials containing spherical inclusions at non-dilute concentration. Int. J. Solids Struct., 14:349–364.Google Scholar
Cheng, H. and Greengard, L.. (1997). On the numerical evaluation of electrostatic fields in a dense random dispersions of cylinders. J. Comput. Phys., 136:626–639.CrossRefGoogle Scholar
Cheng, H. and Greengard, L.. (1998). A method of images for the evaluation of electrostatic fields in a system of closely spaced conducting cylinders. SIAM J. Appl. Math., 50:122–141.CrossRefGoogle Scholar
Cherkaev, A.V. (2000). Variational Methods for Structural Optimization.Springer-Verlag, Berlin.CrossRefGoogle Scholar
Chinh, Ph.D. (1997). Overall properties of planar quasisymmetric randomly inhomogeneous media: Estimates and cell models. Phys. Rev. E, 56:652–660.CrossRefGoogle Scholar
Chou, T.-W. and Ko, F.K., eds. (1989). Textile Structural Composites.Elsevier Science, Amsterdam.
Christensen, R.M. (1979). Mechanics of Composite Materials.John Wiley, New York.Google Scholar
Chung, J.W., De Hosson, J.Th.M. and van der Giessen, E.. (1996). Fracture of a disordered 3-D spring network: A computer simulation methodology. Phys. Rev. B, 54:15094–15100.CrossRefGoogle Scholar
Clerc, J.P., Giraud, G., Laugier, J.M. and Luck, J.M.. (1990). The electrical conductivity of binary disordered systems, percolation clusters, fractals and related models. Adv. Phys., 39(3):191–309.CrossRefGoogle Scholar
Courant, R.S. and Hilbert, D.. (1953). Methods of Mathematical Physics.John Wiley, New York.Google Scholar
Coussot, P. (2002). Flows of concentrated granular mixtures. In: Transport Processes in Bubbles, Drops and Particles (Chhabra, R.P. and De Kee, D., eds.), Taylor & Francis, London, pp. 291–315.Google Scholar
Craster, R.V. and Obnosov, Yu.V.. (2004). A three-phase tessellation: Solution and effective properties. Proc. R. Soc. London, A, 460:1017–1037.CrossRefGoogle Scholar
Curtin, W.A. and Scher, H.. (1990a). Brittle fracture in disordered materials: A spring network model. J. Mater. Res., 5:535–553.CrossRefGoogle Scholar
Curtin, W.A. and Scher, H.. (1990b). Mechanical modeling using a spring network. J. Mater. Res., 5:554–562.CrossRefGoogle Scholar
Del Maso, G. (1993). An Introduction to Γ-Convergence.Birkhäuser, Boston.CrossRefGoogle Scholar
Diaz, A.R. and Kikuchi, N.. (1992). Solutions to shape and topology eigenvalue optimization problems using a homogenization method. Int. J. Num. Meth. Engng, 35:1487–1502.CrossRefGoogle Scholar
Dieudonne, J.A. (1969). Treatise on Analysis.Academic Press, New York.Google Scholar
Ding, J., Warriner, H.E. and Zasadzinski, J.A.. (2002). Viscosity of two-dimensional suspensions. Phys. Rev. Lett., 88(16):168102.1-168102.4.CrossRefGoogle ScholarPubMed
Dobrodumov, A.M. and El'yashevich, A.M.. (1973). Simulation of brittle fracture of polymers by a network model in the Monte Carlo method. Sov. Solid State Phys., 15:1259–1260.Google Scholar
Doyle, W.T. (1978). The Clasius–Mossotti problem for cubic arrays of spheres. J. Appl. Phys., 49:795–797.CrossRefGoogle Scholar
Drummon, J.E. and Tahir, M.I.. (1984). Laminar viscous flow through regular arrays of parallel solid cylinders. Int. J. Multiphase Flow, 10:515–540.CrossRefGoogle Scholar
Drygaś, P. and Mityushev, V.. (2009). Effective conductivity of unidirectional cylinders with interfacial resistance. Quarterly J. Mech. Appl. Math., 62(3):235–262.CrossRefGoogle Scholar
Dykhne, A.M. (1971). Conductivity of a two-dimensional two-phase system. Sov. Phys., 32(63):63–65.Google Scholar
Einstein, A. (1906). Eine neue Bestimmung der Molekuldimensionen. Ann. Phys., 19:289–306.CrossRefGoogle Scholar
Ekeland, I. and Temam, R.. (1976). Convex Analysis and Variational Problems.North Holland, Amsterdam.Google Scholar
Evans, L.C. and Gangbo, W.. (1999). Differential equation methods for the Monge–Kantorovich mass transfer problem. Mem. Amer. Math. Soc., 137(653):viii+66.Google Scholar
Evans, L.C. and Gariepy, R.F.. (1992). Measure Theory and Fine Properties of Functions.CRC Press, Boca Raton, FL.Google Scholar
Feng, N.A. (1985). Percolation properties of granular elastic networks in two dimensions. Phys. Rev. B, 32(1):510–513.CrossRefGoogle ScholarPubMed
Feng, N.A. and Acrivos, A.. (1985). On the viscosity of concentrated suspensions of solid spheres. Chem. Engng Sci., 22:847–853.Google Scholar
Flaherty, J.E. and Keller, J.B.. (1973). Elastic behavior of composite media. Comm. Pure Appl. Math., 26:565–580.CrossRefGoogle Scholar
Flory, P.J. (1941). Molecular size distribution in three dimensional polymers. I. Gelation. J. Amer. Chem. Soc., 63:3083–3090.CrossRefGoogle Scholar
Fox, L. (1964). An Introduction to Numerical Linear Algebra.Clarendon Press, Oxford.Google Scholar
Francfort, G.A. and Murat, F.. (1986). Homogenization and optimal bounds in linear electricity. Arch. Rational Mech. Anal., 94(4):307–334.CrossRefGoogle Scholar
Frenkel, N.A. and Acrivos, A.. (1967). On the viscosity of concentrated suspension of solid spheres. Chem. Engng Sci., 22:847–853.CrossRefGoogle Scholar
Friis, E.A., Lakes, R.S. and Park, J.B.. (1988). Negative Poisson's ratio polymeric and metallic foams. J. Mater. Sci., 23:4406–4414.CrossRefGoogle Scholar
Gakhov, F.D. (1966). Boundary Value Problems.Pergamon Press, Oxford.Google Scholar
Garboczi, E.J. and Douglas, J.F.. (1996). Intrinsic conductivity of objects having arbitrary shape and conductivity. Phys. Rev. E, 53(6):6169–6180.CrossRefGoogle ScholarPubMed
Gaudiello, A. and Kolpakov, A.G.. (2011). Influence of non degenerated joint on the global and local behavior of joined rods. Int. J. Engng. Sci., 49(3):295–309.CrossRefGoogle Scholar
Good, I.J. (1949). The number of individuals in a cascade process. Math. Proc. Cambridge Phil. Soc., 45:360–363.CrossRefGoogle Scholar
Goto, H. and Kuno, H.. (1984). Flow of suspensions containing particles of two different sizes through a capillary tube. II. Effect of the particle size ratio. J. Rheol., 28:197–205.CrossRefGoogle Scholar
Graham, A.L. (1981). On the viscosity of a suspension of solid particles. Appl. Sci. Res., 37:275–286.CrossRefGoogle Scholar
Greengard, L. and Lee, J.-Y.. (2006). Electrostatics and heat conduction in high contrast composite materials. J. Comput. Phys., 211(1):64–76.CrossRefGoogle Scholar
Greengard, L. and Moura, M.. (1994). On the numerical evaluation of electrostatic fields in composite materials. Acta Numerica, 3:379–410.CrossRefGoogle Scholar
Grigolyuk, E.I. and Filshtinskij, L.A.. (1972). Periodical Piecewise Homogeneous Elastic Structures (in Russian).Nauka, Moscow.Google Scholar
Grimet, G. (1992). Percolation.Springer-Verlag, Berlin.Google Scholar
Gupta, P.K. and Cooper, A.R.. (1990). Topologically disordered networks of rigid polytopes. J. Non-Crystal. Solids, 123(14):14–21.CrossRefGoogle Scholar
Halperin, B.I., Feng, S. and Sen, P.N.. (1985). Difference between lattice and continuum percolation transport exponents. Phys. Rev. Lett., 54:2391–2394.CrossRefGoogle Scholar
Happel, J. (1959). Viscous flow relative to arrays of cylinders. AIChE J., 5:174–177.CrossRefGoogle Scholar
Hasimoto, H. (1959). On the periodic fundamental solutions of the Stokes equations and their application to viscous flow past a cubic array of spheres. J. Fluid Mech., 5:317–328.CrossRefGoogle Scholar
Haug, E.J., Choi, K.K. and Komkov, V.. (1986). Design Sensitivity Analysis of Structural Systems.Academic Press, Orlando, FL.Google Scholar
Herrmann, H.J., Hansen, A. and Roux, S.. (1989). Fracture of disordered, elastic lattices in two dimensions. Phys. Rev. B, 39:637–648.CrossRefGoogle ScholarPubMed
Hill, R. (1963). Elastic properties of reinforced solids: Some theoretical principles. J. Mech. Phys. Solids, 11:357–372.CrossRefGoogle Scholar
Hill, R. (1996). Characterization of thermally conductive epoxy composite fillers. Proc. Technical Program “Emerging Packing Technology”,Surface Mount Tech. Symp., pp. 125–131.Google Scholar
Hill, R.F. and Supancic, P.H.. (2002). Thermal conductivity of platelet-filled polymer composite. J. Am. Cer. Soc., 85:851–857.CrossRefGoogle Scholar
Hinsen, K. and Felderhof, B.U.. (1992). Dielectric constant of a suspension of uniform spheres. Phys. Rev. B, 46(20):12955–12963.CrossRefGoogle ScholarPubMed
Hrennikoff, A. (1941). Solution of a problem of elasticity by the framework method. J. Appl. Mech., 8:169–175.Google Scholar
Jabin, P.-E. and Otto, F.. (2004). Identification of the dilute regime in particle sedimentation. Commun. Math. Phys., 250:415–432.CrossRefGoogle Scholar
Jeffrey, D.J. and Acrivos, A.. (1976). The rheological properties of suspensions of rigid particles. AIChE J., 22:417–432.CrossRefGoogle Scholar
Jikov, V.V., Kozlov, S.M. and Oleinik, O.A.. (1994). Homogenization of Differential Operators and Integral Functionals.Springer-Verlag, Berlin.CrossRefGoogle Scholar
Kalamkarov, A.L. and Kolpakov, A.G.. (1996). On the analysis and design of fiber reinforced composite shells. Trans. ASME. J. Appl. Mech., 63(4):939–945.CrossRefGoogle Scholar
Kalamkarov, A.L. and Kolpakov, A.G.. (1997). Analysis, Design and Optimization of Composite Structures.John Wiley, Chichester.Google Scholar
Karal, F.C. Jr. and Keller, J.B.. (1966). Effective dielectric constant, permeability, and conductivity of a random medium and the velocity and attenuation coefficient of coherent waves. J. Math. Phys., 7:661–670.Google Scholar
Kato, T. (1976). Perturbation Theory for Linear Operators.Springer-Verlag, New York.Google Scholar
Keller, J.B. (1963). Conductivity of a medium containing a dense array of perfectly conducting spheres or cylinders or nonconducting cylinders. J. Appl. Phys., 4(34):991–993.CrossRefGoogle Scholar
Keller, J.B. (1964). A theorem on the conductivity of a composite medium. J. Math. Phys., 5:548–549.CrossRefGoogle Scholar
Keller, J.B. (1987). Effective conductivity of a periodic composite composed of two very unequal conductors. J. Math. Phys., 10(28):2516–2520.CrossRefGoogle Scholar
Keller, J.B. and Sachs, D.. (1964). Calculations of conductivity of a medium containing cylindrical inclusions. J. Appl. Phys., 35:537–538.CrossRefGoogle Scholar
Kellomaki, M., Astrom, J. and Timonen, J.. (1996). Rigidity and dynamics of random spring networks. Phys. Rev. Lett., 77:2730–2733.CrossRefGoogle ScholarPubMed
Kelly, A. and Rabotnov, Yu.N., eds. (1988). Handbook of Composites.North Holland, Amsterdam.
Kesten, H. (1992). Percolation Theory for Mathematicians.Birkhäuser, Boston.Google Scholar
Kolmogorov, A.N. and Fomin, S.V.. (1970). Introductory Real Analysis.Prentice Hall, Englewood Cliffs, NJ.Google Scholar
Kolpakov, A.A. (2007). Numerical verification of existence of the energy-concentration effect in a high-contrast high-filled composite material. J. Engng Phys. Thermophys., 80(4):812–819.CrossRefGoogle Scholar
Kolpakov, A.A. and Kolpakov, A.G.. (2007). Asymptotics of the capacity of a system of closely placed bodies. Tamm's shielding effect and network models. Doklady Phys., 415(2):188–192.Google Scholar
Kolpakov, A.A. and Kolpakov, A.G.. (2010). Capacity and Transport in Contrast Composite Structures: Asymptotic Analysis and Applications.CRC Press, Boca Raton, FL.Google Scholar
Kolpakov, A.G. (1987). Averaged characteristics of thermoelastic frames. Izvestiay of the Academy of Science of the USSR. Mechanics of Solids, 22(6):53–61.Google Scholar
Kolpakov, A.G. (1985). Determination of the average characteristics of elastic frameworks. J. Appl. Math. Mech., 49:739–745.CrossRefGoogle Scholar
Kolpakov, A.G. (1988). Asymptotics of the first boundary value problem for an elliptic equation in a region with a thin covering. Siberian Math. J., 6:74–84.Google Scholar
Kolpakov, A.G. (1992). Glued bodies. Differential Equations, 28(8):1131–1139.Google Scholar
Kolpakov, A.G. (2004). Stressed Composite Structures: Homogenized Models for Thin-Walled Nonhomogeneous Structures with Initial Stresses.Springer-Verlag, Berlin.CrossRefGoogle Scholar
Kolpakov, A.G. (2005). Asymptotic behavior of the conducting properties of high-contrast media. J. Appl. Mech. Tech. Phys., 46(3):412–422.CrossRefGoogle Scholar
Kolpakov, A.G. (2006a). The asymptotic screening and network models. J. Engng Phys. Thermophys., 2:39–47.Google Scholar
Kolpakov, A.G. (2006b). Convergence of solutions for a network approximation of the two-dimensional Laplace equation in a domain with a system of absolutely conducting disks. Comp. Math. Math. Phys., 46(9):1682–1691.CrossRefGoogle Scholar
Kolpakov, A.G. (2011). Influence of non degenerated joint on the global and local behavior of joined plates. Int. J. Engng. Sci., 49(11):1216–1231.CrossRefGoogle Scholar
Koplik, J. (1982). Creeping flow in two-dimensional networks. J. Fluid Mech., 119:219–247.CrossRefGoogle Scholar
Kozlov, S.M. (1978). Averaging of random structures (in Russian). Doklady Acad. Nauk SSSR, 241(5):1016–11019.Google Scholar
Kozlov, S.M. (1980). Averaging of random operators. Math. USSR Sbornik, 37:167–180.CrossRefGoogle Scholar
Kozlov, S.M. (1989). Geometric aspects of averaging. Russian Math. Surv., 2(44):91–144.CrossRefGoogle Scholar
Kozlov, S.M. (1992). On the domain of variations of apparent added masses, polarization and effective characteristics of composites. J. Appl. Math. Mech., 56(1):102–107.CrossRefGoogle Scholar
Kuchling, H. (1980). Physics.VEB Fachbuchverlag, Leipzig.Google Scholar
Kun, F. and Herrmann, H.. (1996). A study of fragmentation processes using a discrete element method. Comput. Meth. Appl. Mech. Engng, 138:3–18.CrossRefGoogle Scholar
Ladd, A.J.C. (1997). Sedimentation of homogeneous suspensions of non-Brownian spheres. Phys. Fluids, 9(3):491–499.CrossRefGoogle Scholar
Ladyzhenskaya, O.A. and Ural'tseva, N.N.. (1968). Linear and Quasilinear Elliptic Equations.Academic Press, New York.Google Scholar
Lakes, R. (1991). Deformation mechanisms of negative Poisson's ratio materials: Structural aspects. J. Mater. Sci., 26:2287–2292.CrossRefGoogle Scholar
Lamb, H. (1991). Hydrodynamics.Dover, New York.Google Scholar
Landauer, R. (1978). Electrical conductivity in inhomogeneous media. In: Electrical Transport and Optical Properties of Inhomogeneous Media (Garland, J.C., Tanner, D.B., eds.), American Institute of Physics. Woodbury, New York, pp. 2–43.Google Scholar
Leal, G. (1992). Laminar Flow and Convective Transport Processes: Scaling Principles and Asymptotic Analysis.Butterworth-Heinemann, Amsterdam.Google Scholar
Leighton, D. and Acrivos, A.. (1987). Measurement of shear-induced self-diffusion in concentrated suspensions of spheres. J. FluidMech., 177:109–131.CrossRefGoogle Scholar
Lenczner, M. (1997). Homogénéisation d'un circuit électrique. C.R. Acad. Sci. Paris, Série II B, 324(9):537–542.Google Scholar
Lieberman, G.M. (1988). Boundary regularity for solutions of degenerate elliptic equations. Nonlinear Anal., 12(11):1203–1219.CrossRefGoogle Scholar
Limat, L. (1988). Percolation and Cosserat elasticity: Exact results on a deterministic fractal. Phys. Rev., B, 37:672–675.CrossRefGoogle ScholarPubMed
Lions, J.-L. (1978). Notes on some computational aspects of the homogenization method in composite materials. In: Computational Methods in Mathematics, Geophysics and Optimal Control,Nauka, Novosibirsk, pp. 5–19.Google Scholar
Lions, J.-L. and Magenes, E.. (1972). Non-Homogeneous Boundary Value Problems and Applications, Vol. 1, 2. Springer-Verlag, Berlin.Google Scholar
Lipton, R. (1994). Optimal bounds on the effective elastic tensor for orthotropic composites. Proc. R. Soc. London, A, 444:399–410.CrossRefGoogle Scholar
Love, A.E.H. (1929). A Treatise on the Mathematical Theory of Elasticity.Oxford University Press, Oxford.Google Scholar
Lu, J.-K. (1995). Complex Variable Methods in Plane Elasticity.World Scientific, Singapore.CrossRefGoogle Scholar
Lévy, T. (1986). Application of homogenization to the study of a suspension of force-free particles. In: Trends in Applications of Pure Mathematics to Mechanics. Lecture Notes in Physics 249, Springer-Verlag, Berlin, pp. 349–353.CrossRefGoogle Scholar
Makaruk, S.F., Mityushev, V.V. and Rogosin, S.V.. (2006). An optimal design problem for two-dimensional composite materials. A constructive approach. In: Analytic Methods of Analysis and Differential Equations. AMADE 2003 (Kilbas, A.A. and Rogosin, S.V., eds.). Cambridge Scientific, Cottenham, Cambridge, pp. 153–167.Google Scholar
Markov, K.Z. (2000). Elementary micromechanics of heterogeneous media. In: Heterogeneous Media: Micromechanics Modeling Methods and Simulation (Markov, K. and Preziosi, L., eds.), Birkhauser, Basel, pp. 1–162.CrossRefGoogle Scholar
Maury, B. (1999). Direct simulations of 2D fluid-particle flows in biperiodic domains. J. Comput. Phys., 156(2):325–351.CrossRefGoogle Scholar
Maxwell, J.C. (1873). Treatise on Electricity and Magnetism.Clarendon Press, Oxford.Google Scholar
McAllister, L.E. and Lachman, W.L.. (1983). Multidirectional carbon-carbon composites. In: Handbook of Composites, Vol. 4. Fabrication of Composites (Kelly, A. and Mileiko, S.T., eds.), North Holland, Amsterdam, pp. 109–176.Google Scholar
McKenzie, D.R., McPhedran, R.C. and Derrik, G.H.. (1978). The conductivity of a lattice of spheres II. The body centered and face centered lattices. Proc. R. Soc. London, A, 362:211–232.CrossRefGoogle Scholar
McPhedran, R. (1986). Transport property of cylinder pairs and of the square array of cylinders. Proc. R. Soc. London, A, 408:31–43.CrossRefGoogle Scholar
McPhedran, R., Poladian, L. and Milton, G.W.. (1988). Asymptotic studies of closely spaced, highly conducting cylinders. Proc. R. Soc. London, A, 415:195–196.CrossRefGoogle Scholar
McPhedran, R.C. and McKenzie, D.R.. (1978). The conductivity of a lattice of spheres I. The simple cubic lattice. Proc. R. Soc. London, A, 359:45–63.CrossRefGoogle Scholar
McPhedran, R.C. and Milton, G.W.. (1987). Transport properties of touching cylinder pairs and of a square array of touching cylinders. Proc. R. Soc. London, A411:313–326.CrossRefGoogle Scholar
Meester, R. and Roy, R.. (1992). Continuum Percolation.Cambridge University Press, Cambridge.Google Scholar
Melrose, D.B. and McPhedran, R.C.. (1991). Electromagnetic Processes in Dispersive Media.Cambridge University Press, Cambridge.CrossRefGoogle Scholar
Meredith, R.E. and Tobias, C.W.. (1960). Resistance to potential flow through a cubical array of spheres. J. Appl. Physics, 31:1270–1273.CrossRefGoogle Scholar
Mertensson, E. and Gafvert, U.. (2003). Three-dimensional impedance networks for modeling frequency dependent electrical properties of composite materials. J. Phys. D: Appl. Phys., 36:1864–1872.CrossRefGoogle Scholar
Mertensson, E. and Gafvert, U.. (2004). A three-dimensional network model describing a non-linear composite material. J. Phys. D: Appl. Phys., 37:112–119.CrossRefGoogle Scholar
Michel, J.C., Moulinec, H. and Suquet, P.. (2000). A computational method based on augmented Lagrangians and fast Fourier transforms for composites with high contrast. Comp. Model. Engng Sci., 1(2):79–88.Google Scholar
Michel, J.C., Moulinec, H. and Suquet, P.. (2002). A computational scheme for linear and non-linear composites with arbitrary phase contrast. Int. J. Numer. Meth. Engng., 52:139–160.CrossRefGoogle Scholar
Milton, G.M. (1992). Composite materials with Poisson's ratios close to —1. J. Mech. Phys. Solids, 40:1105–1137.CrossRefGoogle Scholar
Milton, G.W. (2002). The Theory of Composites.Cambridge University Press, Cambridge.CrossRefGoogle Scholar
Mityushev, V. (1993). Plane problem for the steady heat conduction of a material with circular inclusions. Arch. Mech., 45(2):211–215.Google Scholar
Mityushev, V. (1994). Solution of the Hilbert boundary value problem for a multiply connected domain. Slupskie Prace Mat.-Przyr., 9a:33–67.Google Scholar
Mityushev, V. (1997a). A functional equation in a class of analytic functions and composite materials. Demostratio Math., 30:63–70.Google Scholar
Mityushev, V. (1997b). Functional equations and their applications in the mechanics of composites. Demonstratio Math., 30(1):64–70.Google Scholar
Mityushev, V. (1998). Hilbert boundary value problem for multiply connected domains. Complex Variables, 35:283–295.Google Scholar
Mityushev, V. (1999). Transport properties of two-dimensional composite materials with circular inclusions. Proc. R. Soc. London, A455:2513–2528.CrossRefGoogle Scholar
Mityushev, V. (2001). Transport properties of doubly periodic arrays of circular cylinders and optimal design problems. Appl. Math. Optim., 44:17–31.CrossRefGoogle Scholar
Mityushev, V. (2005). R-linear problem on the torus and its application to composites. Complex Variables, 50(7–10):621–630.Google Scholar
Mityushev, V. (2009). Conductivity of a two-dimensional composite containing elliptical inclusions. Proc. R. Soc. A, 465:2991–3010.CrossRefGoogle Scholar
Mityushev, V. and Adler, P.M.. (2002a). Longitudinal permeability of a doubly periodic rectangular array of cylinders. I. Z. Angew. Math. Mech., 82:335–345.3.0.CO;2-D>CrossRefGoogle Scholar
Mityushev, V. and Adler, P.M.. (2002b). Longitudinal permeability of a doubly periodic rectangular array of cylinders. II. An arbitrary distribution of cylinders inside the unit cell. Z. Angew. Math. Phys., 53:486–517.CrossRefGoogle Scholar
Mityushev, V., Pesetskaya, E. and Rogosin, S.. (2008). Analytical methods for heat conduction in composites and porous media in cellular and porous materials. In: Cellular and Porous Materials: Thermal Properties Simulation and Prediction (Ochsner, A., Murch, G. and de Lemos, M., eds.), Wiley-VCH, Weinheim.Google Scholar
Mityushev, V. and Rogozin, S.V.. (2000). Constructive Methods for Linear and Nonlinear Boundary Value Problems of Analytic Function Theory.Chapman & Hall/CRC, Boca Raton, FL.Google Scholar
Mityushev, V.V. (1997). Transport properties of doubly-periodic arrays of circular cylinders. Z Angew. Math. Mech., 77:115–120.CrossRefGoogle Scholar
Mizohata, S. (1973). The Theory of Partial Differential Equations.Cambridge University Press, Cambridge.Google Scholar
Molchanov, S. (1994). Lectures on random media. In: Lectures on Probability Theory (Bakry, D., Gill, R.D. and Molchanov, S.A., eds.), Springer-Verlag, Berlin, pp. 242–411.Google Scholar
Molyneux, J. (1970). Effective permittivity of a polycrystalline dielectric. J. Math. Phys., 11(4):1172–1184.CrossRefGoogle Scholar
Movchan, A.B., Movchan, N.V. and Poulton, C.G.. (2002). Asymptotic Models of Fields in Dilute and Densely Packed Composites.Imperial College Press, London.CrossRefGoogle Scholar
Nemat-Nasser, S. and Hori, M.. (1993). Micromechanics. Elsevier Science, Amsterdam.Google Scholar
Nettelblad, B., Mårtensson, E., Önneby, C., Gäfvert, U. and Gustafsson, A.. (2003). Two percolation thresholds due to geometrical effects: Experimental and simulated results. J. Phys. D:Appl. Phys., 36(4):399–405.CrossRefGoogle Scholar
Newman, M.E.J. (2003). The structure and functions of complex networks. SIAM Rev., 45(2): 167-256.CrossRefGoogle Scholar
Nicorovici, N.A. and McPhedran, R.C.. (1996). Transport properties of arrays of elliptical cylinders. Phys. Rev. E, 54:1945–1957.Google ScholarPubMed
Noor, A.K. (1988). Continuum modeling for repetitive structures. Appl. Mech. Rev., 41(7): 285–296.CrossRefGoogle Scholar
Nott, P.R. and Brady, J.F.. (1994). Pressure-driven flow of suspensions: Simulation and theory. J. Fluid Mech., 275:157–199.CrossRefGoogle Scholar
Novikov, A. (2009). A discrete network approximation for effective conductivity of non-ohmic high-contrast composites. Commun. Math. Sci., 7(3):719–740.CrossRefGoogle Scholar
Novikov, V.V. and Friedrich, Chr.. (2005). Viscoelastic properties of composite materials with random structure. Phys. Rev. E, 72:021506-1-021506-9.CrossRefGoogle ScholarPubMed
Novozilov, V.V. (1970). On the relationship between average values of the stress tensor and strain tensor in statistically isotropic elastic bodies. Appl. Math. Mech., 34(1):67–74.Google Scholar
Nunan, K.C. and Keller, J.B.. (1984a). Effective elasticity tensor for a periodic composite. J. Mech. Phys. Solids, 32:259–280.CrossRefGoogle Scholar
Nunan, K.C. and Keller, J.B.. (1984b). Effective velocity of aperiodic suspension. J. Fluid Mech., 142:269–287.CrossRefGoogle Scholar
Oleinik, O.A., Shamaev, A.S. and Yosifian, G.A.. (1962). Mathematical Problems in Elasticity and Homogenization.North Holland, Amsterdam.Google Scholar
Ostoja-Starzewski, M. (2006). Material spatial randomness – from statistical to representative volume element. Probab. Eng. Mech., 21(2):112–132.CrossRefGoogle Scholar
Panasenko, G.P. (2005). Multi-Scale Modeling for Structures and Composites.Springer-Verlag, Berlin.Google Scholar
Panasenko, G.P. and Virnovsky, G.. (2003). Homogenization of two-phase flow: high contrast of phase permeability. C.R. Mecanique, 331:9–15.CrossRefGoogle Scholar
Papanicolaou, G.C. (1995). Diffusion in random media. In: Surveys in Applied Mathematics (Keller, J.B., McLaughlin, D. and Papanicolaou, G., eds.), Plenum Press, New York, pp. 205–255.CrossRefGoogle Scholar
Papanicolaou, G.C. and Varadhan, S.R.S.. (1981). Boundary value problems with rapidly oscillating random coefficients. Seria Coll. Janos Bolyai, 27:835–873.Google Scholar
Perrins, W.T., McPhedran, R.C. and McKenzie, D.R.. (1979). Transport properties of regular arrays of cylinders. Proc. R. Soc. London, A, 369:207–225.CrossRefGoogle Scholar
Pesetskaya, E.V (2005). Effective conductivity of composite materials with random positions of cylindrical inclusions: Finite number inclusions in the cell. Applic. Anal., 84(8):843–865.CrossRefGoogle Scholar
Peterseim, D. (2010). Triangulating a system of disks. In: Proc. 26th Eur. Workshop Comp. Geometry, pp. 241–244.Google Scholar
Peterseim, D. (2012). Robustness of finite elements simulation in densely packed random particle composites. Networks Meter. Media, 7(1):113–126.Google Scholar
Pham Huy, H. and Sanchez-Palencia, E.. (1974). Phénomènes de transmission à travers des couches minces de conductivité élevée. J. Math. Anal. Appl., 47:284—309.Google Scholar
Phillips, R.J., Armstrong, R.C., Brown, R.A., Graham, A.L. and Abbot, J.R.. (1992). A constitutive equation for concentrated suspensions that accounts for shear-induced particle migration. Phys. Fluids, A, 4:30–40.CrossRefGoogle Scholar
Poincaré, H. (1886). Sur les integrals irregulieres des equations lineaires. Ada Math., 8:295–344.Google Scholar
Poslinski, A.J., Ryan, M.E., Gupta, R.K., Seshadri, S.G. and Frechette, F.J.. (1988). Rheological behavior of filled polymeric systems II. The effect of bimodal size distribution of particulates. J. Rheol., 32:751–771.CrossRefGoogle Scholar
Prager, S. (1963). Diffusion and viscous flow in concentrated suspension. Physica, 29:129–139.CrossRefGoogle Scholar
Pshenichnov, G.I. (1993). A Theory of Latticed Plates and Shells.World Scientific, Singapore.CrossRefGoogle Scholar
Rayleigh, Lord (Strutt, J.W.). (1892). On the influence of obstacles arranged in rectangular order upon the properties of the medium. Phil. Mag., 34(241):481—491.CrossRefGoogle Scholar
Reuss, A. (1929). Berechnung der Flieβgrenze von Mischkristallen auf Grund der Plastizitätsbedingung für Einkristalle. Z. Angew. Math. Mech., 9:49–58.CrossRefGoogle Scholar
Robinson, D.A. and Friedman, S.F. (2001). Effect of particle size distribution on the effective dielectric permittivity of saturated granular media. Water Resour. Res., 37(1):33–40.CrossRefGoogle Scholar
Rockafellar, R.T. (1969). Convex Functions and Duality in Optimization Problems and Dynamics.Springer-Verlag, Berlin.CrossRefGoogle Scholar
Rockafellar, R.T. (1970). Convex Analysis.Princeton University Press, Princeton, NJ.CrossRefGoogle Scholar
Roux, S. and Guyon, E.. (1985). Mechanical percolation: A small beam lattice study. J. Physique Lett., 46:999–1004.CrossRefGoogle Scholar
Rudin, W. (1964). Principles of Mathematical Analysis.McGraw-Hill, New York.Google Scholar
Rudin, W. (1992). Functional Analysis.McGraw-Hill, New York.Google Scholar
Runge, I. (1925). Zur elektrischen Leitfahigkeit metallischer Aggregate. Z. Tech. Physic, 61(6):61–68.Google Scholar
Rylko, N. (2000). Transport properties of a rectangular array of highly conducting cylinders. J. Engng. Math., 38:1–12.CrossRefGoogle Scholar
Rylko, N. (2008a). Effect of polydispersity in conductivity of unidirectional cylinders. Arch. Mater. Sci. Engng, 29:45–52.Google Scholar
Rylko, N. (2008b). Structure of the scalar field around unidirectional circular cylinders. Proc. R. Soc. London, A, 464:391–407.CrossRefGoogle Scholar
Sab, K. (1992). On the homogenization and the simulation of random materials. Eur. J. Mech., A/Solids, 11(5):585–607.Google Scholar
Sahimi, M. (2003). Heterogeneous Materials, Vol. 1, 2. Springer-Verlag, New York.Google Scholar
Sanchez-Palencia, E. (1974). Problemes de perturbations liés aux phénomènes de conduction à travers des couches minces de grande résistivité. J. Math. Pure Appl., 53:251–270.Google Scholar
Sanchez-Palencia, E. (1980). Non-Homogeneous Media and Vibration Theory.Springer-Verlag, Berlin.Google Scholar
Sangani, A.S. and Acrivos, A.. (1983). The effective conductivity of a periodic array of spheres. Proc. R. Soc. London, A, 386:263–275.CrossRefGoogle Scholar
Schwartz, L. (1966). Theorie des Distributions.Hermann, Paris.Google Scholar
Schwartz, L.M., Johnson, D.L. and Feng, S.. (1984). Vibration modes in granular materials. Phys. Rev. Lett., 52(831):831–834.CrossRefGoogle Scholar
Shermergor, T.D. (1977). Elasticity Theory of Micro-Inhomogeneous Media (in Russian).Nauka, Moscow.Google Scholar
Shook, C.A and Rocko, M.C.. (1991). Slurry Flow, Principles and Practice.Butterworth-Heinemann, Boston, MA.Google Scholar
Sierou, A. and Brady, J.F.. (2002). Rheology and micro structure in concentrated noncolloidal suspensions. J. Rheol., 46(5):1031–1056.CrossRefGoogle Scholar
Simonenko, I.B. (1974). Electrostatics problems for an inhomogeneous medium: A case of thin dielectric with high dielectric constant: I. Differential Equations, 10:301–309.Google Scholar
Simonenko, I.B. (1975a). Electrostatics problems for an inhomogeneous medium: A case of thin dielectric with high dielectric constant: II. Differential Equations, 11:1870–1878.Google Scholar
Simonenko, I.B. (1975b). Limit problem of conductivity in an inhomogeneous medium. Siberian Math. J., 16:1291–1300.Google Scholar
Smythe, W.R. (1950). Static and Dynamical Electricity, 2nd ed. McGraw-Hill, New York.Google Scholar
Sobolev, S.L. (1937). On the boundary value problem for polyharmonic functions (in Russian). Matem. Zbornik, 2(3):465–499.Google Scholar
Sobolev, S.L. (1950). Some Applications of Functional Analysis to Mathematical Physics (in Russian). Leningrad State University, Leningrad.Google Scholar
Stauffer, D. and Aharony, A.. (1992). Introduction to Percolation Theory.Taylor & Francis, London.Google Scholar
Stockmayer, W.H. (1943). Theory of molecular size distribution and gel formation in branched-chain polymers. J. Chem. Phys., 11:45–55.CrossRefGoogle Scholar
Subia, S., Ingber, M.S., Mondy, L.A., Altobelli, S.A. and Graham, A.L.. (1998). Modeling of concentrated suspensions using a continuum constitutive equation. J. Fluid Mech., 373:193–219.CrossRefGoogle Scholar
Szczepkowski, J., Malevich, A.E. and Mityushev, V.. (2003). Macroscopic properties of similar arrays of cylinders. Quart. J. Appl. Math. Mech., 56(4):617–628.CrossRefGoogle Scholar
Tamm, I.E. (1979). Fundamentals of the Theory of Electricity.Mir Publishers, Moscow.Google Scholar
Temam, R. (1979). Navier-Stokes Equations.North Holland, Amsterdam.Google Scholar
Thovert, J.F. and Acrivos, A.. (1989). The effective thermal conductivity of a random polydispersed suspension of spheres to order c2. Chem. Eng. Comm., 82:177–191.CrossRefGoogle Scholar
Thovert, J.F., Kim, I.C., Torquato, S. and Acrivos, A.. (1990). Bounds on the effective properties of polydispersed suspensions of spheres: An evaluation of two relevant morphological parameters. J. Appl. Phys., 67:6088–6098.CrossRefGoogle Scholar
Timoshemko, S. and Goodier, J.N.. (1951). Theory of Elasticity.McGraw-Hill, New York.Google Scholar
Torquato, S. (2002). Random Heterogeneous Materials.Springer-Verlag, Berlin.CrossRefGoogle Scholar
van Lint, J.H. and Wilson, R.M.. (2001). A Course in Combinatorics, 2nd ed. Cambridge University Press, Cambridge.CrossRefGoogle Scholar
Vinogradov, V. and Milton, G.W.. (2005). An accelerated fast Fourier transform algorithm for nonlinear composites. Advances Comp. Experim. Enging. Set Proc. ICCES'05. Available at www.math.utah.edu/vladim/papers/publications.html.Google Scholar
Voigt, W. (1910). Lehrbuch der Kristallphysik.Teubner, Stuttgart.Google Scholar
Voronoi, G. (1908). Nouvelles applications des paramètres continus à la théorie des formes quadratiques. Deuxieme Memoire. Recherches sur les parallelloedres primitifs. J. ReineAngew. Math., 134(198):198–287.Google Scholar
Walpole, L.J. (1966). On bounds for the overall elastic moduli of inhomogeneous systems. J. Mech. Phys. Solids, 14:151–162.CrossRefGoogle Scholar
Weil, A. (1976). Elliptic Functions According to Eisenstein andKronecker.Springer-Verlag, Berlin.CrossRefGoogle Scholar
Wermer, J. (1974). Potential Theory.Springer-Verlag, Berlin.CrossRefGoogle Scholar
West, B.W. (2000). Introduction to Graph Theory.Prentice Hall, NJ.Google Scholar
Willis, J.R. (2002). Lectures on mechanics of random media. In: Mechanics of Random and Multiscale Microstructures, CISM Lecture Notes (Jeulin, D. and Ostoja-Starzewski, M., eds.), Springer-Verlag, Vienne, pp. 221–267.Google Scholar
Yan, Y., Li, J. and Sander, L.M.. (1989). Fracture growth in 2-D elastic networks with the Born model. Europhys. Lett., 10:7–13.CrossRefGoogle Scholar
Yang, C.S. and Hui, P.M.. (1991). Effective nonlinear response in random nonlinear resistor networks: Numerical studies. Phys. Rev. B, 44:12559–12561.CrossRefGoogle ScholarPubMed
Yardley, J.G., Reuben, A.J. and McPhedran, R.C.. (2001). The transport properties of layers of elliptical cylinders. Proc. R. Soc. London, A, 457:395–423.CrossRefGoogle Scholar
Yeh, R.H.T. (1970a). Variational principles of elastic moduli of composite materials. J. Appl. Phys., 41(8):3353–3356.CrossRefGoogle Scholar
Yeh, R.H.T. (1970b). Variational principles of transport properties of composite materials. J. Appl. Phys., 41(1):224–226.CrossRefGoogle Scholar
Yosida, K. (1971). Functional Analysis.Springer-Verlag, Berlin.CrossRefGoogle Scholar
Yurinski, V.V. (1980). Average of an elliptic boundary problem with random coefficients. Siberian Math. J., 21:470–482.CrossRefGoogle Scholar
Yurinski, V.V. (1986). Averaging of symmetric diffusion in a random medium. Siberian Math. J., 27(4):603–613.CrossRefGoogle Scholar
Zeidler, E. (1995). Applied Functional Analysis: Applications to Mathematical Physics.Springer-Verlag, Berlin.Google Scholar
Zuzovsky, M. and Brenner, H.. (1977). Effective conductivities of composite materials composed of a cubic arrangement of spherical particles embedded in an isotropic matrix. Z. Angew. Math. Phys., 28(6):979–992.CrossRefGoogle Scholar

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  • References
  • Leonid Berlyand, Pennsylvania State University, Alexander G. Kolpakov, Alexei Novikov, Pennsylvania State University
  • Book: Introduction to the Network Approximation Method for Materials Modeling
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  • Book: Introduction to the Network Approximation Method for Materials Modeling
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  • Chapter DOI: https://doi.org/10.1017/CBO9781139235952.010
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