Abstract
Contemporary composite materials are widely used in modern engineering.
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Hogg, P.J. 2006. Composites in armor. Science 314: 1100–1101.
Cox, B., and Q. Vang. 2006. In quest of virtual tests for structural composites. Science 314: 1102–1107.
Guz, A.N., and Y.Y. Rushchitskii. 2003. Nanomaterials: On the mechanics of nanomaterials. International Applied Mechanics 39 (11): 1271–1293.
Lubin, G. 2014. Handbook of composites. Berlin: Springer.
Wilson, M., K. Kannangara, G. Smith, M. Simmons, and B. Raguse. 2002. Nanotechnology: Basic science and emerging technologies. Boca Raton: Chapman and Hall/CRC.
Cowin, S.C. (ed.). 2001. Bone mechanics handbook. Boca Raton: CRC Press.
Bogdanovich, A.E., and C.M. Pastore. 1996. Mechanics of textile and laminated composites. London: Chapman and Hall.
Starr, T. 1995. Carbon and high performance fibers directory and databook. London: Chapman and Hall.
Vanin, G.A. 1985. Micromechanics of composite materials. Kyiv (in Russian): Naukova Dumka.
Landauer, R. 1952. The electrical resistance of binary metallic mixture. Journal of Applied Physics 23 (7): 779–784.
Mossotti, O.F. 1852. Sobre las fuerzas que rigen la constituciòn de los cuerpos. Memorie di Matematica e di Fisica della Societá Italiana delle Scienze Residente in Modena 24 (2): 49–74.
Clausius, R. 1879. Die Mechanische Behandlung der Elektrizität. Braunschweig: F. Vieweg.
Lorenz, L. 1880. Über die Refraktionskonstante. Annalen der Physik und Chemie 247 (9): 70–103.
Lorentz, H.A. 1880. Über die Beziehung zwischen der Fortpflanzungsgeschwindigkeit des Lichtes der Körperdichte. Annalen der Physik und Chemie 245 (4): 641–665.
Lorentz, H.A. 1909. The theory of electrons. Leipzig, B.G. Teubner.
Lichtenecker, K. 1926. Die Dielektrizitötskonstante natürlicher und künstlicher Mischkörper, Physikalische Zeitschrift 27(4,5), pp. 115–158.
Shvidler, M.I. 1985. Statistical hydrodynamics of porous media. Moscow: Nedra.
Kerner, E.H. 1956. The elastic and thermo-elastic properties of composite media. Proceedings of Physical Society B 69 (8): 808–813.
Kerner, E.H. 1956. The electrical conductivity of composite media. Proceedings of Physical Society B 69 (8): 802–807.
Van der Poel, C. 1958. On the rheology of concentrated dispersions. Rheologica Acta 1: 198–205.
Bruggeman, D.A.G. 1935. Berechnung verschiedener physikalischer konstanten von heterogenen Substanzen, I. Dielecktrizitätskonstanten und Leitfähigkeiten der Mischkörper aus isotropen Substanzen, Annalen der Physik 416 (7): 636–664.
Bruggeman, D.A.G. 1936. Berechnung verschiedener physikalischer Konstanten von heterogenen Substanzen. II. Dielecktrizitätskonstanten und Leitfähigkeiten von Vielkristallen der nichtregulären Systeme. Annalen der Physik 417 (7): 645–672.
Bruggeman, D.A.G. 1937. Berechnung verschiedener physikalischer Konstanten von heterogenen Substanzen. III. Die elastischen Konstanten der quasiisotropen Mischörper aus isotropen Substanzen. Annalen der Physik 421 (2): 160–178.
Odelevski, V.I. 1951. Calculation of the generalized conductivity of heterogeneous systems. Zh Tech Physics 21 (6): 667–685.
Maxwell, J.C. 1873. Treatise on electricity and magnetism. Oxford: Clarendon Press.
Garnett, J.C.M. 1904. Colours in metal glasses and in metallic films. Philosophical Transactions of the Royal Society of London Series A 203: 385–420.
Milton, G.W. 2002. The theory of composites. Cambridge: Cambridge University Press.
Torquato, S. 2002. Random heterogeneous materials: microstructure and macroscopic properties. New York: Springer
Voigt, W. 1889. Über die Beziehung zwischen den beiden Elasticitätsconstanten isotroper Körper. Annalen der Physik und Chemie 38: 573–587.
Reuss, A. 1929. Berechnung der Flie\(\beta \)grenze on Mischkristallen auf Grund der Plastizitätsbedingungen für Einkristall. ZAMM 9: 49–58.
Wiener, O. 1889. Die Theorie des Mischkörpers für das Feld der stationären Strömung. Erste Abhandlung die Mittelwertsätze für Kraft, Polarisation und Energie. Abhandlungen der Mathematisch-Physischen Klasse der Königlich Sächsischen Gesellschaft der Wissenschaften 32 (6): 507–604.
Hill, R. 1952. The elastic behaviour of a crystalline aggregate. Proceedings of the Physical Society Section A 65: 349–354.
Hashin, Z., and S. Shtrikman. 1962. A variational approach to the theory of the effective magnetic permeability of multiphase materials. Journal of Applied Physics 33: 1514–1517.
Hashin, Z., and S. Shtrikman. 1963. A variational approach to the theory of the elastic behaviour of multiphase materials. Journal of the Mechanics and Physics of Solids 11: 127–140.
Milton, G.W. 1982. Bounds on the elastic and transport properties of two-component composites. Journal of the Mechanics and Physics of Solids 30: 177–191.
Milton, G.W., and N. Phan-Thien. 1982. New bounds on the effective moduli of two-component materials. Proceedings of the Royal Society of London Series A 380: 305–331.
Ponte Castaneda, P., and P. Suquet. 1998. Nonlinear composites. Advances in Applied Mechanics 34: 171–302.
Talbot, D.R.S. 2001. Improved bounds for the overall properties of a nonlinear composite dielectric. Proceedings of the Royal Society of London Series A 457: 587–597.
Torquato, S. 1991. Random heterogeneous media: Microstructure and improved bounds on the effective properties. Applied Mechanics Reviews 44: 37–76.
Willis, J.R. 1991. On methods to bound the overall properties of nonlinear composites. Journal of the Mechanics and Physics of Solids 39: 73–86.
Beran, M.J. 1968. Statistical continuum theories. New York: Wiley.
Bergman, D.J. 1978. The dielectric constant of a composite material: A problem in classical physics. Physics Reports 34: 377–407.
Bergman, D.J. 1993. Hierarchies of Stieltjes functions and their application to the calculation of bounds for the dielectric constant of a two-components composite medium. SIAM Journal of Applied Mathematics 53: 915–930.
Telega, J.J., S. Tokarzewski, and A. Galka. 2000. Effective conductivity of nonlinear two-phase media: homogenization and two-point Padé approximants. Acta Applicandae Mathematics 61: 295–315.
Tokarzewski, S. 1996. Two-point Padé approximants for the expansion of Stieltjes functions in real domain. Journal of Computational and Applied Mathematics 67: 59–72.
Tokarzewski, S., and I. Andrianov. 2001. Effective coefficients for real non-linear and fictitious linear temperature-dependent periodic composites. International Journal of Non-Linear Mechanics 36: 187–195.
Tokarzewski, S., and J.J. Telega. 1996. S-continued fraction to complex transport coefficients of two-phase composites. Computer Assisted Methods in Engineering and Science 3: 109–119.
Tokarzewski, S., and J.J. Telega. 1996. Two-point Padé approximants to Stieltjes series representations of bulk moduli of regular composites. Computer Assisted Methods in Engineering and Science 3: 121–132.
Tokarzewski, S., and J.J. Telega. 1997. S-continued fraction method for the investigation of a complex dielectric constant of two-phase composite. Acta Applicandae Mathematics 49: 55–83.
Tokarzewski, S., I.V. Andrianov, and V. Danishevs’kyy. 1997. The investigation of a complex conductivity of regular arrays of spheres. Theoretical Foundations of Civil Engineering 5: 414–425.
Tokarzewski, S., I.V. Andrianov, and V. Danishevs’kyy. 1998. Dynamiczne moduly skretne pretow sprezystych porami wypelnionymi ciecza lepka. Theoretical Foundations of Civil Engineering 6: 393–398.
Tokarzewski, S., I.V. Andrianov, and V. Danishevs’kyy. 2001. Parametric complex bounds on effective transport coefficients of two-phase media. Theoretical Foundations of Civil Engineering 9: 433–440.
Tokarzewski, S., I.V. Andrianov, V. Danishevs’kyy, and Starushenko, G. 2001. Analytical continuation of asymptotic expansions of effective transport coefficients by Padé approximants. Nonlinear Analysis 47: 2283–2292.
Tokarzewski, S., J. Blawzdziewicz, and I. Andrianov. 1994. Effective conductivity for densely packed highly conducting cylinders. Applied Physics A 59: 601–604.
Tokarzewski, S., J. Blawzdziewicz, and I. Andrianov. 1994. Two-point Padé approximants for effective conductivity of a periodic array of cylinders. Advances in Structured and Heterogeneous Continua, 263–267. New York: Allerton Press.
Tokarzewski, S., A. Galka, I.V. Andrianov, and V. Danishevs’kyy. 1999. Padé bounds on temperature-dependent conductivities of heterogeneous materials. Theoretical Foundations of Civil Engineering 7: 412–427.
Tokarzewski, S., A. Galka, I.V. Andrianov, and V. Danishevs’kyy. 2002. Parametric inclusion regions for transport coefficients of two-phase media. Theoretical Foundations of Civil Engineering 10: 465–470.
Berryman, J.G., and G.W. Milton. 1988. Microgeometry of random composites and porous media. Journal of Physics D: Applied Physics 21: 87–94.
Gibiansky, L.V., and S. Torquato. 1995. Rigorous links between the effective conductivity and elastic moduli of fibre-reinforced composite materials. Philosophical Transactions of the Royal Society of London 343: 243–278.
Gibiansky, L., and S. Torquato. 1996. Connection between the conductivity and elastic moduli of isotropic composite materials. Proceedings of the Royal Society of London Series A 452: 253–283.
Shermergor, T.D. 1977. The theory of microinhomogeneous media. Moscow: Nauka.
Einstein, A. 1906. Eine Neue Bestimmung der Moleküldimensionen. Annalen der Physik 324: 289–306.
Einstein, A. 1911. Berichtigung zu meiner Arbeit: Eine neue Bestimmung der Moleküldimensionen. Annalen der Physik 339: 591–592.
Eshelby, J.D. 1957. The determination of the elastic field of an ellipsoidal inclusion and related problems. Proceedings of the Royal Society of London Series A 241: 376–396.
Eshelby, J.D. 1982. The stresses on and in a thin inextensible fibre in a stretched elastic medium. Engineering Fracture Mechanics 16 (3): 453–455.
Buryachenko, V.A. 2001. Multiparticle effective field and related methods in micromechanics of composite materials. Applied Mechanics Reviews 54: 1–47.
Buryachenko, V.A. 2007. Micromechanics of heterogeneous materials. Berlin: Springer.
Christensen, R.M. 2005. Mechanics of composite materials. Mineola, NY: Dover Publications.
Christensen, R.M., and K.H. Lo. 1979. Solutions for effective shear properties in three phase and cylinder models. Journal of the Mechanics and Physics of Solids 27: 315–330.
Hashin, Z. 1983. Analysis of composite materials—A survey. Journal of Applied Mechanics 50: 481–505.
Keller, J.B. 1963. Conductivity of a medium containing a dense array of perfectly conducting spheres or cylinders or nonconducting cylinders. Journal of Applied Physics 34: 991–993.
Batchelor, G.K., and R.W. O’Brien. 1977. Thermal or electrical conduction through a granular material. Proceedings of the Royal Society of London Series A 355: 313–333.
Van Tuyl, A.H. 1996. Asymptotic expansions with error bounds for the coefficients of capacity and induction of two spheres. SIAM Journal of Mathematical Analysis 27: 782–804.
Lagzdins, A.Zh., V.P. Tamuzh, G.A. Teters, and A.F. Kregers. 1992. Orientational Averaging in Mechanics of Solids. Harlow, Essex: Longman Scientific and Technical.
Andrianov, I.V., V.V. Danishevs’kyy, and S. Tokarzewski. 1996. Two-point quasifractional approximants for effective conductivity of a simple cubic lattice of spheres. International Journal of Heat and Mass Transfer 39: 2349–2352.
Andrianov, I.V., V.V. Danishevs’kyy, and S. Tokarzewski. 2000. Quasifractional approximants in the theory of composite materials. Acta Applicandae Mathematics 61: 29–35.
Grigolyuk, E.I., and L.A. Fil’shtinsky. 1970. Perforated Plates and Shells. Moscow (in Russian): Nauka.
Gluzman, S., V. Mityushev, and W. Nawalaniec. 2017. Computational Analysis of structured Media. Academic Press.
Pobedrya, B.Ye. 1983. On the theory of viscoelasticity of structurally inhomogeneous media. Journal of Applied Mathematics and Mechanics 47: 103–109.
Pobedrya, B.Ye. 1984. Mechanics of Composite Materials. Moscow: MGU.
Fil’shtinskii, L.A., and D. Bardzokas. 1995. Averaging the electrical properties of fiber-reinforced metal composites. Mechanics of Composite Materials 31 (4): 390–396.
Fil’shtinskii, L.A., and D. Bardzokas. 1997. Averaging the electrical properties of fiber-reinforced metal composites with hollow fibers. Mechanics of Composite Materials 33 (3): 269–274.
Fil’shtinskii, L.A., and Yu.V. Shramko. 1998. Averaging the physical properties of fibrous piezocomposites. Mechanics of Composite Materials 34 (1): 87–93.
Rayleigh, R.S. 1892. On the influence of obstacles arranged in rectangular order upon the properties of medium. Philosophical Magazine 34: 481–502.
McKenzie, D.R., R.C. McPhedran, and G.H. Derrick. 1978. The conductivity of lattices of spheres. II. The body-centred and face-centred lattices. Proceedings of the Royal Society of London Series A 362: 211–232.
McPhedran, R.C. 1986. Transport properties of cylinder pairs and of the square array of cylinders. Proceedings of the Royal Society of London Series A 408: 31–43.
McPhedran, R.C., and D.R. McKenzie. 1978. The conductivity of lattices of spheres. 1. The simple cubic lattice. Proceedings of the Royal Society of London Series A 359: 45–63.
McPhedran, R.C., and G.W. Milton. 1987. Transport properties of touching cylinder pairs and of the square array of touching cylinders. Proceedings of the Royal Society of London Series A 411: 313–326.
McPhedran, R.C., L. Poladian, and G.W. Milton. 1988. Asymptotic studies of closely spaced highly conducting cylinders. Proceedings of the Royal Society of London Series A 415: 185–196.
Willis, J.R. 1983. The overall elastic response of composite materials. Transactions ASME Journal of Applied Mechanics 50: 1202–1209.
Bakhvalov, N., and G. Panasenko. 1989. Averaging processes in periodic media. Mathematical problems in mechanics of composite materials. Kluwer, Dordrecht.
Oleynik, O.A., A.S. Shamaev, and G.A. Yosif’yan. 1992. Mathematical problems in elasticity and homogenization. Amsterdam: North-Holland.
Berdichevsky, V.L. 1983. Variational principles of the continuum mechanics. Moscow (in Russian): Nauka.
Sanchez-Palencia, E. 1980. Non-homogeneous media and vibrations theory. Berlin: Springer.
Sanchez-Palencia, E. 1987. Boundary layers and edge effects in composites. In Homogenization techniques for composite materials, ed. E. Sanchez-Palencia, and A. Zaoui, 122–193. Berlin, NY: Springer
Babushka, I. 1979. The computational aspects of the homogenization problem. Lecture Notes in Mathematics 704: 309–316.
Bensoussan, A., J.-L. Lions, and G. Papanicolaou. 1978. Asymptotic analysis for periodic structures. Amsterdam: North-Holland.
Tartar, L. 1990. H-measure, a new approach for studying homogenization, oscillation and concentration effects in partial differential equations. Proceedings of the Royal Society of Edinburgh Section A 115: 193–230.
Duvaut, G. 1976. Analyse fonctionelle et mecanique des milieux continue. Application á l’étude des matériaux composites élastiques a structure périodique-homogénéisation. Theoretical and Applied Mechanics, Koiter, W.T. (ed.), North-Holland, Amsterdam, 1976, 119–132.
Duvaut, G. 1977. Comportement macroscopique d’une plaque perforée périodiquement. Lecture Notes in Mathematics 594: 131–145.
Manevitch, L.I., I.V. Andrianov, and V.O. Oshmyan. 2002. Mechanics of periodically heterogeneous structures. Berlin: Springer.
Boutin, C. 1995. Microstructural influence on heat conduction. International Journal of Heat and Mass Transfer 38: 3181–3195.
Boutin, C. 1996. Microstructural effects in elastic composites. International Journal of Solids and Structures 33: 1023–1051.
Boutin, C. 2000. Study of permeability by periodic and self-consistent homogenization. European Journal of Mechanics—A/Solids 19: 603–632.
Cherednichenko, K.D., and V.P. Smyshlyaev. 2004. On full two-scale expansion of the solutions of nonlinear periodic rapidly oscillating problems and higher-order homogenised variational problems. Archive for Rational Mechanics and Analysis 174: 385–442.
Gambin, B., and E. Kröner. 1989. High order terms in the homogenized stress-strain relation of periodic elastic media. Physica Status Solidi B 151: 513–519.
Smyshlyaev, V.P., and K.D. Cherednichenko. 2000. On rigorous derivation of strain gradient effects in the overall behaviour of periodic heterogeneous media. Journal of the Mechanics and Physics of Solids 48: 1325–1357.
Allaire, G. 1992. Homogenization and two-scale convergence. SIAM Journal on Mathematical Analysis 23: 1482–1518.
Cherednichenko, K.D., V.P. Smyshlyaev, and V.V. Zhikov. 2006. Non-local homogenized limits for composite media with highly anisotropic periodic fibres. Proceedings of the Royal Society of Edinburgh 136A: 87–114.
Zhikov, V.V. 2000. On an extension of the method of two-scale convergence and its applications. Sbornik: Mathematics 191: 973–1014.
Pernin, J.N., and E. Jacquet. 2001. Elasticity in highly heterogeneous composite medium: Threshold phenomenon and homogenization. International Journal of Engineering Sciences 39: 755–798.
Mityushev, V.V., E.V. Pesetskaya, and S.V. Rogosin. 2007. Analytical methods for heat conduction in composites and porous media. In: G. Murch, A. Öchsner and M. de Lemos (Eds.). Cellular and Porous Materials. Thermal Properties Simulation and Prediction. Amsterdam: Wiley-VCH: 124–167.
Kolpakov, A.A., and A.G. Kolpakov. 2010. Capacity and Transport in Contrast Composite Structures: Asymptotic Analysis and Applications. CRC Press, Boca Raton: Taylor and Francis.
Ponte Castaneda, P. J.J. Telega, and B. Gambin. (eds.). 2004. Linear comparison methods for nonlinear composites. Nonlinear Homogenization and its Applications to Composites, Polycrystals and Smart Materials, Dordrecht: Kluwer.
Needleman, A. 1987. A continuum model for void nucleation by inclusion debonding. Journal of Applied Mechanics 54: 525–531.
Needleman, A. 1990. An analysis of tensile decohesion along an interface. Journal of the Mechanics and Physics of Solids 38: 289–324.
Needleman, A. 1992. Micromechanical modelling of interfacial decohesion. Ultramicroscopy 40: 203–214.
Espinosa, H.D., S.K. Dwivedi, and H.-C. Lu. 2000. Modelling impact induced delamination of woven fibre reinforced composites with contact/cohesive laws. Computer Methods in Applied Mechanics and Engineering 183: 259–290.
Espinosa, H.D., P.D. Zavattieri, and S.K. Dwivedi. 1998. A finite deformation continuum/discrete model for the description of fragmentation and damage in brittle materials. Journal of the Mechanics and Physics of Solids 46: 1909–1942.
Espinosa, H.D., P.D. Zavattieri, and G.L. Emore. 1998. Adaptive FEM computation of geometric and material nonlinearities with application to brittle failure. Mechanics of Materials 29: 275–305.
Tvergaard, V. 1990. Effect of fibre debonding in a whisker-reinforced metal. Materials Science and Engineering A 125: 203–213.
Tvergaard, V. 1995. Fiber debonding and breakage in a whisker reinforced metal. Materials Science and Engineering A 90: 215–222.
Tvergaard, V., and J.W. Hutchinson. 1992. The relation between crack growth resistance and fracture process parameters in elastic-plastic solids. Journal of the Mechanics and Physics of Solids 40: 1377–1397.
Tvergaard, V., and J.W. Hutchinson. 1993. The influence of plasticity on mixed-mode interface toughness. Journal of the Mechanics and Physics of Solids 41: 1119–1135.
Camacho, G.T., and M. Ortiz. 1996. Computational modelling of impact damage in brittle materials. International Journal of Solids and Structures 33: 2899–2938.
Chandra, N., H. Li, C. Shet, and H. Ghonem. 2002. Some issues in the application of cohesive zone models for metal-ceramic interfaces. International Journal of Solids and Structures 39: 2827–2855.
Geubelle, P.H., and J.S. Baylor. 1998. Impact-induced delamination of composites: A 2D simulation. Composites B 29: 589–602.
Huang, Y., and H. Gao. 2001. Intersonic crack propagation. Part I: The fundamental solution. Journal of Applied Mechanics 68: 169–175.
Kubair, D.V., P.H. Geubelle, and Y. Huang. 2003. Analysis of a rate-dependent cohesive model for dynamic crack propagation. Engineering Fracture Mechanics 70: 685–704.
Ortiz, M., and A. Pandolfi. 1999. Finite-deformation irreversible cohesive element for three-dimensional crack-propagation analysis. International Journal for Numerical Methods in Engineering 44: 1267–1282.
Raghavan, P., and S. Ghosh. 2005. A continuum damage mechanics model for unidirectional composites undergoing interfacial debonding. Mechanics of Materials 37: 955–979.
Samudrala, O., and A.J. Rosakis. 2003. Effect of loading and geometry on the subsonic/intersonic transition of a bimetallic interface crack. Engineering Fracture Mechanics 70: 309–337.
Samudrala, O., Y. Huang, and A.J. Rosakis. 2002. Subsonic and intersonic mode. Part II: Crack propagation with a rate-dependent cohesive zone. Journal of the Mechanics and Physics of Solids 50: 1231–1268.
Xu, X.-P., and A. Needleman. 1994. Numerical simulations of fast crack growth in brittle solids. Journal of the Mechanics and Physics of Solids 42: 1397–1434.
Zhong, X.A., and W.G. Knauss. 1997. Analysis of interfacial failure in particle-filled elastomers. Journal of Engineering Materials and Technology 119: 198–204.
Zhong, X.A., and W.G. Knauss. 2000. Effects of particle interaction and size variation on damage evolution in filled elastomers. Mechanics of Composite Materials and Structures 7: 35–53.
Levy, A.J. 1996. The effective dilatational response of fiber reinforced composites with nonlinear interface. Journal of Applied Mechanics 63: 357–364.
Levy, A.J. 2000. The fiber composite with nonlinear interface. Part I: Axial tension. Journal of Applied Mechanics 67: 727–732.
Levy, A.J., and Z. Dong. 1998. Effective transverse response of fiber composites with nonlinear interface. Journal of the Mechanics and Physics of Solids 46: 1279–1300.
Tan, H., C. Liu, Y. Huang, and P.H. Geubelle. 2005. The cohesive law for the particle/matrix interfaces in high explosives. Journal of the Mechanics and Physics of Solids 53: 1892–1917.
Aboudi, J. 1987. Damage in composites—modelling of imperfect bonding. Composites Science and Technology 28: 103–128.
Achenbach, J.D., and H. Zhu. 1989. Effect of interfacial zone on mechanical behavior and failure of fibre-reinforced composites. Journal of the Mechanics and Physics of Solids 7: 381–393.
Achenbach, J.D., and H. Zhu. 1990. Effect of interphases on micro and macromechanical behavior of hexagonal-array fiber composites. Journal of Applied Mechanics 57: 956–963.
Benabou, L., M. Naït-Abdelaziz, and N. Benseddiq. 2004. Effective properties of a composite with imperfectly bonded interface. Theoretical and Applied Fracture Mechanics 41: 15–20.
Benveniste, Y. 1985. The effective mechanical behavior of composite materials with imperfect contact between constituents. Mechanics of Materials 4: 197–208.
Benveniste, Y., and T. Chen. 2001. On the Saint-Venant torsion of composite bars with imperfect interfaces. Proceedings of the Royal Society of London A 457: 231–255.
Benveniste, Y., and T. Miloh. 2001. Imperfect soft and stiff interfaces in two-dimensional elasticity. Mechanics of Materials 33: 309–324.
Chen, X., and Y. Liu. 2001. Multiple-cell modelling of fiber-reinforced composites with the presence of interphases using the boundary element method. Computational Materials Science 21: 86–94.
Hashin, Z. 1990. Thermoelastic properties of fiber composites with imperfect interface. Mechanics of Materials 8: 333–348.
Hashin, Z. 1991. Thermoelastic properties of particulate composites with imperfect interface. Journal of the Mechanics and Physics of Solids 39: 745–762.
Jasiuk, I., and M.W. Kouider. 1993. The effect of an inhomogeneous interphase on the elastic constants of transversely isotropic comoposites. Mechanics of Materials 15: 53–63.
Lagache, M., A. Agbossou, J. Pastor, and D. Muller. 1994. Role of interphase on the elastic behavior of composite materials: theoretical and experimental analysis. Journal of Composite Materials 28: 1140–1157.
Lenci, S. 2000. Melan’s problems with weak interface. Journal of Applied Mechanics 67: 22–28.
Lenci, S., and G. Menditto. 2000. Weak interface in long fibre composites. International Journal of Solids and Structures 37: 4239–4260.
Lipton, R., and B. Vernescu. 1995. Variational methods, size effects and extremal microgeometries for elastic composites with imperfect interface. Mathematical Models and Methods in Applied Sciences 5: 1139–1173.
Nie, S., and C. Basaran. 2005. A micromechanical model for effective elastic properties of particulate composites with imperfect interfacial bonds. International Journal of Solids and Structures 42: 4179–4191.
Pagano, N.J., and G.P. Tandon. 1990. Modelling of imperfect bonding in fiber reinforced brittle matrix composites. Mechanics of Materials 9: 49–64.
Qu, J. 1993. The effect of slightly weakened interfaces on the overall elastic properties of composite materials. Mechanics of Materials 14: 269–281.
Van Fo Fy, G.A. 1971. Theory of Reinforced Materials with Coatings. Kyiv: Naukova Dumka.
Wu, Y., Z. Ling, and Z. Dong. 1999. Stress-strain fields and the effectiveness shear properties for three-phase composites with imperfect interface. International Journal of Solids and Structures 37: 1275–1292.
Zhu, H., and J.D. Achenbach. 1991. Effect of fiber-matrix interphase defects on microlevel stress states at neighboring fibers. Journal of Composite Materials 25: 224–238.
Hashin, Z. 2001. Thin interphase/imperfect interface in conduction. Journal of Applied Physics 89: 2261–2267.
Hashin, Z. 2002. Thin interphase/imperfect interface in elasticity with application to coated fiber composites. Journal of the Mechanics and Physics of Solids 50: 2509–2537.
Miloh, T., and Y. Benveniste. 1999. On the effective conductivity of composites with ellipsoidal inhomogeneities and highly conducting interfaces. Proceedings of the Royal Society of London Series A 455: 2687–2706.
Dumontet, H. 1986. Study of a boundary layer problem in elastic composite materials. Mathematical Modelling and Numerical Analysis 20: 265–286.
Neuss-Radu, M. 2000. A result on the decay of the boundary layers in the homogenization theory. Asymptotic Analysis 23: 313–328.
Neuss-Radu, M. 2001. The boundary behavior of a composite material. Mathematical Modelling and Numerical Analysis 35 (3): 407–435.
Allaire, G., and M. Amar. 1999. Boundary layer tails in periodic homogenization. ESAIM: Control, Optimisation Calculus of Variations 4: 209–243.
Bystrov, V.M., A.N. Guz’, and Yu.V. Kokhanenko. 1987. Numerical study of the edge effect in composites. International Applied Mechanics 23 (8): 707–711.
Mishuris, G., and A. Öchsner. 2005. Edge effects connected with thin interfaces in composite materials. Composite Structures 68: 409–417.
Kalamkarov, A.L. 1992. Composite and Reinforced Elements of Construction. Chichester, NY: Wiley.
Kalamkarov, A.L., and A.V. Georgiades. 2002. Modeling of smart composites on account of actuation. Thermal Con-ductivity and Hygroscopic Absorption, Composites, Part B 33 (2): 141–152.
Kalamkarov, A.L., and A.G. Kolpakov. 1997. Analysis, design and optimization of composite Structures. Chichester, NY: Wiley.
Argatov, I.I., and S.A. Nazarov. 1993. Junction problem of shashlik (skewer) type. Comptes Rendus de l’Académie des Sciences 1316: 1329–1334.
Argatov, I.I., and S.A. Nazarov. 1996. Asymptotic analysis of problems on junctions of domains of different limit dimensions. A body pierced by a thin rod. Izvestiya Mathematics 60 (1): 1–37.
Hashin, Z. 1965. Viscoelastic behavior of heterogeneous media. Journal of Applied Mechanics 8: 630–636.
Hashin, Z. 1966. Viscoelastic fiber reinforced materials. AIAA Journal 8: 1411–1417.
Brinson, L.C., and W.S. Lin. 1998. Comparison methods for effective properties of multiphase viscoelastic composites. Composite Structures 41: 353–367.
Mori, T., and K. Tanaka. 1973. Average stress in the matrix and average elastic energy of materials with misfitting inclusions. Acta Metallurgica 21: 571–574.
Gibiansky, L.V., G.W. Milton, and J.G. Berryman. 1999. On the effective viscoelastic moduli of two-phase media. III. Rigorous bounds on the complex shear modulus in two dimensions. Proceedings of the Royal Society A 455: 2117–2149.
Beurthey, S., and A. Zaoui. 2000. Structural morphology and relaxation spectra of viscoelastic heterogeneous materials. European Journal of Mechanics—A/Solids 19: 1–16.
Scheiner, S., and C. Hellmich. 2009. Continuum microviscoelasticity model for aging basic creep of early-age concrete. Journal of Engineering Mechanics 135: 307–323.
Berlin, A.A., S.A. Wolfson, V.G. Oshmyan, and N.S. Enikolopyan. 1990. Principles for polymer composites design. Moscow (in Russian): Chemistry.
Snarskii, A.A., I.V. Bezsudnov, V.A. Sevryukov, A. Morozovskiy, and J. Malinsky. 2016. Transport processes in macroscopically disordered media (from medium field theory to percolation). Berlin: Springer.
Vinogradov, A.P. 2001. Elecrodynamics of composites. Moscow: URSS.
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Andrianov, I.V., Awrejcewicz, J., Danishevskyy, V.V. (2018). Introduction. In: Asymptotical Mechanics of Composites. Advanced Structured Materials, vol 77. Springer, Cham. https://doi.org/10.1007/978-3-319-65786-8_1
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