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Konferencja
Proceedings of the IX Conference "Applications of algebra" (9 ; 07-13.03.2005 ; Zakopane, Poland)
Języki publikacji
Abstrakty
A review of studies concerning models of crystal defects in solids is presented. The emphasis is on describing imperfections in nonlocal elastic continuum. Nonlocal theory reduces to the classical theory of elasticity in the long wave-length limit and to the atomic lattice theory in the short wave-length limit.
Rocznik
Tom
Strony
107--129
Opis fizyczny
Bibliogr. 137 poz.
Twórcy
autor
- Institute of Mathematics and Computer Science Jan Długosz University of Częstochowa, al. Armii Krajowej 13/15, 42-200 Częstochowa, Poland
Bibliografia
- [1] A.C. Damask, G.J. Diens. Point Defects in Metals. Gordon and Breach Science Publishers, New York, 1963.
- [2] H.G. Van Bueren. Defects in Solids. North-Holland Publishing Company, Amsterdam, 1960.
- [3] J. Fridel. Dislocations. Pergamon Press, New York, 1964.
- [4] L.D. Landau, E.M. Lifshitz. Cource of Theoretical Physics. Theory of Elasticity. Pergamon Press, Oxford, 1986.
- [5] J.P. Hirth, J. Lothe. Theory of Dislocations. McGraw-Hill, New York, 1968.
- [6] A.E. Romanov, V.I. Vladimirov. Disclinations in solids. Physica status solidi (a), 78, pp. 11-34,1983.
- [7] A.E. Romanov, V.I. Vladimirov. Disclinations in crystalline solids. Dislocations in Solids, Vol. 9. (Edited by F.R.N. Nabarro). North-Holland, Amsterdam, pp. 191-402, 1992.
- [8] R.M. Thomson, F. Seitz. Structure of Solids. Fracture: An Advanced Treatise. Vol. 1. Microscopic and Macroscopic FundamentaIs. (Edited by H. Liebowitz). Academic Press, New York, pp. 1-97, 1968.
- [9] A. Kelly, G.W. Groves, P. Kidd. Crystallography and Crystal Defects. Wiley, Chichester, 2000.
- [10] Fracture: A Topical Encyclopedia of Current Knowledge. (Edited by G.P. Cherepanov). Krieger, Melbourne, 1998.
- [11] J.D. Eshelby. The continuum theory of lattice defects. Solid State Physics. Vol. 3. (Edited by F. Seitz and D. Turnbull). Academic Press, New York, pp. 79-144, 1956.
- [12] T. Mura. Micromechanics of Defects in Solids. Martinus Nijhoff Pub., Dordrecht, 1987.
- [13] E. Kröner. Kontinuumstheorie der Versetzungen und Eigenspannungen. Springer-Verlag, Berlin, 1958.
- [14] C.Teodosiu. Elastic Models of Crystal Defects. Springer-Verlag, Berlin, 1982.
- [15] V. Volterra. Sur l'equilibre des corps élastiques multiplement connexes. Annal. Ecole Norm. Super., Ser. 3, 24, pp. 401-517, 1907.
- [16] A.E.H. Love. A Treatise on the Mathematical Theory of Elasticity. Cambridge University Press, Cambridge, 1927.
- [17] T. Mura. Semi-microscopic plastic distortion and disclinations. Arch. Mech., 24, pp. 449-456, 1972.
- [18] M. Polanyi. Über eine Art Gitterstörung, die einem Kristall plastisch machen könnte. Z. Phys., 89, S. 660-664, 1934.
- [19] G.I. Taylor. The mechanism of plastic deformation of crystals. I-II. Proc. Roy. Soc., A145, pp. 362-388, 1934.
- [20] E. Orowan. Zur Kristallplastizitát. III. Über die Mechanismus des Gleitvorganges. Z. Phys., 89, S. 634-659, 1934
- [21] A.H. Cottrell. Dislocations and Plastic Flow in Crystals. Oxford University Press, Oxford, 1953.
- [22] W.T. Read. Dislocations in Crystals. McGraw-Hill, New York, 1953.
- [23] F.R.N. Nabarro. Theory of Crystal Dislocations. Clarendon Press Oxford 1967.
- [24] A.M. Kosevich. Dislocations in the Theory of Elasticity. Naukova Dumka, Kiev, 1978. (In Russian).
- [25] D. Hull, D.J. Bacon. Introduction to Dislocations, 4th Edition . Pergamon Press, Oxford, 2001.
- [26] F. Kroupa. Circular edge dislocation loop. Czech. J. Phys. Ser. B, 10, pp. 284-293, 1960.
- [27] F. Kroupa. Dislocation loops. Theory of Crystal Defects. (Edited by B. Gruber). Academia, Prague, pp. 275-316, 1966.
- [28] M.J. Marcinkowski, K.S. Sree Harsha. Properties of finite circular dislocation glide loops. J. Appl. Phys., 39, pp. 1775-1783, 1968.
- [29] T.A. Khraishi, J.P. Hirth, H.M. Zbib, M.A. Khaleel. The displacement, and strain-stress fields of a general circular Volterra dislocation loop. Int. J. Engng. Sci., 38, pp. 251-266,2000.
- [30] A.L. Kolesnikova, A.E. Romanov. Circular dislocation-disclination loops and their application to boundary problem solution in the theory of defects, Ioffe Physico- Technical Institute, Leningrad, Preprint No. 1019, 1986. (In Russian).
- [31] J.C.M. Li, J.J. Gilman. Disclination loops in polymers. J. Appl. Phys., 41, pp. 4248-4256, 1970.
- [32] Y. Bouligand. Geometry and topology of defects in liquid crystals. Physique des Défauts. (Edited by F.R.N. Nabarro). North Holland, Amsterdam, pp. 665-711, 1981.
- [33] W.F. Harris. The geometry of disclinations in crystals. Surface and Defect Properties of Solids. Vol. 3. Burlington House, London, pp. 57-92, 1974.
- [34] J.C.M. Li. Disclination model of high angle grain boundaries Surface Sci., 31, pp. 12-26,1972.
- [35] A. Richter, A.E. Romanov, W. Pompe, V.I. Vladimirov. Geometry and energy of disclinations in topologically disordered systems. Physica status solidi (b), 122, pp. 35-45, 1984.
- [36] V.A. Likhachev, R.Yu. Khairov. Introduction to the Theory of Disclinations. Leningrad University Press, Leningrad, 19 (In Russian).
- [37] R. de Witt. Linear theory of static disclinations. Fundamental Aspects of Dislocation. (Edited by J.A. Simmons, R. de Witt and R. Bullough). National Bureau of Standards (US), Special Publication 317, vol. 1, pp. 651-673, 1970.
- [38] R. de Witt. Theory of disclinations: II. Continuous and discrete disclinations in anisotropic elasticity. J. Res. Nat. Bureau Stand., 77 A, pp. 49-100, 1973.
- [39] R. de Witt. Theory of disclinations: III. Continuous and discrete disclinations in isotropic elasticity. J. Res. Nat. Bureau Stand., 77 A, pp. 359-368, 1973.
- [40] R. de Witt. Theory of disclinations: IV. Straight disclinations. J. Res. Nat. Bureau Stand., 77 A, pp. 607-658, 1973.
- [41] W. Huang, T. Mura. Elastic fields and energies of a circular edge disclination and a straight screw disclination. J. Appl. Phys., 41, pp. 5175-5179, 1970.
- [42] G.C.T. Liu, J.C.M. Li. Strain energies of disclination loops. J. Appl. Phys., 42, pp. 3313-3315, 1971.
- [43] H.H. Kuo, T. Mura. Elastic field and strain energy of a circular wedge disclination. J. Appl. Phys., 43, pp. 1454-1457, 1972.
- [44] H.H. Kuo, T. Mura, J. Dundurs. Moving circular twist disclination loop in homogeneous and two-phase materials. Int. J. Engng Sci., 11, pp. 193-201, 1973
- [45] N.I. Muskhelishvili. Some Basic Problems of Mathematical Theory oj Elasticity. Noordhoff, Groningen, Holland, 1953.
- [46] G.P. Cherepanov. Mechanics of Brittle Fracture. Nauka, Moscow, 1974. (In Russian).
- [47] I.N. Sneddon, M. Lowengrub. Crack Problems in the Classical Theory of Elasticity. Wiley, New York, 1969.
- [48] J.N. Goodier. Mathematical theory of equilibrium cracks. Fracture. An Advanced Treatise. Vol. 2. Mathematical Fundamentals. (Edited by H. Liebowitz). Academic Press, New York, pp. 1-66, 1968.
- [49] J.R. Rice. Mathematical analysis in the mechanics of fracture. Fracture. An Advanced Treatise. Vol. 2. Mathematical Fundamentals. (Edited by H. Liebowitz). Academic Press, New York, pp. 191-311, 1968.
- [50] B.A. Bilby, J.D. Eshelby. Dislocations and the theory of fracture. Fracture. An Advanced Treatise. Vol. 1. Microscopie and Macroscopie FundamentaIs. (Edited by H. Liebowitz). Academic Press, New York, pp. 99-182, 1968.
- [51] H. Kanzaki. Point defect in face-centred cubic lattice - I: distortion around defects. J. Phys. Chem. Solids, 2, pp. 24-36, 1957.
- [52] J.H. Hardy. A theoretical study of point defects in the rocksaIt structure substitutional K+ in NaCI. J. Phys. Chem. Solids, 15, pp. 39-49, 1960.
- [53] J. W. Flocken, J.R Hardy. Application of the method of lattice statics to interstitial Cu atoms in Cu. Phys. Rev., 175, pp. 919- 927, 1968.
- [54] J.W. Flocken, J.R Hardy. Application of the method of lattice statics to vacancies in Na, K, Rb, and Cs. Phys. Rev., 177, pp. 1054-1062, 1969.
- [55] H.P. Schober. Point defects and the macroscopic host crystal. Physica. Ser. BC, 131, pp. 27-33, 1985.
- [56] J.H. Harding. Computer simulation of defects in ionic solids. Rep. Progr. Phys., 53, pp. 1403-1400, 1990.
- [57] E.A. Kotomin, RI. Eglitis, G. Borstel, P. W.M. Jacobs. Modeling of Point Defects, Polarons and Excitons in Ferroelectric Perovskites. Computational Materials Science. (Edited by R Catlow and E. Kotomin). Vol. 187 of NATO Science Series, Series III: Computer and Systems Sciences, lOS Press Ohmsha, Washington, DC, pp. 291-307,2003.
- [58] L. Tewordt. Distortion of the lattice around an interstitial, a crowdion, and a vacancy in copper. Phys. Rev., 109, pp. 61-68, 1958.
- [59] W.-M. Shyu, D. Brust, F.G. Fumi. Relaxation effects around vacancies in sodium metal. J. Phys. Chem. Solids, 28, pp. 717- 724, 1967.
- [60] R.A. Johnson, E. Brown. Point defects in copper. Phys. Rev., 127, pp. 446-454, 1962.
- [61] A. Lidiard. The Mott-Littleton method: an introductory survey. J. Chem. Soc., Faraday Trans., Part 2, 85, pp. 341-349, 1989.
- [62] Computer ModelIing in Inorganic Crystallography. (Edited by C.R.A. Catlow). Academic Press, London, 1997.
- [63] V. Celli. Screw dislocation in crystals with diamond structure. J. Phys. Chem. Solids, 19, pp. 100-104, 1961
- [64] L.L. Boyer, J.R. Hardy. Lattice statics applied to screw dislocations in cubic metals. Phil. Mag., 24, pp. 647-671, 1971.
- [65] Dislocations. C.r. colloq. int. CNRS dislocations: Structure de coeur et propriétés physiques. (Edited by P. Veyssiére, L. Kubin and J. Castaing). Aussois, Paris, 1984.
- [66] J.A. Moriarty, V. Vitek, V.V. Bulatov, S. Yip. Atomistic simulations of dislocations and defects. J. Computer-Aided Mater. Design, 9, pp. 99-132, 2002.
- [67] T.A. Kontorova, J.l. Frenkel. Theory of plastic deformation and twinning. J. Exp. Theor. Phys. (Zhurnal Eksperimentalnoj i Teoreticheskoj Fiziki), 8, pp. 89-95, 1938. (In Russian).
- [68] R.E. Peierls. The size of a dislocaton. Proc. Phys. Soc. London, 52, pp. 34-37, 1940
- [69] F.R.N. Nabarro. Dislocations in a simple cubic lattice. Proc. Phys. Soc. London, 59, pp. 256-272, 1947.
- [70] V.V. Bulatov, E. Kaxiras. Semidiscrete variational Peierls framework for dislocation core properties. Phil. Mag. Lett., 78, pp. 4221-4224, 1997.
- [71] A.H.W. Ngan. A new model for dislocation kink-pair activation at low temperature based on the Peierls-Nabarro concept. Phil. Mag. A, 79, pp. 1697-1720, 1999.
- [72] G. Lu, N. Kioussis, V.V. Bulatov, E. Kaxiras. The Peierls Nabarro model revisited. Phil. Mag. Lett., 80, pp. 675-682, 2000.
- [73] G. Schoeck. The core structure, recombination energy and Peierls energy for dislocations in Al. Phil. Mag. A, 81, pp. 1161-1176, 2001.
- [74] M.S. Duesbery. Modeling of the dislocation core. Dislocations in Solids. Vol. 8. Basic Problems and Applications. (Edited by F.R.N. Nabarro). North-Holland, Amsterdam, pp. 67-173, 1989.
- [75] M.S. Duesbery, G.Y. Richardson. The dislocation core in crystalline materials. Crit. Rev. Solid State Mater. Sci., 17, pp. 1-46, 1991.
- [76] M. Doyama, R.M.J. Cotteril. Atomic configurations of disclinations by computer simulation. Phil. Mag., 50, pp. L7-L10, 1984.
- [77] A.J. Mikhailin, A.E. Romanov. Amorphization of a disclination core. Solid State Phys. (Fizika Tverdogo Tela), 28, pp. 601-603, 1986. (In Russian).
- [78] V. Vitek, L. Lejćek, V. Paidar. Models of the cores of dislocations in metals and disclinations in liquid crystals. Czech. J. Phys., 45, pp. 1003-1018, 1995.
- [79] M.Ya. Leonov, V.V. Panasyuk. Development of the smallest cracks in the solid. Appl. Mech. (Prikladnaya Mekhanika), 5, pp. 391-401,1959. (In Ukrainian).
- [80] V.V. Panasyuk. Limit Equilibrium of Brittle Bodies with Cracks. Naukova Dumka, Kiev, 1968. (In Russian).
- [81] D.S. Dugdale. Yielding of steel sheets containing slits. J. Mech. Phys. Solids, 8, pp. 100-104, 1960.
- [82] G.I. Barenblatt. The mathematical theory of equilibrium cracks in brittle fracture. Adv. Appl. Mech., 7, pp. 55-129, 1962.
- [83] C.Hsieh, R. Thomson. Lattice theory of fracture and crack creep. J. Appl. Phys., 44, pp. 2051-2063, 1973.
- [84] D.M. Esterling. Lattice theory of three-dimensional cracks. J. Appl. Phys., 47, pp. 486-493, 1976.
- [85] R. Thomson. Physics of Fracture. Atomistics of Fracture. (Edited by R.M. Latanision and J.R. Pickens), Plenum Press, New York, pp. 167-204, 1983.
- [86] J.H. Weiner, M. Pear. Crack and dislocation propagation in an idealized crystal model. J. Appl. Phys., 46, pp. 2398-2405, 1975.
- [87] W.T. Ashurst, W.G. Hoove. Microscopic fracture studies in the two-dimensional triangular lattice. Phys. Rev., 14, pp. 1465- 1473, 1976.
- [88] K. Sieradzki, G.J. Dienes, A. Paskin, B. Massoumzadeh. Atomistics of crack propagation. Acta Met., 36, pp. 651-663, 1988.
- [89] G.J. Dienes, A. Paskin. Computer modeling of cracks. Atomistics of Fracture. (Edited by R.M. Latanision and J.R. Pickens), Plenum Press, New York, pp. 671-704, 1983.
- [90] J.E. Sinclair, B.R. Lawn. An atomic study of cracks in diamond structure crystals. Proc. Roy. Soc. London, A329, pp. 83-103, 1972.
- [91] P.C. Gehlen. Crack extension in a model of α-iron. Scripta Met., 7, pp. 1115-1118, 1973.
- [92] J.E. Sinclair. The influence of the interatomic force law and of kinks on the propagation of brittle cracks. Phil. Mag., 31, pp. 647-671, 1975.
- [93] J.E. Sinclair, P.C. Gehlen, R.G. Hoagland, J.P. Hirth. Flexible boundary conditions and nonlinear geometric effects in atomic dislocation modeling. J. Appl. Phys., 49, pp. 3890-3897, 1978.
- [94] H.F. Fischmeister, H.E. Exner, M.-H. Poech, S. Kohlhoff, P. Gumbsch, S. Schmauder, L.S. SigI, R. Spiegler. Modelling fracture processes in metals and composite materials. Z. Metallk., 80, pp. 839-846, 1989.
- [95] S. Kohlhoff, P. Gumbsch, H.F. Fischmeister. Crack propagation in b.c.c. crystals studied with a combined finite-element and atomistic model. Phil. Mag. A, 64, pp. 851-878, 1991.
- [96] P. Gumbsch. An atomistic study of brittle fracture: Toward explicit failure criteria from atomistic modeling. J. Mater. Res., 10, pp. 2897-2907, 1995.
- [97] M.W. Finnis. Interatomic forces and the simulation of cracks. Chemistry and Physics of Fracture. (Edited by R.M. Latanision and R.H. Jones). Martinus Nijhoff Publ., Dordrecht, pp. 177-194, 1987.
- [98] R. Thomson, S.J. Zhou, A.E. Carlsson, V.K. Tewary. Lattice imperfections studied by use of lattice Green's functions. Phys. Rev. B, 46, pp. 10613-1022, 1992.
- [99] E.B. Tadmor, M. Ortiz, R. Phillips. Quasicontinuum analysis of defects in solids. Phil. Mag. A, 73, pp. 1529-1563, 1996.
- [100] H. Gao, P. Klein. Numerical simulation of crack growth in an isotropie solid with randomized internal cohesive bonds. J. Mech. Phys. Solids, 46, pp. 187-218, 1998.
- [101] E. Kröner. Elasticity theory with long-range cohesive forces. Int. J. Solids Siruciures, 3, pp. 731-742, 1967.
- [102] E. Kröner, B.K. Datta. Nichtlokale Elastostatik: Ableitung aus der Gitteltheorie. Z. Phys., 196, S. 203-211, 1966.
- [103] Y.S. Podstrigach. On one nonlocal theory of deformation of solids. Appl. Mech. (Prikladnaya Mekhanika), 3, (2), pp. 71-76. 1967. (In Russian).
- [104] A.C. Eringen. Linear theory of nonlocal elasticity and dispersion of plane waves. Int. J. Engng Sci., 10, pp. 425-435, 1972.
- [105] A.C. Eringen. Nonlocal polar field theories. Continuum Physics. Vol. 4. Polar and Nonlocal Field Theories. (Edited by A.C. Eringen). Academic Press, New York, pp. 205-267, 1976.
- [106] D.G.B. Edelen. Nonlocal field theories. Continuum Physics. Vol. 4. Polar and Nonlocal Field Theories. (Edited by A.C. Eringen). Academic Press, New York, pp. 75-204, 1976.
- [107] I.A. Kunin. Theory of elastic media with microstructure. Nonlocal theory of elasticity. Nauka, Moscow , 1973. (In Russian).
- [108] D. Rogula. On nonlocal continuum theory of elasticity. Arch. Mech., 25, pp. 233-251,1973.
- [109] A.C. Eringen. Vistas of nonlocal continuum physics. Int. J. Engng. Sci., 30, pp. 1551-1565, 1992.
- [110] A.C. Eringen. Nonlocal Continuum Field Theories. Springer Verlag, New York, 2002.
- [111] A.C. Eringen. On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves. J. Appl. Phys., 54, pp. 4703-4710, 1983.
- [112] Y.Z. Povstenko. Axisymmetric ring loading in nonlocal elastic space. Int. J. Engng. Sci., 39, pp. 285-302, 2001.
- [113] Y.Z. Povstenko. Circular dislocation loops in non-local elasticity. J. Phys. D: Appl. Phys., 28, pp. 105-111, 1995.
- [114] Y.Z. Povstenko. Non-local equations in mathematics and physics. Theory of non-local elasticity. Prace Naukowe WSP w Częstochowie. Matematyka, V, pp. 89-96, 1997.
- [115] L Kovács, G. Vörös. Lattice defects in nonlocal elasticity. Physica. Ser. B., 96, pp. 111-115, 1979.
- [116] L Kovács. Nonlocal elastic interactions between point defects and dislocations. Arch. Mech., 33, pp. 901-908, 1981.
- [117] R. Wang. Non-local elastic interaction energy between a dislocation and a point defect. J. Phys. D: Appl. Phys., 23, pp. 263-265, 1990.
- [118] R. Wang, G.L. Chen, Z.Q. Sun. Application of nonlocal elasticity to the energetics for solute atoms in body-centered cubic transition metals with dislocation. Met. Trans. Ser. A., 23, pp. 3115-3120, 1992.
- [119] Y.Z. Povstenko. Point defect in a nonlocal elastic medium. Math. Methods and Physicomechanical Fields, 41, No. 3, pp. 85-89, 1998. (In Ukrainian). English translation: J. Math. Sci., 104, pp. 1501-1505, 2001.
- [120] A.C. Eringen. Edge dislocation in nonlocal elasticity. Int. J. Engng. Sci., 15, pp. 177-183,1977.
- [121] A.C. Eringen. Screw dislocation in nonlocal elasticity. J. Phys. D: Appl. Phys., 10, pp. 671-678, 1977.
- [122] F. Gao. Screw dislocation in a bi-medium in non-local elasticity, J. Phys. D: Appl. Phys., 23, pp. 328-333, 1990.
- [123] Y.Z. Povstenko. Straight disclinations in nonlocal elasticity. In J. Engng Sci., 33, pp. 575-582, 1995.
- [124] Y.Z. Povstenko. Stress fields produced by circular defects i non-local elastic solid. Elasticity, Viscoelasticity and Optimal Control. Theoretical and Numerical Aspects. Univ. Claude Bernard, Lyon, pp. 133-134, 1995.
- [125] Y.Z. Povstenko, O.A. Matkovskii. Circular disclination loops in nonlocal elasticity. Int. J. Solids and Structures, 37, pp. 6419- 6432, 2000.
- [126] Y.Z. Povstenko. Circular rotational dislocation loop in nonlocal elastic medium. Math. Methods and Physicomechanical Fields, 38, pp. 95-98, 1995. (In Ukrainian).
- [127] A.C. Eringen. Line crack subject to shear. Int. J. Fracture., 14, pp. 367-379, 1978.
- [128] A.C. Eringen, N. Eri. Nonlocal stress field at Griffith crack. Cryst. Latt. Def. Amorph. Mat., 10, pp. 33-38, 1983.
- [129] A.C. Eringen, C.G. Speciale, B.S. Kim. Crack-tip problem in nonlocal elasticity. J. Mech. Phys. Solids, 25, pp. 339-355, 1977.
- [130] L.Y. Jiang, J. Cheng. Non-local theory for cracks in laminated media. Theor. Appl. Fracture Mech., 34, pp. 235-242, 2000.
- [131] R.K.T. Hsieh. Volume defects in nonlocal micropolar elasticity. Int, J. Engng. Sci., 20, pp. 261-270, 1982.
- [132] Y.Z. Povstenko. Modelling of crystal imperfections in non-local elastic continuum. Multiple Scale Analysis and Coupled Physical Systems: Saint- Venant Symposium. Press de l'Ėcole nat. des ponts et chaussées, Paris, pp. 535-542, 1997.
- [133] Y.Z. Povstenko. Imperfections in nonlocal elasticity. Proc. 2nd European Conf. „Mechanics of Materials with Intrinsic Length Scale", Magdeburg, Germany, pp. 299-306, 1998.
- [134] Y.Z. Povstenko. Imperfections in nonlocal elasticity. J. Phys. (Paris) , 8, pp. 309-316, 1998.
- [135] Y.Z. Povstenko. The nonlocal theory of elasticity and its application to the description of defects in solid bodies. Math. Methods and Physicomechanical Fields, 41, No. 1, pp. 90-96, 1998. (In Ukrainian). English translation: J. Math. Sci., 97, pp. 3840- 3845, 1999.
- [136] Y.Z. Povstenko. Nonlocal and gradient elasticity theories and their application to description of imperfections in solids. Math. Methods and Physicomechanical Fields, 46, pp. 136-146, 2003. (In Ukrainian).
- [137] Y.Z. Povstenko, L Kubik. Concentrated ring loading in a nonlocal elastic medium. Int. J. Engng. Sci., 43, pp. 457-471, 2005.
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Bibliografia
Identyfikator YADDA
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