×

zbMATH — the first resource for mathematics

Multiparticle effective field and related methods in micromechanics of random structure components. (English) Zbl 1128.74301
Summary: In this paper, linearly thermoelastic composite media are treated, which consist of a homogeneous matrix containing a statistically homogeneous random set of ellipsoidal uncoated or coated inclusions. Effective properties (such as compliance, thermal expansion, stored energy) as well as the first statistical moments of stresses in the components are estimated for both the general case of nonhomogeneity of the thermoelastic inclusion properties and arbitrary choice of comparison medium. The micromechanical approach is based on Green’s function techniques as well as on the generalization of the “multiparticle effective field” method (MEFM), previously proposed for the estimation of stress field averages in the components for the case of coinciding elastic moduli of the matrix and comparison medium. The author considers in detail the connection of methods proposed with numerous related methods and demonstrates that the MEFM includes, as particular cases, the well-known methods of mechanics of strongly heterogeneous media (such as the effective medium and the mean field methods and some others).

MSC:
74A40 Random materials and composite materials
74A60 Micromechanical theories
74E30 Composite and mixture properties
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Willis, J. R., ASME J. Appl. Mech. 50 pp 1202– (1983) · Zbl 0539.73003 · doi:10.1115/1.3167202
[2] Shermergor, T D., The Theory of Elasticity of Microinhomogeneous Media (1977)
[3] Christensen, R. M., Mechanics of Composite Materials (1979)
[4] Willis, J. R., Advances in Applied Mechanics 21 pp 1– (1981) · Zbl 0476.73053 · doi:10.1016/S0065-2156(08)70330-2
[5] Kanaun, S. K., Elastic Media with Microstructure pp 165– (1983)
[6] DOI: 10.1007/978-94-009-3489-4 · doi:10.1007/978-94-009-3489-4
[7] Kreher, W., Internal Stresses in Heterogeneous Solids (1989) · Zbl 0760.73001
[8] Nemat-Nasser, S., Micromechanics: Overall Properties of Heterogeneous Materials (1993) · Zbl 0924.73006
[9] Kanaun, S. K., Advances in Mathematical Modeling of Composite Materials pp 1– (1994)
[10] Markov, K. Z., Heterogeneous Media: Micromechanics, Modeling, Methods, and Simulations pp 1– (1999)
[11] Khoroshun, L. P., Prikl. Mekh. 30 pp 30– (2000)
[12] Buryachenko, V A., Appl. Mech. Reviews 54 pp 1– (2001) · doi:10.1115/1.3097287
[13] Hill, R., J. Mech. Phys. Solids 13 pp 212– (1965)
[14] Mori, T., Acta Metall 21 pp 571– (1973) · doi:10.1016/0001-6160(73)90064-3
[15] Benveniste, Y., Mech. Mater 6 pp 147– (1987) · doi:10.1016/0167-6636(87)90005-6
[16] Morse, P M., Methods of Theoretical Physics: Parts I and II (1953) · Zbl 0051.40603
[17] Foldy, L. L., Physical Review 67 pp 107– (1945) · Zbl 0061.47304 · doi:10.1103/PhysRev.67.107
[18] Lax, M., Phys. Rev 85 pp 621– (1952) · Zbl 0047.23501 · doi:10.1103/PhysRev.85.621
[19] Chaban, I. A., Akust. Zhurn. 10 pp 351– (1965)
[20] Kachanov, M., Advances in Applied Mechanics 30 pp 259– (1993) · doi:10.1016/S0065-2156(08)70176-5
[21] Buryachenko, V A., J. Mech. Phys. Solids 43 pp 1105– (1995) · Zbl 0881.73093 · doi:10.1016/0022-5096(95)00029-I
[22] Buryachenko, V A., Europ. J. Mech. A/Solids 16 pp 79– (1997)
[23] Lekhnitskii, A. G., Theory of Elasticity of an Anisotropic Elastic Body (1963)
[24] Buryachenko, V A., Mathematics and Mechanics of Solids 6 pp 299– (2001) · Zbl 1028.74006 · doi:10.1177/108128650100600306
[25] Gel’fand, I. A., Generalized Functions (1964)
[26] Buryachenko, V A., Mekh. Kompoz. Mater 3 pp 420– (1990)
[27] Buryachenko, V A., European Journal of Mechanics A/Solids 17 pp 763– (1998) · Zbl 0929.74024 · doi:10.1016/S0997-7538(98)80004-1
[28] Buryachenko, V A., International Journal of Solids and Structures 37 pp 3177– (2000) · Zbl 0992.74007 · doi:10.1016/S0020-7683(98)00304-7
[29] Buryachenko, V A., Fiz. Zemli 8 pp 32– (1995)
[30] Willis, J. R., Q. J. Mech. App L. Mech. 29 pp 163– (1976) · Zbl 0338.73038 · doi:10.1093/qjmam/29.2.163
[31] Ju, J. W., ASME J. Appl. Mech. 66 pp 570– (1999) · doi:10.1115/1.2791090
[32] Eshelby, J. D., Progress in Solid Mechanics pp 89– (1961) · Zbl 0097.17602
[33] Dvorak, G. J., Proc. Roy. Soc. London 437 pp 291– (1992) · Zbl 0748.73003 · doi:10.1098/rspa.1992.0062
[34] Buryachenko, V A., Int. J. Comput. Civil & Structural Engng. (2001)
[35] Buryachenko, V A., Z. Angew. Math. Phys. 50 pp 934– (1999) · Zbl 0972.74023 · doi:10.1007/s000330050187
[36] Buryachenko, V A., Priklad. Mekh. 11 pp 105– (1986)
[37] Kunin, I. A., Elastic Media with Microstructure (1983) · Zbl 0536.73003 · doi:10.1007/978-3-642-81960-5
[38] Khoroshun, L. P., Priklad. Mekh. 14 (2) pp 3– (1978)
[39] Khoroshun, L. R?, Priklad Mekh. 23 (10) pp 100– (1987)
[40] Buryachenko, V A., Proc. of 9th Int. Conf. on Composites pp 398–
[41] Buryachenko, V A., Priklad. Mekh. Tekhn. Fiz. 3 pp 149– (1989)
[42] Kanaun, S. K., Mekhanika Kompozitnikh Materialov 26 pp 702– (1990)
[43] Chen, H. S., Int. J. Solids Structures 14 pp 349– (1978) · Zbl 0389.73014 · doi:10.1016/0020-7683(78)90017-3
[44] Buryachenko, V A., IUTAMSymp. on Transformation Problems in Composite and Active Materials pp 197– (1998)
[45] Ponte Castanieda, IP, J Mech. Phys. Solids 43 pp 1919– (1995) · Zbl 0919.73061 · doi:10.1016/0022-5096(95)00058-Q
[46] Levin, V M., Docl. Akad. Nauk SSSR 220 pp 1042– (1975)
[47] Levin, V M., Prikl. Matem. Mekh. 41 pp 735– (1977)
[48] Stang, H., Int. J. Solids Structures 22 pp 1259– (1986) · Zbl 0602.73062 · doi:10.1016/0020-7683(86)90080-6
[49] Levin, V M., Izv ANSSSR, Mekh. Tverd. Tela 2 pp 88– (1967)
[50] Rosen, B. W., Int. J. Engng. Sci. 8 pp 157– (1970) · doi:10.1016/0020-7225(70)90066-2
[51] Buryachenko, V A., Int. J. Solids Structures 36 pp 3837– (1999) · Zbl 0963.74015 · doi:10.1016/S0020-7683(98)00170-X
[52] Khoroshun, L. P., Priklad. Mekh. 32 (5) pp 22– (1996)
[53] Willis, J. R., J. Mech. Phys. Solids 25 pp 185– (1977) · Zbl 0363.73014 · doi:10.1016/0022-5096(77)90022-9
[54] Buryachenko, V A., Compos. Sci. Technol. 60 pp 2465– (2000) · doi:10.1016/S0266-3538(00)00041-5
[55] Buryachenko, V A., Archive Appl. Mech. 71 pp 249– (2001) · Zbl 1097.74508 · doi:10.1007/s004190000122
[56] Kreger, I. W., Advances in Colloid and Interface Sci. 3 pp 111– (1972) · doi:10.1016/0001-8686(72)80001-0
[57] Norris, A. N., ASME J. Appl. Mech. 56 pp 83– (1989) · Zbl 0728.73047 · doi:10.1115/1.3176070
[58] Ferrari, M., Mech. Mater 11 pp 251– (1991) · doi:10.1016/0167-6636(91)90006-L
[59] Benveniste, Y., J. Mech. Phys. Solids 39 pp 929– (1991) · Zbl 0754.73018 · doi:10.1016/0022-5096(91)90012-D
[60] Weng, G. J., Int. J Engng. Sci. 28 pp 1111– (1990) · Zbl 0719.73004 · doi:10.1016/0020-7225(90)90111-U
[61] Ju, J. W., Macroscopic Behavior of Heterogeneous Materialsfi-om the Microstructure pp 95– (1992)
[62] Ju, J. W., J. Appl. Mech. 61 pp 349– (1994) · Zbl 0837.73051 · doi:10.1115/1.2901451
[63] Ju, J. W., Acta Mech. 103 pp 103– (1994) · Zbl 0811.73045 · doi:10.1007/BF01180221
[64] Ju, J. W., Acta Mech. 103 pp 123– (1994) · Zbl 0811.73044 · doi:10.1007/BF01180222
[65] Ju, J. W., Int. J. Solids Structures 35 pp 941– (1998) · Zbl 0931.74061 · doi:10.1016/S0020-7683(97)00090-5
[66] Ju, J. W., Int. J. Solids Structures 33 pp 4327– (1996) · Zbl 0921.73064 · doi:10.1016/0020-7683(95)00232-4
[67] Ju, J. W., Int. J. Solids Structures 38 pp 4045– (2001) · Zbl 1047.74045 · doi:10.1016/S0020-7683(00)00270-5
[68] Kosheleva, A. A., Mekhanika Kompozititnykh Materialov 19 pp 416– (1983)
[69] Kachanov, M., Int. J. Solids Structures 23 pp 23– (1987) · Zbl 0601.73096 · doi:10.1016/0020-7683(87)90030-8
[70] Zhou, S. A., Int. J. Engng Sci. 24 pp 1195– (1986) · Zbl 0587.73010 · doi:10.1016/0020-7225(86)90014-5
[71] Fassi-Fehri, O., Int. J. Engng. Sci. 27 pp 495– (1989) · Zbl 0682.73014 · doi:10.1016/0020-7225(89)90002-5
[72] Lipinski, P., Int. J. Plasticity 5 pp 149– (1989) · Zbl 0695.73013 · doi:10.1016/0749-6419(89)90027-2
[73] Lipinski, P., Archive of Appl. Mechanics 65 pp 295– (1995) · Zbl 0837.73028 · doi:10.1007/BF00789222
[74] Kanaun, S. K., Zhurnal Prikladnoi i Tehknich. Fiziki 18 (2) pp 160– (1977)
[75] Ju, J. W., Int. J Damage Mechanics 1 pp 102– (1992) · doi:10.1177/105678959200100106
[76] Ju, J. W., Int. J. Damage Mechanics 4 pp 23– (1995) · doi:10.1177/105678959500400103
[77] Budiansky, Y., J. Mech. Phys. Solids 13 pp 223– (1965) · doi:10.1016/0022-5096(65)90011-6
[78] Christensen, R. M., J. Mech. Phys. Solids 27 pp 315– (1979) · Zbl 0419.73007 · doi:10.1016/0022-5096(79)90032-2
[79] Hori, M., Mech. Mater 14 pp 189– (1993) · doi:10.1016/0167-6636(93)90066-Z
[80] Huang, Y., J. Mech. Phys. Solids 94 pp 491– (1994) · Zbl 0794.73039 · doi:10.1016/0022-5096(94)90028-0
[81] Zheng, Q.-S., J. Mech. Phys. Solids 49 pp 2265– (2001)
[82] Norris, A. N., J. Mech. Phys. Solids 33 pp 525– (1985) · Zbl 0579.73114 · doi:10.1016/0022-5096(85)90001-8
[83] Buryachenko, V A., Priklad. Mekh. Tekhn. Fiz. 3 pp 148– (1992)
[84] Willis, J. R., Continuum models of disordered systems pp 185– (1978)
[85] Dyskin, A. V., Continuum Modelsfor Materials with Microstructure pp 69– (1995)
[86] Berveiller, M., International Journal of Engineering Science 25 pp 691– (1987) · Zbl 0612.73010 · doi:10.1016/0020-7225(87)90058-9
[87] Rodin, G. J., International Journal of Solids and Structures 27 pp 145– (1991) · doi:10.1016/0020-7683(91)90225-5
[88] Moschovidis, Z. A., ASME J. Appl. Mech. 42 pp 847– (1975) · Zbl 0338.73015 · doi:10.1115/1.3423718
[89] Hori, M., J. Mech. Phys. Solids 35 pp 000– (1987) · Zbl 0616.73091 · doi:10.1016/0022-5096(87)90019-6
[90] Buryachenko, V A., Acta Mech. 119 pp 93– (1996) · Zbl 0877.73040 · doi:10.1007/BF01274241
[91] Buryachenko, V A., Mech. Res. Commun. 25 pp 117– (1998) · Zbl 0928.74022 · doi:10.1016/S0093-6413(98)00014-7
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.