članak: 1 od 1  
Theoretical and Applied Mechanics
2002, br. 28-29, str. 113-144
jezik rada: engleski
neklasifikovan
doi:10.2298/TAM0229113F

Metode homogenizacije i mehanika generalisanih kontinuuma - deo drugi
Ecole des Mines de Paris CNRS, Centre des Mat_eriaux, France

e-adresa: samuel.forest@mat.ensmp.fr

Sažetak

Potreba za uvođenjem generalisanih kontinuuma nastaje u više oblasti mehanike heterogenih materijala i to posebno u teoriji homogenizacije. Neki generalisani homogeni ekvivalentni medijum je na globalnom nivou potreban kada je struktura kompozita izložena oštrim promenama srednjih polja ili kada su unutrašnje (sopstvene) dužine uporedive sa talasnom dužinom promene srednjih polja. U ovom radu se sistematski metod, zasnovan na polinomijalnim razvojima, koristi za zamenu klasičnog kompozitnog materijala ekvivalentnim Cosserat ili mikromorfnim materijalom. U drugom delu smesa mikromorfnih sastojaka se homogenizuje asimptotskim metodom sa više skala. Pokazuje se da rezultujući makroskopski medijum može biti Cauchy-jev, Cosserat, mikrodeformacioni ili mikromorfni medijum zavisno od karakterističnih dužina problema.

Reference

Beran, M.J., McCoy, J.J. (1970) Mean field variations in a statistical sample of heterogeneous linearly elastic solids. International Journal of Solids and Structures, 6:1035-1054
Besdo, D., Dorau, H.U. (1988) Zur modellierung von verbundmaterialien als homogenes cosserat - kontinuum. Zeitschrift fur angewandte Mathematik und Mechanik / ZAMM, 68:T153-T155
Boutin, C. (1996) Microstructural efects in elastic composites. International Journal of Solids and Structures, 33:1023-1051
Bouyge, F., Jasiuk, I., Ostoja, M. (2001) A micromechanically based couple-stress model of an elastic two-phase composite. International Journal of Solids and Structures, 38:1721-1735
Bouyge, F., Jasiuk, I., Boccara, S., Ostoja, M. (2002) A micromechanically based couple-stress model of an elastic orthotropic two-phase composite. European Journal of Mechanics, A: Solids, 21:465-481
Diener, G., Kaseberg, F. (1976) Efiective linear response in strongly heterogeneous media-self-consistent approach. International Journal of Solids and Structures, 12:173- 184
Diener, G., Hurrich, A., Weissbarth, J. (1984) Bounds on the non-local effective elastic properties of composites. Journal of the Mechanics and Physics of Solids, 32:21-39
Drugan, W.J., Willis, J.R. (1996) A micromechanics-based nonlocal constitutive equation and estimates of representative volume element size for elastic composites. Journal of the Mechanics and Physics of Solids, 44, 4, 497-524
Drugan, W.J. (2000) Micromechanics-based variational estimates for a higher-order nonlocal constitutive equation and optimal choice of effective moduli for elastic composites. Journal of the Mechanics and Physics of Solids, 48, 7, 1359-1387
Eringen, A.C. (1999) Microcontinuum field theories. Berlin, itd: Springer Verlag
Forest, S. (1999) Aufbau und Identifikation von Stoffgleichungen für höhere Kontinua mittels Homogenisierungsmethoden. Technische Mechanik, Band 19, Heft 4:297-306
Forest, S. (2001) Cosserat media. u: K.H.J.Buschow R. W. Cahn, M. C. Flemings, B. Ilschner, E. J. Kramer, and S. Mahajan (ur.) Encyclopedia of materials: Science & technology, Amsterdam, itd: Elsevier, pages 1715-1718
Forest, S., Pradel, F., Sab, K. (2001) Asymptotic analysis of heterogeneous Cosserat media. International Journal of Solids and Structures, 38, 27, 4585-4608
Forest, S. (1998) Mechanics of generalized continua: Construction by homogenization. Journal de Physique, IV, 8:Pr4-39-48
Forest, S. (1999) Homogenization methods and the mechanics of generalized continua. u: G.Maugin (ur.) International Seminar on Geometry, Continuum and Microstructure, str.No. 60
Forest, S., Sab, K. (1998) Cosserat overall modeling of heterogeneous materials. Mechanics Research Communications, 25, 4, 449-454
Forest, S., Barbe, F., Cailletaud, G. (2000) Cosserat modelling of size effects in the mechanical behaviour of polycrystals and multi-phase materials. International Journal of Solids and Structures, 37, 47, 7105-7126
Gambin, B., Kroner, E. (1989) Homogenized stress-strain relation of periodic media. Physica Status Solidi (b), 151:513-519
Geers, M.G.D., Kouznetsova, V., Brekelmans, W. (2001) Gradient-enhanced computational homogenization for the micro-macro scale transition. Journal de Physique, IV, 11:Pr5-145-152
Gologanu, M., Leblond, J.B., Devaux, J. (1997) Continuum micromechanics, Recent extensions of Gurson's model for porous ductile metals. Berlin, itd: Springer Verlag
Jonasch, G. (1986) Zur numerischen Behandlung spezieller Scheibenstrukturen als Cosserat - Kontinuum. Fortschr. -Ber. Reihe, Dusseldorf, 18 Nr. 34
Koiter, W.T. (1963) Couple-stresses in the theory of elasticity. Proc. K. Ned. Akad. Wet., B67:17-44
Muhlhaus, H.B. (1995) Continuum models for materials with microstructure. New York, itd: Wiley
Sanchez-Palencia, E. (1974) Comportements local et macroscopique d'un type de milieux physiques h\'et\'erogenes. International Journal of Engineering Science, 12, 331-351
Smyshlyaev, V.P., Cherednichenko, K.D. (2000) On rigorous derivation of strain gradient effects in the overall behavior of periodic heterogeneous media. Journal of the Mechanics and Physics of Solids, 48:1325-1357, 140
Smyshlyaev, V.P., Fleck, N.A. (1994) Bounds and estimates for linear composites with strain gradient effects. Journal of the Mechanics and Physics of Solids, 42, 12, 1851-1882
Stojanović, R. (1972) Recent developments in the theory of polar continua. CISM Courses and Lectures, Berlin, br. 27
Triantafyllidis, N., Bardenhagen, S. (1996) The influence of scale size on the stability of periodic solids and the role of associated higher order gradient continuum models. Journal of the Mechanics and Physics of Solids, 44, 11, 1891-1928