Identyfikatory
Warianty tytułu
Metody homogenizacji stosowane w mechanice ośrodków porowatych
Języki publikacji
Abstrakty
The present paper surveys and compares methods of homogenisation appiled to porous media mechanics. In particular, it details the methods: volumetric averaging, averaging by weight, self-consistent, asymptotic homogenisation method for periodic structures as well as two-scale convergence. The closure hypothesis for a representative volume element has been discussed.
W artykule dokonano przeglądu i porównania metod homogenizacji stosowanych w mechanice ośrodków porowatych. W szczególności przedstawiono metody: objętościowego uśredniania wagowego, metody samouzgodnień, asymptotycznej metody homogenizacji dla struktur periodycznych oraz tzw. Metody zbieżności wg podwójnej skali. Omówiono zagadnienie hipotezy zamykającej dla reprezentatywnej elementarnej objętości.
Słowa kluczowe
Czasopismo
Rocznik
Tom
Strony
657--679
Opis fizyczny
Bibliogr. 49 poz., rys.
Twórcy
Bibliografia
- 1. ALLAIRE G., 1992, Homogenization and Two-Scale Convergence, SIAM J. Math. Anal, 23, 6, 1482-1518.
- 2. AURIAULT J.L., 1991, Dynamic Behaviour of Porous Media, in Transport Processes in Porous Media, J. Bear and M.Y. Corapcioglu (edit.), Kluwer Academic Publishers, 471-519.
- 3. AURIAULT J.L., BOUTIN C, 1992, Deformable Porous Media with Double Porosity. Quasistatics. I: Coupling Effects, Transport in Porous Media, 7, 63-82.
- 4. AURIAULT J.L., BOUTIN C, 1993, Deformable Porous Media with Double Porosity. Quasistatics. II: Memory Effects, Transport in Porous Media, 10,153-169.
- 5. AURIAULT J.L., SANCHEZ-PALENCIA E., 1977, Étude de comportement macroscopique d'un milieu poreux saturé deformable, Journal de Mécanique, 16, 4, 575-603.
- 6. AURIAULT J.L, 1987, Nonsaturated Deformable Porous Media: Quasistatics, Transport in Porous Media, 2, 45-64.
- 7. BARRERÉ J., GIPOULOUX O., WHITAKER S., 1992, On the Closure Problem for Darcy's Law, Transport in Porous Media, 7, 209-222.
- 8. BEDFORD A., DRUMHELLER D.S., 1983, Theories of Immiscible and Structured Mixtures, Int. J. Engng. Sci, 21, 8, 863-960.
- 9. BENSOUSSAN A., LIONS J.L., PAPANICOLAU G., 1978, Asymptotic Analysis for Periodic Structures, North-Holland Publishing Company, Amsterdam.
- 10. BOUTIN C, 1996, Microstructulal Effects in Elastic Composities, Int. J. Solids Structures, 33, 7, 1023-1051.
- 11. BOUTIN C, AURIAULT J.L., 1990, Dynamic Behaviour of Porous Media Saturated by a Viscous Fluid. Application to Bituminous Concretes, Int. J. Engng. Sci., 28, 11, 1157-1181.
- 12. BUDIANSKY B., O'CONNELL R.J., 1976, Elastic Moduli of a Cracked Solid, Int. J. Solids and Struct., 12, 81-96.
- 13. DE BUHAN P., TALIERCIO A., 1991, A Homogenization Approach to the Yield Strength of Composite Material, Eur. J. Mech., A/Solids, 10, 2, 129-154.
- 14. BUISSON M., MOLINARI A., BERVEILLER M., 1990, On a Constitutive Relation for Heterogeneous Thermoelastic Media, Arch. Mech., 42, 2, 197-221.
- 15. EMERIAULT F., CAMBOU B., MAHBOUBI A., 1996, Homogenization for Granular Materials: Non-Reversible Behaviour, Mechanics of Cohesive-Frictional Materials, 1, 199-218.
- 16. ENE H.I., POLISEWSKI D., 1987, Thermal Flow in Porous Media, D. Reidel Publishing Company, Boston.
- 17. GAŁKA A., TELEGA J.J., WOJNAR R., 1994, Thermodiffusion in Heterogeneous Elastic Solids and Homogenization, Arch. Mech., 46, 3, 267-314.
- 18. GEE L.M. ET AL., 1990, Liquid to Solidlike Transitions of Molecularly Thin Films under Shear, J. Chem. Phys., 93, 3, 1895-1906.
- 19. GILBERT F., 1990, Change of Scale in Multiphase Media: the Case of Saturated Soils, in: Geomaterials: Constitutive Equations and Modelling, F. Darve (edit.), 329-347.
- 20. HASHIN Z., 1983, Analysis of Composite Materials: a Survey, J. Appl. Mech., 50, 481-505.
- 21. HASHIN Z., 1988, The Diffrential Scheme and its Application to Cracked Materials, J. Mech. Phys. Solids, 36, 719-734.
- 22. HASSANIZADEH S.M., GRAY W.G., 1990, Mechanics and Thermodynamics of Multiphase Flow in Porous Media Including Interphase Boundaries, Adw. Water Res., 169-186.
- 23. HILL R., 1965, A Self Consistent Mechanics of Composite Materials, J. Mech. Phys. Solids, 13, 213-222.
- 24. KACHANOV M., 1992, Effective Properties of Cracked Solids: Critical Review of Some Basic Concepts, Appl. Mech. Rev., 45, 8, 304-335.
- 25. KAVIANY M., 1991, Principles of Heat Transfer in Porous Media, Springer-Verlag, New York.
- 26. KISIEL I. (EDIT.), 1982, Mechanika skał i gruntów, seria Mechanika Techniczna, VII, PWN, Warszawa10 — Mechanika Teoretyczna.
- 27. LASON M., 1988, Specific Surface of Porous Materials, Arch. Min. Sci., 33, 475-497.
- 28. KELLER J.B., 1980, Darcy's Law for Flow in Porous Media and the Two-Space Method, in: Nonlinear Partial Differential Equations in Engineering and Applied Science, edit. Sternberg R., Kalinowski A., Papadakis J., Lecture Notes in Pure and Applied Mathematics, 54, 429-443.
- 29. KRONER E., 1972, Statistical Continuum Mechanics, Springer-Verlag, Wien.
- 30. KRONER E., 1980, Effective Elastic Moduli of Periodic and Random Media: a Unification, Mechanics Research Comunications, 7, 5, 323-327.
- 31. LYDZBA D., 1996a, Introduction to the Homogenization Method in Geomechanics, Report de EUDIL de Universite des Sciences et Technologies de Lille.
- 32. LYDZBA D., AURIAULT J.L., 1996, Gas Filtration Through Porous Coal Medium. Effect of the Gas Constrained in Micropores, Arch. Mech., 48, 3, 447-473.
- 33. LYDZBA D., 1996, Consolidation of Porous Medium Saturated with Gas and with Sorption Phenomenon. Part I - Asymptotic Analysis, Studia Geot. Mech., 1-2, 45-58.
- 34. LYDZBA D., 1997, Consolidation of Porous Medium Saturated with Gas and with Sorption Phenomenon. Part II - Parameters' Identification, Studia Geot. Mech., 1-2, 63-77.
- 35. MEI C.C., AURIAULT J.L., 1989, Mechanics of Heterogeneous Porous Media with Several Spatial Scales, Proc. R. Soc. Lond., A 426, 391-423.
- 36. MEI C.C., AURIAULT J.L., 1991, The Effect of Weak Inertia on Flow Through a Porous Medium, J. Fluid Mech., 222, 647-663.
- 37. MURAD M.A., BENNETHUM L.S., CUSHMAN J.H., 1995, A Multi-Scale Theory of Swelling Porous Media: I. Application to One-Dimensional Consolidation, Transport in Porous Media, 19, 93-122.
- 38. NGUETSENG G., 1989, A General Convergence Result for a Functional Related to the Theory of Homogenization, SIAM J. Math. Anal., 20, 608-623.
- 39. NIGMATULIN R.I., 1981, Three-Dimensional Averaging in the Mechanics of Heteregoneous Media, Fluids Mechanics-Soviet Research, 10, 4, 72-105.
- 40. RUBINSTAIN J., TORQUATO S., 1989, Flow in Random Porous Media: Variational Principles and Rigorous Bounds, J. Fluid Mech., 206, 25-46.
- 41. SANCHEZ-PALENCIA E., 1987, Boundary Layers and Edge Effects in Compo-sities, in: Homogenization Techniques for Composities Media, Lecture Notes in Physics, 272, Springer-Verlag, Berlin.
- 42. SANCHEZ-PALENCIA E., 1980, Non-Homogeneous Media and Vibration Theory, Lecture Notes in Physics, 127, Springer-Verlag, Berlin
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BWM1-0002-0039