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Minimal kinematic boundary conditions for computational homogenization of the permeability coefficient

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Języki publikacji
EN
Abstrakty
EN
In the paper, computational homogenization approach is used for recognizing the macroscopic permeability from the microscopic representative volume element (RVE). Flow of water, at both macro and micro level, is assumed to be ruled by Darcy law. A special averaging constraint is used for numerical flow analysis in RVE, which allows to apply macroscopic pressure gradient without the necessity to use directly Dirichlet or Neumann boundary conditions. This approach allows arbitrarily shaped representative volumes and eliminates undesirable boundary effects. Generated effective permeability takes into account the structuring effects, what is an advantage over other homogenization methods, like self-consistent one.
Rocznik
Strony
199--203
Opis fizyczny
Bibliogr. 17 poz., rys.
Twórcy
  • Technical University of Lodz, Department of Civil Engineering, Architecture and Environmental Engineering, Chair of Geotechnics and Engineering Structures, Al. Politechniki 6, 90-924 Łódź, Poland
Bibliografia
  • 1. Babuška I., Strouboulis T. (2001), The finite element method and its reliability, Clarendon Press, Oxford.
  • 2. Bertsekas D.P. (1982), Constrained optimization and Lagrange multiplier methods, Athena Scientific, Belmont, Massachusetts.
  • 3. Boutin C., Kacprzak G., Thiep D. (2011), Compressibility and permeability of sand–kaolin mixtures. Experiments versus non-linear homogenization schemes, International Journal for Numerical and Analytical Methods in Geomechanics, 35(1), 21-52.
  • 4. Brenner S.C., Scott R. (2007), The mathematical theory of finite element methods (Vol. 15), Springer Science & Business Media.
  • 5. Chapuis R.P. (1990), Sand-bentonite liners: predicting permeability from laboratory tests, Canadian Geotechnical Journal, 27(1), 47-57.
  • 6. Du X., Ostoja-Starzewski M. (2006), On the size of representative volume element for Darcy law in random media, in Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science, 462(2074), 2949-2963, The Royal Society.
  • 7. Feyel F. (2003), A multilevel finite element method (FE 2) to describe the response of highly non-linear structures using generalized continua, Computer Methods in Applied Mechanics and Engineering, 192(28), 3233-3244.
  • 8. Geers M.G.D., Kouznetsova V.G., Brekelmans W.A.M. (2001), Gradient-enhanced computational homogenization for the micromacro scale transition, Le Journal de Physique IV, 11(PR5), Pr5-145.
  • 9. Hill R. (1965), Continuum micro-mechanics of elastoplastic polycrystals, Journal of the Mechanics and Physics of Solids, 13(2), 89-101.
  • 10. Inglis H.M., Geubelle P.H., Matouš K. (2008), Boundary condition effects on multiscale analysis of damage localization, Philosophical Magazine, 88(16), 2373-2397.
  • 11. Juang, C.H., Holtz R.D. (1986), Fabric, pore size distribution, and permeability of sandy soils, Journal of Geotechnical Engineering, 112(9), 855-868.
  • 12. Kacprzak G. (2006), Etude du comportement mécanique des mélanges sable/argile, PhD ENTPE/INSA, Lyon.
  • 13. Kouznetsova V.G., Geers M.G.D., Brekelmans W.A.M. (2010), Computational homogenisation for non-linear heterogeneous solids, Multiscale Modeling in Solid Mechanics: Computational Approaches, 3, 1-42.
  • 14. Mesarovic S.D., Padbidri J. (2005), Minimal kinematic boundary conditions for simulations of disordered microstructures, Philosophical Magazine, 85(1), 65-78.
  • 15. Revil A., Cathles L.M. (1999), Permeability of shaly sands, Water Resources Research, 35(3), 651-662.
  • 16. Wojciechowski M. (2014) Fempy – finite element method in python, http://fempy.org, http://geotech.p.lodz.pl:5080/fempy, last access: August 2017.
  • 17. Wojciechowski M., Lefik M. (2016), On the static nature of minimal kinematic boundary conditions, Engineering Transactions, 64(4), 581-587.
Uwagi
Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-11be123a-610e-4c25-ac8d-377f77fd9ee0
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