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Thin layer shear and second order homogenization method

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Wybrane pełne teksty z tego czasopisma
Identyfikatory
Warianty tytułu
Konferencja
Polish Conference on Computer Methods in Mechanics (16 ; 21-24.06.2005 ; Częstochowa, Poland
Języki publikacji
EN
Abstrakty
EN
This paper deals with the second-order computational homogenisation of a heterogeneous materiał under-going smali displacements. Typically, in this approach a representative volume element (RVE) of nonlinear heterogeneous materiał is defined. An a priori given discretised microstructure is considered, without fo-cusing on detailed specific discretisation techniąues. The key contribution of this paper is the formulation of eąuations coupling micro- and macro-variables and the definition of generalized boundary conditions for the microstructure. The coupling between macroscopic and microscopic levels is based on Hill's aver-aging theorem. We focus on deformation-driven microstructures where overall macroscopic deformation is controlled. In the end a numerical example of a thin layer shear is presented.
Rocznik
Strony
537--546
Opis fizyczny
Bibliogr. 10 poz., rys., wykr.
Twórcy
  • Cracow University of Technology, Institute for Computational Civil Engineering ul. Warszawska 2A, 31-155 Kraków, Poland
Bibliografia
  • [1] M. Ainsworth. Essential boundary conditions and multi-point constraints in finite element analysis. Comput. Methods Appl. Mech. Engrg., 190: 6323-6339, 2001.
  • [2] F. Feyel. Multiscale FE2 elastoviscoplastic analysis of composite structures. Comput. Mater. Sci., 16: 344-354, 1999.
  • [3] F. Feyel. A multilevel finite element method (FE2) to describe the response of highly non-linear structures using generalized continua. Comput. Methods Appl. Mech. Engrg., 192: 3233-3244, 2003.
  • [4] L. Kaczmarczyk. Numerical analysis of multiscale problems in mechanics of inhomogeneous media. Ph.D. thesis, Cracow University of Technology, 2006, http://www.15.pk.edu.pl/~likask/phd.html
  • [5] V.G. Kouznetsova. Computational Homogenization for the Multi-scale Analysis of Multi-phase Materials. Ph.D. thesis, Technishe Universiteit, Eindhoven, 2002.
  • [6] V.G. Kouznetsova, M.G.D. Geers, W.A.M. Brekelmans. Size of a representative volume element in a second-order computational homogenization framework. Int. J. Multiscale Comput. Engrg., 2(4): 575-598, 2004.
  • [7] C. Miehe, A. Koch. Computational micro-to-macro transitions of discretized microstructures undergoing small strains. Arch. Appl. Mech., 72: 300-317, 2002.
  • [8] R.D. Mindlin. Second gradient of strain and surface-tension in linear elasticity. Int. J. Solids Struct., 1: 417-438, 1965.
  • [9] S. Nemat-Nasser, M. Hori. Micromechanics: Overall Properties of Heterogeneous Materials. Elsevier, 1999.
  • [10] J.Y. Shu, W.E. King, N.A. Fleck. Finite element for materials with strain gradient effects. Int. J. Num. Meth. Engrg., 44: 373-391, 1999.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BPB2-0025-0056
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