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The mechanical modeling of foams is discussed on a microscopic, mesoscopic and macroscopic scale. A homogenization procedure is proposed to relate the models and to give detailed insight into the deformation behavior of foams. The mesoscopic model of open-cell foams is based on beam elements and evaluated for regular hexagonal structures considering small deformations. This approach gives rise to a Cosserat continuum on the macroscopic scale. Especially the misfit in the parameters governing the standard macroscopic model can be explained by the proposed homogenization procedure. This misfit results from f.he nej-lect of the rotations of the cell walls, see Diebels and Steeb.
Rocznik
Tom
Strony
49--63
Opis fizyczny
Bibliogr. 26 poz., rys.
Twórcy
autor
- Saarland University, Faculty of Material Science and Production Engineering, 66123 Saarbrücken, Germany
autor
- Saarland University, Faculty of Material Science and Production Engineering, 66123 Saarbrücken, Germany
autor
- Saarland University, Faculty of Material Science and Production Engineering, 66123 Saarbrücken, Germany
Bibliografia
- [1] R. de Borst. Numerical modelling of bifurcation and localization in cohesive-frictional materials. Pageoph., 137: 386-390, 1991.
- [2] D. Cioranescu, P. Donato. An introduction to homogenization. Oxford University Press, Oxford, 1999.
- [3] E. Cosserat, F. Cosserat. Theorié des corps déformable. A. Herman et Fils, Paris, 1909.
- [4] S. Diebels. Mikropolare Zweiphasenmodelle: Formulierung auf der Basis der Theorie Poröser Medien. Institut für Mechanik (Bauwesen), Lehrstuhl II, II-4, 2001.
- [5] S. Diebels, W. Ehlers. Homogenization method for granular assemblies. In: W. Wall, K.-U. Bletzinger, K. Schweizerhof, eds., Trends in Computational Mechanics, 79-88. CIMNE, Barcelona, 2001.
- [6] S. Diebels, H. Steeb. The size effect in foams and its theoretical and numerical investigation. Proc. R. Soc. Lond. A, 458: 2869-2883, 2002.
- [7] S. Diebels, H. Steeb. Stress and couple stress in foams. Comp. Mat. Science, 28: 714-722, 2003.
- [8] T. Ebinger. Modelling and homogenization of foams. Institut für Mechanik (Bauwesen), Lehrstuhl II, 11-23, 2002.
- [9] W. Ehlers, S. Diebels, E. Ramm, G. d'Addetta. From particle ensembles to cosserat continua: homogenization of contact forces towards stresses and couple stresses. Int. J. Solids Structures, in press.
- [10] A. Eringen. Microcontinuum field theories. Volume I: Foundations and solids. Springer-Verlag, Berlin, 1999.
- [11] A. Eringen, C. Kafadar. Polar field theories. In: A. Eringen, ed., Volume IV: Polar and nonlocal field theories, 1-73, Academic Press, Boston-New York, 1976.
- [12] S. Forest. Mechanics of generalized continua: Construction by homogenization. Journal de Physique IV, 8: 39-48, 1998.
- [13] S. Forest, K. Sab. Cosserat overall modeling of heterogeneous materials. Mechanics Research Communications, 25: 449-454, 1998.
- [14] L. Gibson, M. Ashby. Cellular solids. Structure and properties. Cambridge University Press, Cambridge, 1997.
- [15] Z. Hashin. Analysis of composite materials - a survey. ASME J. Appl. Mech., 50: 481-505, 1983.
- [16] P. Hill. A self-consistent mechanics of composite materials. J. Mech. Phys. Solids, 13: 213-222, 1965.
- [17] J. Hohe, W. Becker. Effective stress-strain relations for two-dimensional cores: Homogenization, material models and properties. Appl. Mech. Rev., 55: 61-87, 2002.
- [18] C. Huet. An integrated micromechanics and statistical continuum thermodynamics approach for studying the fracture behavior of microcracked heterogeneous materials with delayed response. Eng. Fracture Mech., 58: 459-556, 1997.
- [19] Y. Kouznetsoya. Computational homogenization for the multi-scale analysis of multi-phase materials. Technical University Eindhoyen, Eindhoyen, 2002.
- [20] R. Lakes. Experimental microelasticity of two porous solids. Int. J. Solids Structures, 22: 55-63, 1986.
- [21] S. Nemat-Nasser, M. Hori. Micromechanics: Overall properties of heterogeneous materials. Elsevier, Amsterdam, 1993.
- [22] P. Onck, E. Andrews, L. Gibson. Size effects in ductile cellular solids. Part I: Modeling. Int. J. Mech. Sci., 43: 681-699, 2001.
- [23] M. Schrad, N. Triantafyllidis. Scale effects in media with periodic and nearly periodic microstructures. Part 1: Macroscopic properties. ASME J. Appl. Mech., 64: 751-762, 1997.
- [24] C. Tekoglu and P. R. Onck. A comparison of discrete and Cosserat continuum analyses for cellular materials. In: J. Banhart, N. Fleck, eds., Cellular Metals and Metal Forming Technology, MIT-Verlag, 2003, to appear.
- [25] W. Warren, E. Byskoy. Three-field symmetry restrictions on two-dimensional micropolar materials. Eur. J. Mech., A/Solids, 21: 779-792, 2002.
- [26] W. Yolk. Untersuchung des Lokalisierungsyerhaltens mikropolarer poröser Medien. Institut für Mechanik (Bauwesen), Lehrstuhl II, II-2, 1999.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BPB1-0013-0011