Abstract
This paper describes a numerical method for evaluating the micro and macromechanical response of two-dimensional heterogeneous materials with both periodic and random distribution of the second phase. The proposed method uses two different numerical programs, based on the Voronoi Cell Finite Element Method, developed by the authors. Various numerical examples are executed for validating the effectiveness of the proposed method in evaluating the overall elastic constants of heterogeneous materials, and different comparison with analytical models and experimental results are shown. In order to validate the accuracy of the programs for predicting the stress micro-fields around the inclusion, some comparisons with a FEM commercial numerical code are performed.
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References
Benssousan, A., Lions, J.L. and Papanicoulau, G. (1978). Asymptotic analysis for periodic structure, in Studies in Mathematics and Its Applications, Vol. 5. North-Holland Publishing, Amsterdam.
L. Bertini V. Montanari G. Straffelini (1998) ArticleTitleTensile and bending behaviour of sintered alloys: experimental results and modeling ASME Journal of Engineering Materials and Technology 120 IssueID3 248–255 Occurrence Handle1:CAS:528:DyaK1cXks1Gmurg%3D
B. Budiansky (1965) ArticleTitleOn the elastic moduli of some heterogeneous materials Journal of the Mechanics and Physics of Solids 14 223–227
Cesari, F., Furgiuele, F.M. and Maletta, C. (2003). L’elemento finito ibrido applicato a materiali contenenti vuoti o inclusioni rigide. Proceedings of the XXXII AIAS Conference, Salerno, Italy.
Cesari, F., Furgiuele, F.M. and Martini, D. (2001a). Analisi di Strutture Piane in Materiale Eterogeneo con l’Elemento Finito Ibrido. Proceedings of the XXX AIAS Conference, Alghero, Italy, pp. 1093–1101.
Cesari, F., Furgiuele, F.M. and Martini, D. (2001b). An automatic mesh generator for random composites. Proceedings of the 12th international conference on design tools and methods in industrial design, Rimini, Italy.
H.S. Chen A. Acrivos (1978) ArticleTitleThe effective elastic moduli of composite materials containing spherical inclusions at non-dilute concentrations International Journal Solids Structures 14 315–330
R.M. Christensen K.H. Lo (1979) ArticleTitleSolutions for effective shear properties in three phase sphere and cilinder models Journal of the Mechanics and Physics of Solids 27 315–330 Occurrence Handle10.1016/0022-5096(79)90032-2 Occurrence Handle1:CAS:528:DyaL3cXpsVyhug%3D%3D
Eshelby, J.D. (1958). The determination of the elastic field of an ellipsoidal inclusions and related problems. Proceeding of the Royal Society, Vol. 241A, London, pp. 376–396.
A. Fotiu S. Nemat-Nasser (1995) ArticleTitleOverall properties of elastic-viscoplastic periodic composites International Journal of Plasticity 12 163–190
S. Ghosh S.N. Mukhopadhyay (1991) ArticleTitleA two-dimensional automatic mesh generator for finite element analysis for random composites Computers Structure 41 245–256
S. Ghosh S.N. Mukhopadhyay (1993) ArticleTitleA material based finite element analysis of heterogeneous media involving dirichlet tassellations Computer Methods in Applied Mechanics and Engineering 104 211–247 Occurrence Handle10.1016/0045-7825(93)90198-7
Halpin, J. and Tsai, S.W. (1969). Effects of environmental factors on composite materials. Air Force Materials Lab-Technical Report.
Z. Hashin S. Strikman (1963) ArticleTitleA variational approach to the theory of the elastic behaviour of multiphase materials Journal of the Mechanics and Physics of Solids 11 127–140 Occurrence Handle10.1016/0022-5096(63)90060-7
R. Hill (1965) ArticleTitleA self consistent mechanics of composite materials Journal of the Mechanics and Physics of Solids 13 213–222
M. Hori S. Nemat-Nasser (1993) ArticleTitleDouble inclusion model and overall moduli of multiphase composites Mechanics of Materials 14 189–206 Occurrence Handle10.1016/0167-6636(93)90066-Z
R Luciano E.J. Barbero (1994) ArticleTitleFormulas for stiffness of composites with periodic microstructure International Journal Solids Structures 31 2933–2944
C.T. Lynch (1975) CRC Handbook of Material Science CRC Press Cleveland
N.I. Muskhelishvili (1953) Some Basic Problems of the Mathematical Theory of Elasticity Noordhoff Groningen
S. Nemat-Nasser N. Yu M. Hori (1993) ArticleTitleBounds and estimates of overall moduli of composites with periodic microstructure Mechanics of Materials 15 163–181 Occurrence Handle10.1016/0167-6636(93)90016-K
R. Piltner (1973) ArticleTitleSpecial finite element with hole and internal cracks International Journal for Numerical Methods in Engineering 7 297–308
T. Slot W.J. O’Donnell (1971) ArticleTitleEffective elastic constants for thick perforated plates with square and triangular penetrations patterns Journal of Engineering for Industry 95 1081–1088
S.W. Tsai H.T. Hahn (1980) Introduction to Composite Materials Technomic Publishing Co. Westport, Connecticut, USA
J. Zhang N. Katsube (1997) ArticleTitleA polygonal element approach to random heterogeneous media with rigid ellipses or elliptical voids Computer Methods in Applied Mechanics and Engineering 148 225–234 Occurrence Handle10.1016/S0045-7825(97)00062-5
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Cesari, F., Furgiuele, F.M. & Maletta, C. The Determination of Stress Distribution and Elastic Properties for Heterogeneous Materials with Hybrid Finite Element. Int J Mech Mater Des 2, 1–13 (2005). https://doi.org/10.1007/s10999-005-3309-2
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DOI: https://doi.org/10.1007/s10999-005-3309-2