Article
MSC:
35B27,
35Q72,
73B27,
73K20,
74E05,
74E30 | MR 1453931 | Zbl 0898.35007 | DOI: 10.1023/A:1023034411371
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Keywords:
composite materials; homogenization; Hashin-Shtrikman bounds; Halpin-Tsai equations; effective properties; auxiliary partial differential equations; unidirectional elastic fiber composite; fitting parameter
composite materials; homogenization; Hashin-Shtrikman bounds; Halpin-Tsai equations; effective properties; auxiliary partial differential equations; unidirectional elastic fiber composite; fitting parameter
Summary:
In this paper we study a unidirectional and elastic fiber composite. We use the homogenization method to obtain numerical results of the plane strain bulk modulus and the transverse shear modulus. The results are compared with the Hashin-Shtrikman bounds and are found to be close to the lower bounds in both cases. This indicates that the lower bounds might be used as a first approximation of the plane strain bulk modulus and the transverse shear modulus. We also point out the connection with the Hashin-Shtrikman bounds and the Halpin-Tsai equations. Optimal bounds on the fitting parameters in the Halpin-Tsai equations have been formulated.
References:
[1] B. D. Agarwal, L. J. Broutman: Analysis and Performance of Fiber Composites. second edn, Wiley Interscience, New York, 1990.
[2] N. Bakhvalov, G. Panasenko: Homogenization:Averaging Processes in Periodic Media. Kluwer Academic Publishers, Dordrecht, 1989. MR 1112788
[3] A. Cherkaev, L. Gibiansky: Coupled estimates for the bulk and shear moduli of a two-dimensional isotropic elastic composite. J. Mech. Phys. Solids 41(5) (1993), 937–980). DOI 10.1016/0022-5096(93)90006-2 | MR 1214022
[4] G. Dal Maso: An Introduction to $\Gamma $-Convergence. Birkhäuser, Boston, 1993. MR 1201152 | Zbl 0816.49001
[5] J. C. Halpin, J. L Kardos: The Halpin-Tsai equations: A review. Polymer Engineering and science 16(5) (1976), 344–352. DOI 10.1002/pen.760160512
[6] Z. Hashin: On elastic behaviour of fibre reinforced materials of arbitrary transverse phase geometry. J. Mech. Phys. Solids 13 (1965), 119–134. DOI 10.1016/0022-5096(65)90015-3
[7] Z. Hashin: Analysis of composite materials-a survey. J. Mech. Phys. Solids 50 (1983), 481–505. Zbl 0542.73092
[8] Z. Hashin, W. Rosen: The elastic moduli of fiber-reinforced materials. Journal of Applied Mechanics (1964), 223–232. DOI 10.1115/1.3629590
[9] Z. Hashin, S. Shtrikman: A variational approach to the theory of elastic behaviour of multiphase materials. J. Mech. Phys. Solids 11 (1963), 127–140. DOI 10.1016/0022-5096(63)90060-7 | MR 0159459
[10] V. Jikov, S. Kozlov, O. Oleinik: Homogenization of Differential Operators and Integral Functionals. Springer-Verlag, Berlin Heidelberg New York, 1994. MR 1329546
[11] R. Lipton: On the behaviour of elastic composites with transverse isotropic symmetry. J. Mech. Phys. Solids 39(5) (1991), 663–681. DOI 10.1016/0022-5096(91)90046-Q | MR 1112738
[12] D. Lukkasen, L.-E. Persson, P. Wall: Some engineering and mathematical aspects on the homogenization method. Composites Engineering 5(5) (1995), 519–531. DOI 10.1016/0961-9526(95)00025-I
[13] D. Lukkasen, L.-E. Persson, P. Wall: On some sharp bounds for the $p$-Poisson equation. Applicable Analysis 58 (1995), 123–135. DOI 10.1080/00036819508840366 | MR 1384593
[14] G. W Milton: On characterizing the set of possible effective tensors of composites: The variational method and the translation method. Communications on Pure and Applied Mathematics XLIII (1990), 63–125. MR 1024190 | Zbl 0751.73041
[15] G. W. Milton, R. V Kohn: Variational bounds on the effective moduli of anisotropic composites. J. Mech. Phys. Solids 36(6) (1988), 597–629. DOI 10.1016/0022-5096(88)90001-4 | MR 0969257
[16] L.-E. Persson, L. Persson, N. Svanstedt, J. Wyller: The Homogenization Method: An Introduction. Studentlitteratur, Lund, 1993. MR 1250833
[17] E. Sanchez-Palencia: Non Homogeneous Media and Vibration Theory. Lecture Notes in Physics 127, Springer Verlag, Berlin, 1980. MR 0578345 | Zbl 0432.70002
[18] P. Wall: Optimal Bounds on the Effective Properties of Multiphase Materials by Homogenization. Thesis 41L, Dept. of Appl. Math., Luleå University of Technology, 1994.
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