A comparison of homogenization, Hashin-Shtrikman bounds and the Halpin-Tsai equations

Applications of Mathematics

Volumn 42, Issue 4, 1997, Pages 245-257

  Wall, Peter ^a  

^a LULEÅ UNIVERSITY OF TECHNOLOGY   (Sweden)

Author keywords

Composite materials; Effective properties; Halpin Tsai equations; Hashin Shtrikman bounds; Homogenization

Indexed keywords

EID: 0006200203     PISSN: 08627940     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1023034411371     Document Type: Article

References (18)

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.
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).
4. G. Dal Maso: An Introduction to Γ-Convergence. Birkhäuser, Boston, 1993.
5. J. C. Halpin, J. L Kardos: The Halpin-Tsai equations: A review. Polymer Engineering and science 16(5) (1976), 344-352.
6. Z. Hashin: On elastic behaviour of fibre reinforced materials of arbitrary transverse phase geometry. J. Mech. Phys. Solids 13 (1965), 119-134.
7. Z. Hashin: Analysis of composite materials-a survey. J. Mech. Phys. Solids 50 (1983), 481-505.
8. Z. Hashin, W. Rosen: The elastic moduli of fiber-reinforced materials. Journal of Applied Mechanics (1964), 223-232.
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.
10. V. Jikov, S. Kozlov, O. Oleinik: Homogenization of Differential Operators and Integral Functional. Springer-Verlag, Berlin Heidelberg New York, 1994.
11. R. Lipton: On the behaviour of elastic composites with transverse isotropic symmetry. J. Mech. Phys. Solids 39(5) (1991), 663-681.
12. D. Lukkasen, L.-E. Persson, P. Wall: Some engineering and mathematical aspects on the homogenization method. Composites Engineering 5(5) (1995), 519-531.
13. D. Lukkasen, L.-E. Persson, P. Wall: On some sharp bounds for the p-Poisson equation. Applicable Analysis 58 (1995), 123-135.
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.
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.
16. L.-E. Persson, L. Persson, N. Svanstedt, J. Wyller: The Homogenization Method: An Introduction. Studentlitteratur, Lund, 1993.
17. E. Sanchez-Palencia: Non Homogeneous Media and Vibration Theory. Lecture Notes in Physics 127, Springer Verlag, Berlin, 1980.
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.