Geodesic
A comparison of homogenization, Hashin-Shtrikman bounds and the Halpin-Tsai equations
Applications of Mathematics, Tome 42 (1997) no. 4, pp. 245-257

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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.
DOI : 10.1023/A:1023034411371
Classification : 35B27, 35Q72, 73B27, 73K20, 74E05, 74E30
Keywords: composite materials; homogenization; Hashin-Shtrikman bounds; Halpin-Tsai equations; effective properties; auxiliary partial differential equations; unidirectional elastic fiber composite; fitting parameter 
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     title = {A comparison of homogenization, {Hashin-Shtrikman} bounds and the {Halpin-Tsai} equations},
     journal = {Applications of Mathematics},
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Wall, Peter. A comparison of homogenization, Hashin-Shtrikman bounds and the Halpin-Tsai equations. Applications of Mathematics, Tome 42 (1997) no. 4, pp. 245-257. doi: 10.1023/A:1023034411371

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