A comparison of homogenization, Hashin-Shtrikman bounds and the Halpin-Tsai equations
The effective parameters of composite materials can be computed by homogenization from properties of the components. Since this computation is not simple (the formulae contain solutions of auxiliary partial differential equations) their estimates are useful. The paper deals with unidirectional elastic fiber composite. Using homogenization the effective parameters (the bulk modulus \(k\) and shear modulus \(\mu \)) are computed for carbon-epoxy composites with different volume fraction of the components. The results are compared with Hashin-Shtrikman bounds, the values are close to the lower bounds. Halpin-Tsai equations with a fitting parameter \(\xi \) represent another approximation of \(k\) and \(\mu \). Using the Hashin-Shtrikman bounds optimal bounds on the fitting parameter \(\xi \) are derived.
auxiliary partial differential equations
scientific article; zbMATH DE number 1203987
scientific article