Читать книгу Properties for Design of Composite Structures - Neil McCartney - Страница 83

Bounds for the effective properties of unidirectional fibre-reinforced composites have been derived using variational techniques by Hashin and Shtrikman [7], and in the review by Hashin [3]. In this section, these bounds are now associated with the results in this chapter derived using Maxwell’s methodology. The results of Section 4.8, derived using Maxwell’s methodology or using the concentric cylinder model of a composite, correspond exactly to one of the bounds. Furthermore, if one bound is known, then the other is obtained simply by interchanging the properties and volume fractions. It is of interest to determine the condition that specifies whether the extreme value is an upper or lower bound.