The Mori–Tanaka stiffness tensor: diagonal symmetry, complex fibre orientations and non-dilute volume fractions

Abstract

This paper considers the diagonal symmetry of the stiffness tensors predicted using the Mori-Tanaka (MT) approach. Since the MT approach may yield asymmetric stiffness tensors this paper considers an alternative approach to ensure the diagonal symmetry. Furthermore, an extension of the MT approach to non-dilute volume fractions is considered. It is shown that the MT approach by Benveniste [Mech. Mater. 6 (1987) 147], may not yield diagonally symmetric stiffness tensors in situations when a statistical fibre orientation function is incorporated. Only when the inclusions are spherical and randomly distributed or fully aligned will the MT predicted stiffness tensor be diagonally symmetric. The extension to non-dilute volume fractions is seen to lie within the Hashin–Shtrikman–Walpole (HSW) bounds and comparison to other approaches and experiments found in the literature shows very good agreement.