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

This paper considers the diagonal symmetry of the stiffness tensors predict ed using the Mori-Tanaka (MT) approach. Since the MT approach may yield asy mmetric stiffness tensors this paper considers an alternative approach to e nsure the diagonal symmetry. Furthermore. an extension of the MT approach t o non-dilute volume fractions is considered. It is shown that the MT approa ch by Benveniste [Mech. Mater. 6 (1987) 147], may not yield diagonally symm etric stiffness tensors in situations when a statistical fibre orientation function is incorporated. Only when the inclusions are spherical and random ly distributed or fully aligned will the MT predicted stiffness tensor be d iagonally symmetric. The extension to non-dilute volume fractions is seen t o lie within the Hashin-Shtrikman-Walpole (HSW) bounds and comparison to ot her approaches and experiments found in the literature shows very good agre ement. (C) 2001 Elsevier Science Ltd. All rights reserved.