Effective elasticities of short-fiber composites with arbitrary orientation distribution

The object of this study is the derivation of the effective elasticities of short-fiber composites with an arbitrarily specified orientation distribution of ellipsoidal fibers. The developed formalism is sufficiently general to include the cases of arbitrary material symmetry of both the fiber and the matrix. Fiber interactions and fiber geometry are accounted for by means of a generalized Mori-Tanaka assumption. The orientation distribution is described by a probability density function, the expansion of which in a series of generalized spherical harmonics permits considerable reductions in the computational work.