Average Eshelby Tensor Research Articles

Analytical determination of the average Eshelby tensor for transversely isotropic fiber orientation distributions

The analytical expression for the average S tensor in Eshelby's equivalent inclusion method of internal stress determination in composite materials is derived for any transversely isotropic fiber orientation distribution function specified by a generic histogram. The analytical average provides a basis for direct application of experimentally measured fiber ODFs in the modelling of internal stresses and effective properties of thermomechanical fiber composites. Upper and lower bound estimates utilizing the analytical expression for the average S tensor are presented and discussed.