Numerical evaluation of isostrain and weighted-average models for elastic moduli of three-dimensional composites

Abstract

The isostrain model is being widely used for predicting the elastic properties of three-dimensional composites, i.e. composites in which the reinforcement extends in the general three-dimensional space. Recently, it has been suggested that a weighted average of the isostrain and isostress model predictions yields better results, when compared to the predictions of the isostrain model alone. Critical evaluation of these models through experiments alone is expensive and time consuming owing to the large number of material and geometric variables involved in these models. We have conducted a numerical study to evaluate the accuracies of these simplistic analytical models. A finite element model, based on the commonly used representative volume element of the three-dimensionally braided composite, was developed for this purpose. The variables considered in this study included the type of loading, the braid angle, the fiber volume fraction, and the yarn elastic properties. The study revealed that a suitable weighted average of the isostrain and isostress model predictions is in better agreement with the corresponding finite element model predictions for the elastic moduli of 3-D braided composites. Furthermore, the weighting factor was observed to be fairly insensitive to braid angles, yarn volume fraction, and the type of loading, but strongly influenced by the non-axial elastic properties of the yarn.