On exact relations for the calculation of effective properties of composite

TL;DR

This paper discusses exact relations for calculating the effective elastic properties of composites, compares numerical methods with these relations, and evaluates their accuracy in predicting composite moduli.

Contribution

It analyzes and compares finite element, generalized method of cells, and recursive cell method estimates against exact relations for composite properties.

Findings

Finite element estimates align closely with exact relations.

Recursive cell method tends to overestimate moduli.

Generalized method of cells tends to underestimate moduli.

Abstract

Numerous exact relations exist that relate the effective elastic properties of composites to the elastic properties of their components. These relations can not only be used to determine the properties of certain composites, but also provide checks on the accuracy on numerical techniques for the calculation of effective properties. In this work, some exact relations are discussed and estimates from finite element calculations, the generalized method of cells and the recursive cell method are compared with estimates from the exact relations. Comparisons with effective properties predicted using exact relations show that the best estimates are obtained from the finite element calculations while the moduli are overestimated by the recursive cell method and underestimated by the generalized method of cells. However, not all exact relations can be used to make such a distinction.