On the homogenization of temperature dependent therm conductivity in composite materials

In general, the constituent thermal properties of fibrous composites are temperature dependent which makes the effective conductivity of the overall composite behave likewise. Of the various techniques available, the asymptotic expansion homogenization (AEH) method appears to be most suitable to address the dependence of the micro-level properties on the macro-level temperatures. The goal of this work which, to our knowledge, appears to be the first effort to validate the AEH methodology for nonlinear situations, is to assess the influence of the perturbative asymptotic terms when encountering temperature-dependent conductivity and thereby assess the pros/cons in comparison to available experimental results. The extent of influence of these perturbative terms are separated into three distinct categories, each defining an approach for homogenization. The comparative study is of these three alternative approaches of numerically estimating the homogenized thermal properties of periodic continuous fiber reinforced composites to assess their accuracy with available experimental results. The three approaches are based on variations of the full three-dimensional finite element asymptotic homogenization technique, also called the classical homogenization procedure, when extending the method to material non-linear problems. In contrast to other homogenization approaches, asymptotic homogenization approach is useful due to its inherent capability to perform both homogenization and localization seamlessly within a single method by considering the microstructural details within a macro-level analysis. Illustrative examples and validations are provided.