Variational bounds for thermal fields in media with heterogeneous microstructure

Abstract

This work develops a rigorous variational upper bound for the difference between thermal fields generated in uniform media and thermal fields generated in heterogeneous media, for the same external loading. The bound can be calculated in a simple manner, with knowledge only of the heterogeneous material properties and a relatively easy-to-compute thermal field associated with a uniform medium. In order to evaluate the bound, the difficult-to-compute thermal field, associated with the heterogeneous material, does not need to be calculated. Three-dimensional numerical examples are provided to illustrate the results.