Variationally consistent computational homogenization of transient heat flow

A framework for variationally consistent homogenization, combined with a generalized macro‐homogeneity condition, is exploited for the analysis of non‐linear transient heat conduction. Within this framework the classical approach of (model‐based) first‐order homogenization for stationary problems is extended to transient problems. Homogenization is then carried out in the spatial domain on representative volume elements (RVE), which are (in practice) introduced in quadrature points in standard fashion. Along with the classical averages, a higher order conservation quantity is obtained. An iterative FE²‐algorithm is devised for the case of non‐linear diffusion and storage coefficients, and it is applied to transient heat conduction in a strongly heterogeneous particle composite. Parametric studies are carried out, in particular with respect to the influence of the ‘internal length’ associated with the second‐order conservation quantity. Copyright © 2009 John Wiley & Sons, Ltd.