Distribution of local fields in composites

The behavior of composites depends crucially on the distribution of local fields. The ways to characterize and find such distributions are poorly understood. In this paper, an attempt is made to present some simple approximate formulas for distributions of the local fields in variational problems. They are given in an explicit form for thermo-elastic composites and heat-conducting composites. The accuracy is tested for the case of heat conductivity of chess-board structures.