BOUNDING OF EFFECTIVE THERMAL-CONDUCTIVITIES OF MULTISCALE MATERIALS BY ESSENTIAL AND NATURAL BOUNDARY-CONDITIONS

We demonstrate the bounding of the effective properties of random mult iscale microstructures by means of essential and natural boundary cond itions. The proposed method involves moderate sized lattices, not modi fied in the boundary zone, thereby allowing much faster calculations t han the method of periodic boundary conditions. In case of a random tw o-phase lattice, scaling laws have been found for a wide range of cont rasts. In the case of a disk-inclusion composite having circular inclu sions with graded interphases, the presence of a graded interphase dra matically changes the effective conductivity compared to that of a com posite with perfect interfaces.