Asymptotic calculation of equivalent electromagnetic and thermal properties for composite materials

In this paper, the asymptotic development method is used to study the electromagnetic and thermal behavior of nonhomogeneous materials. The method, widely used in high frequency applications, is adapted to an induction heating system of partially conducting composites. The asymptotic method, based on the spatial filtering of the electromagnetic field, is applied to study the composite materials with periodic structure. The model is valid when the size of the elementary cell is small compared with the dimensions of the system. For large cells, the model gives an average value of field. A local solution is then used to improve the homogenized field. The conditions of using the model for nonperiodic structures are also discussed