Using Matlab and Comsol Multiphysics for Homogenisation of Composite Materials

The aim of this paper is to introduce a method for creating a homogenous substitute material for composite materials using optimisation algorithms. Composite materials are modern construction materials used, for example, in aircraft construction. However, numerical modelling of these materials is, due to its multi-layer structure, very difficult to compute. This multi-layer structure and loss materials of the composite model are represented, in the numerical simulators, as a very fine grid, resulting in an extremely high density of cells and making the simulation time much longer and the calculation much more complex. When modelling tests for aircraft electromagnetic resistance to lightning, and for other high-intensity electromagnetic fields, the intension was to replace the composite material with a homogenous substitute material having equivalent behaviour to that of the composite material in an electromagnetic field. This homogenous substitute material is then represented by much less detailed grid then the original composite, thus reducing computing time and hardware demands. The main point of the analysed inversion task, referred to below, was to find a frequency flowchart for complex permittivity of this substitute material, where the transmission characteristics are the same as those of the composite material. To solve this inversion task, optimizing algorithms in the MATLAB environment were used. When evaluating a criteria function of the optimizing algorithm, a 2D model of the substitute homogenous dielectric was produced using the Comsol Multiphysics program. Then, also using this program, the distribution of electromagnetic field was calculated for each actual value of complex permittivity calculated by MATLAB.