Parametric optimization of the effective thermal conductivity for a three-phase particle-filled composite

Functionalized materials, consisting of a particle-filled polymer matrix, enable a considerable increase in thermal conductivity compared to standard plastics. This is particularly important in electromobility applications, e.g. in encapsulated circuit boards, to ensure sufficient thermal management. In this paper, a method for the optimization of the effective thermal conductivity (ETC) by considering electrically insulating composites is presented. To show the diversity of microstructural design options by using different filler/matrix compositions, the method is introduced by taking a particle-filled plastic with three phases and high contrast in the conductivities of the individual phases as example. Particles with different sizes and shapes in the micrometer range are considered. The task of setting a target ETC is formulated as a parameter optimization problem. The ETC is determined by microstructure simulation and numerical homogenization where virtually created representative volume elements (RVEs) are used. To study the influence of the different design variables, metamodeling and sensitivity analysis techniques are introduced. It turns out, that only the filler volume fraction, the aspect ratio and the proportions of the individual fillers are sensitive parameters. After neglecting non-sensitive parameters, global optimization in the reduced design space using an evolutionary algorithm is performed. The novelty of the paper is that several fillers with different microstructural parameters, such as diameter, aspect ratio and shape, are included as design variables in the structural optimization. Since the evaluation of the objective function of the structural optimization problem is very expensive, a cheaper surrogate model is introduced in the paper. This approach allows an efficient computation of microstructural realizations with a target ETC and can be extended to other microstructures and effective properties as well.