The robustness of the emergent scaling property of random RC network models of complex materials

The so-called 'universal dielectric response' of composite materials can be reproduced as a power-law emergent response (PLER) of electrical network models. Results are presented for investigations demonstrating the robustness of the PLER of random electrical networks in order to evaluate the usefulness of such models in simulating real composite materials with microstructural disorder. The effect of imposed microstructures has been investigated, looking at both the correlation length and the network size. It is shown that the exact microstructural details may be reasonably omitted, so long as we take care that the general features of the structures, such as their relative smallest and largest scales, are represented.

Anisotropy in the random microstructures is shown to alter the bulk response of the system, with the network responses found to tend towards that expected for purely parallel and series components. The power-law response is shown to be obtainable by taking the geometric mean of the two cases, showing that the bulk response of such systems is an averaged property of these two extreme cases.

It is concluded that, given the longer computing times needed to simulate these more realistic representations, it is reasonable to use the simpler models.