Non-linear elastic behavior of filler aggregates

A filled rubber network consists of polymer chains which are suspended between filler aggregates. In this contribution, the nonlinear elastic behavior of the aggregated filler particles inside the rubber matrix is investigated. Previously, by using scaling theory, the influence of initial length and fractal dimension of aggregates on the elastic response of aggregated structures was studied. Here we additionally take into account a deformation induced evolution of the aggregate structure. To this end, the directional topology of the aggregate structure is represented by its backbone chain. Thus, the analytical approach proposed describes not only the geometrically but also the physically non-linear behavior of aggregates. Our solution can further be generalized for colloidal structures as for example granular materials or suspended solid structures.