Multi-scale modelling of elastic/viscoelastic compounds



The present contribution is concerned with the requirements of an efficient multi-scale modelling approach for elastic/viscoelastic compounds such as bituminous asphalt concrete. Typically, this heterogeneous composite material consist of a mineral filler (e.g. crushed rock), a bituminous binding agent, pores and further additives. The contrast in stiffness between the different is extremely high and accounts for several orders of magnitude. Prediction of effective mechanical properties of such complex materials on the macroscopic level requires a detailed knowledge of the micro-scale behaviour of the particular constituents. In this study, we will focus on modelling aspects due to upscaling routines based on volume averaging. Particularly, we will show that the choice of micro-level boundary conditions not only influences the effective stiffness of the viscoelastic substitute material (upper/lower limit), but also the viscous contribution to the macro-model (shift of maximal attenuation in frequency space). In order to study these fundamental homogenization properties, we introduce a simplified compound consisting of homogeneous viscoelastic binder phase and spherical filler particles with a volume fraction low compared to realistic asphalt concrete. Depending on the chosen boundary condition, stress-relaxation and creep tests are considered. After transformation of the effective stress-strain-relations from time- to frequency space, the viscoelastic properties of the compound will be discussed in frequency domain.