Computational homogenisation from a 3D finite element model of asphalt concrete—linear elastic computations

• A 3D random mesoscale model of asphalt concrete is presented.
• Computational homogenisation using the finite element method is performed.
• Representative volume elements of a linear elastic composite are determined.
• Both the material contrast and the volume fraction govern the representative volume element size.

Asphalt concrete (AC) is a composite material consisting of bituminous binders, mineral aggregate, and voids. Experimental and computational efforts to assess the bulk mechanical properties of AC ubiquitously raise the question of representative sample size. It is well known that the dimension of a sample has to be larger than the largest morphological entity. However, it has been shown that the required size is a function of the morphological and physical properties under consideration, e. g. the difference between the properties of the constituents at the microscale, and their volume fractions. In the present contribution, representative sample sizes are determined numerically for a variation of parameters in terms of a tolerable amount of statistical scatter by conducting virtual experiments. If the scatter between distinct heterogeneous samples falls below a certain threshold, the corresponding volume is called a representative volume element (RVE). Finite element (FE) discretisations of AC volume samples are generated by means of a shrunk Poisson Voronoi tessellation. In order to provide estimates for the evolution of the RVE size under changing material properties of the mortar, the stiffness ratio between rocks and mortar is varied by two orders of magnitude. Furthermore, the influence of a variation in volume fraction is investigated.