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Macroscopic constitutive law for Mastic Asphalt Mixtures from multiscale modeling

A well established framework of an uncoupled hierarchical modeling approach is adopted here for the prediction of macroscopic material parameters of the Generalized Leonov (GL) constitutive model intended for the analysis of flexible pavements at both moderate and elevated temperature regimes. To that end, a recently introduced concept of a statistically equivalent periodic unit cell (SEPUC) is addressed to reflect a real microstructure of Mastic Asphalt mixtures (MAm). While mastic properties are derived from an extensive experimental program, the macroscopic properties of MAm are fitted to virtual numerical experiments performed on the basis of first order homogenization scheme. To enhance feasibility of the solution of the underlying nonlinear problem a two-step homogenization procedure is proposed. Here, the effective material properties are first found for a mortar phase, a composite consisting of a mastic matrix and a fraction of small aggregates. These properties are then introduced in place of the matrix in actual unit cells to give estimates of the model parameters on macroscale. Comparison with the Mori-Tanaka predictions is also provided suggesting limitations of classical micromechanical models.