A novel numerical scheme for random parameterized convex aggregate models with a high-volume fraction of aggregates in concrete-like granular materials

Concrete at a mesoscopic scale is normally regarded as a three-phase composite consisting of cement paste, aggregates and their surrounding interfacial transition zones (ITZs). Establishing mesostructure model close to realistic concrete is very crucial to precisely evaluate its mechanical properties. The preponderance of previous investigations has focused on aggregates as circles, ellipses or polygons constructed by the assembly of sides-sides with a low packing density, and little is known about precise mathematical characterizations for polygonal aggregates with a high packing density more than 60% and their surrounding ITZs. In this work, a novel numerical framework that adopts the deformation of a rhombus to mathematically provide a parametric equation of convex polygon characterizing the geometrical morphology of aggregates, is proposed to generate random polygonal aggregate models (RPAMs) with a high packing density. In this framework, a fast-random packing algorithm (FRPA) is developed to generate a high packing density of aggregates of 70%. Based on the parametric equation of polygonal aggregates, the geometrical topology of ITZs is mathematically realized with a convenient manner, rather than those cumbersome approximate operations reported in the literature. Moreover, the present numerical framework can be extended to the three-dimensional case.