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The establishment of an aggregate model that better matches the actual situation is one of the prerequisites to studying the mechanical properties of concrete materials. Previous models focused on aggregates with more regular shapes, which differed from the morphology of the aggregates, particularly recycled aggregate. Due to the presence of adhered mortar, recycled aggregate has more complex structural characteristics than natural aggregates. Therefore, it is difficult to model the recycled aggregate, especially the distribution of irregular angles and sharp corners on the surface. In this paper, a modeling method based on the compression of circular and sphere shapes is proposed to obtain the aggregates of circular, elliptical, convex polygonal shapes in 2D and sphere, ellipsoidal, convex polyhedral shapes in 3D. The compression method has excellent scalability and applies to both natural and recycled aggregate in 2D and 3D. By using the proposed compression modeling method, the aspect ratio, sharp corners, flakes, edges, and needles of the recycled and natural aggregate can be characterized. The random aggregate models show that the compression modeling method can construct the 2D and 3D geometric models of natural aggregate concrete and recycled aggregate concrete with desirable aggregate distribution and aggregate morphological characteristics.

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This paper develops a 3D base force element method (BFEM) based on the potential energy principle. According to the BFEM, the stiffness matrix and node displacement of any eight-node hexahedral element are derived as a uniform expression. Moreover, this expression is explicitly expressed without a Gaussian integral. A 3D random numerical model of recycled aggregate concrete (RAC) is established. The randomness of aggregate was obtained by using the Monte Carlo random method. The effects of the recycled aggregate substitution and adhered mortar percentage on the elastic modulus and compressive strength are explored under uniaxial compression loading. In addition, the failure pattern is also studied. The obtained data show that the 3D BFEM is an efficient method to explore the failure mechanism of heterogeneous materials. The 3D random RAC model is feasible for characterizing the mesostructure of RAC. Both the substitution of recycled aggregate and the percentage of adhering mortar have a non-negligible influence on the mechanical properties of RAC. As the weak points in the specimen, the old interfacial transition zone (ITZ) and adhered mortar are the major factors that lead to the weakened properties of RAC. The first crack always appears in these weak zones, and then, due to the increase and transfer of stress, approximately two-to-three continuous cracks are formed in the 45°direction of the specimen.

The reuse of recycled aggregate concrete (RAC) is being researched all over the world and lots of works are focused on the notched specimen to study the crack path of RAC. A mathematical algorithm of RAC meshing was presented to explore the failure pattern in RAC. According to this algorithm, the interfacial transition zone can be defined to be an actual thickness at the micron level. Further, a new finite element method (FEM) on the complementary energy principle was introduced to simulate the mechanical behavior of RAC’s mesostructure. The compliance matrix of the element with any shape can be calculated and expressed to be a uniform and explicit expression. Several numerical models of RAC were established, in which the effecting factors of the prenotch size, thickness of ITZ, and the distance from the prenotch to the aggregate were taken into account. Hereafter, these RAC models were subjected to uniaxial tension. The effect of the aforementioned factors on the crack path was simulated. The simulated data manifest that both the mesh mode of RAC and the FEM on complementary energy principle are effective approaches to explore the failure pattern of RAC. The size of the prenotch, thickness of ITZ, and distance from the prenotch to the recycled aggregate have a powerful influence on the path and distribution of the isolated crack, width and length of the crack path, and the shape and path of continuous cracks, respectively.