Generation and property analyses of 3D mesoscale models for plain and fiber reinforced concretes
Introduction
Concrete is a multi-phase and heterogeneous material. It consists of three important phase materials: cement paste, aggregate and the interfacial transition zone (ITZ) [1,2]. ITZ is a thin layer region of the cement paste around the aggregates in normal concrete [3]. Fiber is often added into concrete in practice to improve its mechanical performance, including the flexible strength, toughness, etc. [4]. At mesoscale, fiber-reinforced concrete (FRC) can be simplified as aggregates and fibers embedded in the cement matrix, whereas the ITZ is the interface between different phases. Still, it is very difficult to precisely understand the realistic structure of plain and fiber-reinforced concretes by traditional experimental methods without destroying their structures. X-ray tomography image-based reconstruction technique [5] is a promising approach to solve this problem, however, this new technique requires specialized instruments and is time-consuming, laborious and thus expensive. Numerical and experimental methods are complementary to each other. As an alternative, numerical modeling provides an economic and reliable way to construct the concrete structure at mesoscale.
Various mesoscale models for simulating concrete structures have been developed in recent decades. Aggregate generation technologies, such as Euclidean geometry [6], low polyhedral [7,8] and sphere harmonic function [9], have made remarkable progress. Aggregates are generally treated as spherical particle [1,10], so that complex overlapping detection algorithms can be avoided. Besides, aggregates with regular shapes (i.e., Euclidean geometric polyhedron and ellipsoid) are also used to construct the structural model so that the elastic modulus [11], effective diffusion [12], tensile strength [13] and damage behavior [14] of concrete can be studied. Low polyhedral aggregates were developed to model the static [15] and dynamic [6] behaviors of concrete under various loading conditions, which can be generated by mathematical functions on the basis of ellipsoidal particles [16]. Voronoi tessellation method [17] can also be employed to generate such aggregates. In addition, a “taking” and “placing” method was developed to randomly generate 2D non-convex aggregates [18]. Although random sequential addition (RSA) [19] is a common method to model the packing of non-spherical aggregates, discrete element method (DEM) [[20], [21], [22]] has been proven to yield more realistic concrete structures since the contacts between particles are well considered in DEM. Realistic aggregates are generally generated by sphere harmonic function [8,23], which can be utilized to investigate the fracture behavior of cementitious materials [24] at different scales. Moreover, a method [25] that combines digital image processing, spectral representation and point cloud, was proposed to model 2D and 3D concrete aggregates of arbitrary shapes. X-ray image analysis is able to obtain the real aggregates by scanning the sample's surface. However, the surface fine texture characteristics of aggregates are ignored.
For the generation of randomly distributed fibers, Guan et al. [26] assumed that the shape of fiber is ellipsoid, such that the complex embedding detection between fibers can be avoided. However, elliptical fibers are rarely used in engineering. Liang et al. [27] used Rand function in MATLAB to generate fibers with different length, but still the interactions between fibers are not well considered. Xu et al. [28] proposed a 2D mesoscale model that is able to take both aggregates and fibers into account. Unfortunately, only a limited amount of fibers can be considered in the abovementioned mesoscale models. It is thus quite important to establish the mesoscale model of plain and fiber reinforced concrete with realistic aggregates and fibers, which can be used to predict the volume fraction of ITZs, elastic modulus and mechanical performance of concrete [29].
Calculating the volume fraction of ITZ in concrete by experiments is very difficult, and numerical models seem to be a possible tool. Han et al. [30] proposed an one-point probability function, in which the contraction factor (CF) is employed to generate 2D non-convex aggregate, so that the volume fraction of ITZs can be determined by Monte Carlo approach [31,32]. It is found that the volume fraction of ITZ goes up linearly with the increase of aggregate content. However, 2D models are unable to fully reflect the volume fraction of ITZ in real concrete and 3D models are still required. As for the study on the elastic modulus of concrete, Wriggers et al. [5] proposed a mesoscale model but it is only based on spherical aggregates. Gal et al. [29] studied the effective elastic modulus of FRC consisting of spherical aggregates and straight fibers, and pointed out that there exists an overestimation of the obtained elastic modulus at the increased volume fraction of fibers. Xu et al. [33] derived a Hashin-Shtrikman (HS) model [34] and calculated the effective elastic modulus of three-phase composite materials. It is observed that the effective elastic modulus of composites goes up with the increase of the interfacial elastic modulus, but decreases at the increased thickness of ITZ [35]. Unfortunately, spherical and regular shape of aggregate cannot reflect the real situation in practice.
This paper proposed an economical, effective and reliable method for the generation of plain and fiber reinforced concrete at the mesoscale level, as shown in Fig. 1. The rough surface texture of realistic aggregate and different fibers are both taken into account. The applications of proposed mesoscale model on the prediction of the ITZ volume fraction and the elastic modulus of plain and fiber reinforced concrete are also included. This work is useful in the field of cementitious materials and can be further used to study the mechanical performance of plain and fiber reinforced concrete in combination with other numerical methods, such as FEM, DEM, etc.
Section snippets
A new framework of generation of realistic aggregate with rough surface texture
A new framework of generation of realistic aggregate with rough surface texture is proposed in this work, which consists of four main algorithms: (1) Cell fracture; (2) Surface subdivision (Catmull–Clark subdivision algorithm [36]); (3) Displacement mapping; (4) Laplace smoothing.
Mesoscale models of plain and fiber reinforced concretes
The structures of plain and fiber reinforced concretes generated by the proposed method are shown in Fig. 15, Fig. 16, Fig. 17, Fig. 18. In order to show it more intuitively, the dynamic processes of the cross-section diagrams of plain and fiber reinforced concretes mesoscale models are attached in the data files, and the details are described in the following sections.
Effect of aggregate size on the volume fraction of the ITZ
According to the previous work [51], the ITZ thicknesses are found to be 25 μm, 35-34 μm, 45 μm and 50 μm for limestone aggregate of various sizes (i.e. 5 mm, 10 mm, 20 mm and 30 mm), respectively. The thickness of ITZ tends to be stable when the aggregate size is larger than 30 mm. As illustrated in Fig. 19(a), the relationship between the ITZ thickness and the size of aggregate can be expressed as a function:Where, f (t) represents the thickness of ITZ, Dmaxeq
Conclusions
This work presents a promising, reliable and useful tool to generate plain and fiber reinforced concretes 3D mesoscale model. Realistic aggregates with rough surface texture can be well represented by the proposed method. The influence of aggregates and fibers on the ITZ volume fraction and mechanical properties of concrete are thus quantitatively studied. Main conclusions can be drawn as follows:
- (1)
By combing modified cell fracture, Catmull–Clark subdivision, texture displacement and Laplace
Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgment
The authors gratefully acknowledge the financial support from the Chinese Ministry of Science and Technology under Project (Grant No. 2018YFC0705400), and National Science Foundation of China under Project (Grant No. 201601370519), and financial support from the program of China Scholarships Council (CSC No. 201906130089), as well as the Hunan Provincial Innovation Foundation for Postgraduate (CX2018B220).
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