13th International Conference on Fracture June 16–21, 2013, Beijing, China 3. Fracture processes in the numerical concrete The fracture processes in concrete can be predicted by the lattice fracture model. The material structure of concrete is obtained in the previous section, and the next step is to evaluate its mechanical performance by simulating a uniaxial tensile test on it. To reduce the computational effect, a smaller specimen of the size 40 mm is cut out from the original 150 mm specimen at its center. The 40 mm concrete specimen is then digitized at the resolution of 1 mm, and consists of two solid phases namely stone and mortar. A lattice network is constructed based on the digital concrete specimen, and three types of lattice elements are identified, which represent crushed stone, mortar and interface respectively, as shown in Figure 3. The local mechanical properties are given in Table 1. The properties of the lattice elements representing mortar are varied randomly to reflect the heterogeneity of mortar phase. Figure 3. Lattice mesh of the 40 mm numerical concrete specimen Table 1. Local mechanical properties of stone, mortar and interface elements in concrete Young's modulus (GPa) Tensile strength (MPa) Stone 70 24 Mortar 17~65 1.1~19.5 Interface 41 1 A uniaxial tensile test is simulated on the lattice system meshed from the 40 mm concrete specimen as shown in Figure 3, using the local mechanical properties listed in Table 1. All the lattice nodes on the bottom surface of the specimen are fixed, and a unit prescribed displacement is imposed on the nodes located on the top surface, as illustrated in Figure 4. The lattice fracture analysis consists of multiple steps. At every analysis step it is required to determine the critical element and the corresponding system scaling factor after the calculation of comparative stress in every lattice element. The critical element is the one with highest stress/strength ratio when the system is loaded by a unit prescribed displacement. The inverse of the ratio is defined as a system scaling factor. The system scaling factor, together with the reactions on the restraint boundaries, determines one scenario of critical load-displacement pairs. The critical element is removed from the system and if the system does not fail completely yet, it is recomputed as the system is updated due to the element removal. Multiple analysis steps are carried out until the system fails. Hence a set of load-displacement pairs can be obtained and used to plot the load-displacement diagram, which can be converted to a stress-strain diagram later to represent the -4-
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