Keywords: lattice model, concrete, cohesive fracture model, crack band model, rigid-body-spring network, Voronoi discretization.

Random lattice and random particle models have established themselves as powerful tools for the numerical simulation of fracture of quasi-brittle materials such as concrete. These models are classified as discrete models in that the continuum domain representing the material specimen is modeled by a network of uni-dimensional elements such as truss [1] or beam [2]. Attractive features of the discrete models include the simple manner in which material microstructural features can be directly modeled (in general at the meso-scale level) and the reduction of directional bias on crack propagation through the systematic use of random meshes.

In this paper a three-dimensional irregular lattice model is used to simulate the fracture process in a concrete specimen. The specimen is a notched-beam subjected to the three-point bend test used to determine material fracture parameters. The elastic and fracture behavior are modeled using a rigid-body-spring networks (RBSN), which is a type of lattice model. In the RBSN the elements of the network are scaled according to the geometry of the Voronoi diagram used to discretize the material domain. This model has been used for two-dimensional simulations of fracture of concrete specimens [3] as well as for the analysis of fracture of structural components [4]. In this study the fracture model is extended to three-dimensional analyses. The Voronoi scaling of lattice element properties has also been used for modeling transport phenomena, such as heat and moisture diffusion. When moisture diffusion analysis is combined with the elasticity and fracture models described in this paper, the RBSN can be used to simulate shrinkage induced cracking in cement composite materials and structural components [5].

To test model objectivity with respect to user mesh choice, two simulations with different meshes are carried out. The two meshes differ in the way the area above the notch (i.e. the ligament area) is discretized. In one case the ligament is discretized in a semi-random fashion such that a flat crack surface will develop during the simulation. In the second mesh a completely random approach is used and an irregular crack surface will form. The numerical load-CMOD (crack mouth opening displacement) curves are compared with the experimental curve used for the model calibration. Both simulation results agree well with the actual experimental data. For the two models, the newly forming crack surfaces are plotted at different stages in the simulations where fairly straight crack fronts develop as the fracture progresses. Although the straight front seems to be in contradiction with the saddle type shape that have been observed in previous acoustic-emission [6] and dye penetration [7] tests, it can be attributed to several effects that have not been included at this stage in the simulations. For example, considering the distribution of inclusions in an actual specimen, there are fewer inclusions close to the surface, due to a wall effect, and this might reduce the material toughness in this region. Furthermore, the drying process of concrete and the corresponding stress field generated by this phenomenon likely affects the fracture patterns. The inclusion of these effects in the numerical simulations, and investigation of their relative influences on the material fracture parameters, are future goals of this research study.

1

M. Jirásek and Z.P. Bazant. "Macroscopic fracture characteristics of random particles systems." International Journal of Fracture, 69(3), 201-228, 1995. doi:10.1007/BF00034763

2

E. Schlangen and E.J. Garboczi. "Fracture Simulations of concrete using lattice models: Computational Aspects." Engineering Fracture Mechanics, 57(2/3), 319-332, 1997. doi:10.1016/S0013-7944(97)00010-6

3

J.E. Bolander and S. Saito. "Fracture analysis using spring network with random geometry." Engineering Fracture Mechanics, 615 (5-6), 569-591, 1998. doi:10.1016/S0013-7944(98)00069-1

4

J.E. Bolander, G.S. Hong and K. Yoshitake. "Structural concrete analysis using rigid-body-spring network." Journal of Computer-Aided Civil Infrastructure Engineering, 15, 120-133, 2000. doi:10.1111/0885-9507.00177

5

J.E. Bolander and S. Berton. "Simulation of shrinkage induced cracking in cement composite overlays." Cement & Concrete Composites, in press, 2004. doi:10.1016/j.cemconcomp.2003.04.001

6

C. Ouyang, E. Landis and S.P. Shah. "Damage assessment in concrete using quantitative acoustic emission." Journal of Engineering Mechanics, ASCE, 12(4), 219-232, 1991. doi:10.1061/(ASCE)0733-9399(1991)117:11(2681)

7

S.E. Swartz and T.M. Refai. "Cracked surface revealed by dye and its utility in determining fracture parameters." In Fracture Toughness and Fracture Energy: Test methods for Concrete and Rock, 509-520, Balkema, Brookfield, VT, 1989.

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