13th International Conference on Fracture June 16–21, 2013, Beijing, China -3- you can see in Fig. 1, discretized functions are discontinuous everywhere. So, it is easy to model a crack, which is the discontinuity in a function of displacement. The candidate crack paths are limited to the boundary of the Voronoi blocks. For three dimensions decomposition, we can use ordinary tetrahedral mesh instead of triangular mesh as the Delaunay tessellation, and then for each tetrahedral vertex, the Voronoi block containing the vertex is determined by connecting all the centroids of tetrahedrons containing the vertex. For dynamic analysis, a variation integrator called bilateral symplectic algorithm [9] is adopted as a robust algorithm of the time integration in PDS-FEM [8]. This algorithm is robust for stiffness matrix changes due to crack propagation. Meanwhile it is symplectic, which indicates that the momentum and energy are conserved during the numerical integration. 3. Near field disturbance modeling and simulation Nowadays, the underground velocity structure and the hypocenter still can hardly be modeled accurately [10-12], let alone the detail fault configuration. According to previous researches, one of the best published results of underground velocity structure modeling with the help of the densest distribution of observation stations in Japan still has more than 10% error [13]. In order to carry out earthquake simulation, the configuration of the fault is always estimated with some variances. The effect of the errors in numerical modeling needs to be estimated. Although far from reality, this section carries out a series of trial simulations to quantificationally study the effect of the cracks’ configuration changing on dynamic crack propagation with simple setting. 3.1. Reference model setting The reference model is a thin epoxy resin plate with two anti-symmetric notches located in the middle, subjected to uniform longitudinal uni-axial tensile; see Fig. 2. The material is set to be linearly elastic; see Table 1. For brittle material, a time dependent material strength failure criterion, call Tuler Butcher criterion is adopted [14]: 1 0 0 f f dt K , (1) where and 0 are principle stress (tensile stress in this problem) and a threshold stress, f is fracture duration and Kf is the stress impulse for failure. It is assumed that and Kf = 10 -8. 0 is set to be the static tensile strength, and f is assigned to be the time step used in the time integration. Table 1. Material properties of epoxy resin Young's modulus (Mpa) 3300 Poisson's ratio 0.38 Tensile strength (Mpa) 35.0 Epoxy density (kg/m3) 1180 The displacement boundary condition is applied; the bottom end of the model is fixed, and the top end is pulled up in Z direction. The crack tip is modeled as a notch of the height 0.6 mm, the vertical surface of the notch is discretized by 2 elements, averagely. The average mesh size is 1.0 mm at the top and bottom surfaces of the notch. Due to this discretization, the time increment is set as t = 7.5x10-9s.
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