13th International Conference on Fracture June 16–21, 2013, Beijing, China -2- Both experiment and numerical simulation can be used to study the effect of boundary disturbance. However, there is an advantage to examine the boundary disturbance effect by using numerical methods. At least two samples are needed to conduct this comparison study. The ideal situation is that all the settings are the same except that a specified disturbance is added in one of the samples’ boundary condition. However, in reality, the variability of samples is hard to control, and the designed disturbance in boundary condition cannot be accurately applied. These uncertainties may lead to side effects on this comparison study. While in the numerical analysis, it is much easier to define identical models and add the specified disturbances exactly. This paper studies the effect of two kinds of boundary disturbances, say, the near and far field disturbances. Here, the adjective, “near” and “far” are used to describe the distance between the boundary with disturbance and the region where crack grows. The target is a thin epoxy resin plate with two anti-symmetric notches located in the middle, subjected to uni-axial tensile in longitudinal direction. The near field disturbance is modelled by adjusting the position, size and shape of the notches. The far field disturbance is modelled by adding disturbance to the displacement boundary condition, which is far from the notches. Several kinds of disturbances are adopted. In order to study the Saint-Venant principle in the fracture problem, the crack paths of different model sizes under the same disturbance are compared. For numerical simulation of fracture problems, various kinds of numerical methods have been proposed, such as E-FEM, X-FEM [4], discontinuous Galerkin method [5] and meshfree methods [6]. Besides these methods, the newly developed method, called particle discretization scheme finite element method (PDS-FEM) is another candidate [7,8] to calculate three dimensional dynamic crack propagation, for its numerical efficiency and capability of calculating bifurcation, which is important for brittle materials, such as epoxy resin, rock and concrete. The content of the present paper is as follows: section 2 briefly introduces the characteristics of the adopted numerical method, PDS-FEM. Section 3 and 4 are devoted to study the effect of near and far field disturbances, respectively. Concluding remarks are pointed out in section 5. 2. PDS-FEM The key idea of PDS-FEM is the discretization scheme. PDS or particle discretization scheme is a scheme which uses two sets of non-overlapping characteristic functions to discretize a function and its derivative. One set is made for Voronoi tessellation, and characteristic functions of this tessellation used to discretize a function. The other set is made for Delaunay tessellation, and characteristic functions of this tessellation are used to discretize function derivatives. Voronoi tessellation Delaunay tessellation Figure 1. Two dimension decomposition by using particle discretization scheme Displacement is discretized by the Voronoi, while strain and stress is discretized by Delaunay. As The candidate crack path is limited to the boundary of the Voronoi blocks
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