13th International Conference on Fracture June 16–21, 2013, Beijing, China -1- Three-dimension dynamic simulation of thin epoxy-resin plate and comparison with experiment Hao Chen1,* , Tomoo Okinaka2 1 Key Laboratory of Earthquake Engineering and Engineering Vibration, Institute of Engineering Mechanics, CEA, Sanhe, 065201, China 2 Kinki University, Higashi-Osaka, 577-8502, Japan * Corresponding author: chenhao@iem.ac.cn Abstract This paper presents a 3D dynamic failure analysis of linear elastic body by using particle discretization scheme finite element method (PDS-FEM). PDS-FEM uses two sets of non-overlap characteristic function to discretize function and function derivative. Unlike ordinary FEM, PDS-FEM can easily calculate crack, which is the discontinuity in displacement function. The target is a thin epoxy plate with two anti-symmetric notches under uni-axial tensile boundary condition. A time depend failure criterion, called Tuler - Butcher criterion is applied. The simulation results are compared with the experimental results, which are captured by an image sensor at the rate of one million frames per second. In real world, no ideal isotropic homogeneous body exists. Disturbances exist everywhere. Crack is sensitive to local heterogeneity. Since the mesh configuration determines the candidate crack distribution in PDS-FEM, the uncertainty can be modeled by adding disturbance to the mesh configuration. By using Monte-Carlo simulation, the crack patterns observed in experiment, including bending, kinking and bifurcation are successfully simulated by using PDS-FEM. Keywords Three dimensional dynamic simulation of fracture, stochastic model, brittle failure, photo-elastic experiment 1. Introduction The simulation of fracture has been a challenging problem in solid continuum mechanics [1-2]. There are two difficulties in reproducing experiment results numerically: 1, accuracy and efficient numerical method is needed; 2, due to the limitation of observing technology, a stochastic model, which can represent the uncertainties, needs to be carefully designed. For simulation of crack growth, varieties of numerical methods have been developed, such as E-FEM, X-FEM [3], discontinuous Galerkin method and meshfree methods. However, the original version of these methods has two common drawbacks: (1), the bifurcation or branching could not be calculated, which is essential for brittle materials, such as epoxy resin, rock and concrete; (2), the crack configuration is simple, normally in one dimension, so complex and detail configuration cannot be expressed. Recently, the improved version of above methods has been proposed by many researchers. The static, quasi-static and dynamic analysis can be successfully carried out [4-7]. Besides aforementioned methods, the newly developed method, called particle discretization scheme finite element method (PDS-FEM) is another candidate [8], for its numerical efficiency and capability of calculating bifurcation. In order to verify the accuracy and numerically efficiency of this method, a thin epoxy resin plate with two notches located anti-symmetrically in the middle under uni-axial tensile has been carried out numerically and experimentally. The quasi-static state of PDS-FEM has been developed by Oguni et al [9]. The comparison results show similarity between the simulation and experiment results. In order to study the dynamic crack growth, we extend PDS-FEM to dynamic state [10]. PDS-FEM is originally formulated for Lagrangean at quasi-static state, and hence the extension to dynamic state is straightforward. Special attentions, however, have to be paid to time integration since
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