13th International Conference on Fracture June 16–21, 2013, Beijing, China -8- (2) Friction, thermal as well as acoustic energy consumption mechanics due to cracking have not been considered in this simulation. The released strain energy blurs the simulated photo-elastic fringe patterns. (3) Ductile fracture may happen in the experiments under indoor temperature. 5. Conclusion There is no ideal homogeneous body in the world. In order to model the heterogeneity, PDS-FEM offers a nature way by adding disturbance in the mesh configuration. This paper conducts a tensile fracture experiment of a thin epoxy resin, and builds a stochastic model with the distribution of candidate crack path set as stochastic variables. Monte-Carlo simulation is carried out. With specified basic mesh configuration, the simulation results reproduce the crack growth of corresponding experiments, including bending, kinking and bifurcation. The heterogeneity is successfully modeled. Before crack develops, the stress distribution of simulation shows great similarity with experimental photo-elastic fringe patterns captured by a high speed camera. When crack begins, the fringe patterns of simulation become blurred. Three possible reasons have been proposed and more realistic problem setting is needed to increase the similarity between the results of simulation and experiment in future study. Acknowledgements This research is partially supported by the Central Public-interest Scientific Institution Basal Research Fund of China (Grant No. 2011B-05), China postdoctoral Science Foundation, and Natural Science Foundation of Hei Longjiang Province of China (Grant No. LC2012C32). These supports are greatly appreciated. References [1] J. Oliver, Modelling strong discontinuities in solid mechanics via strain softening constitutive equations. Part 2: Numerical simulation. Int. J. Num. Meth. Eng., 39(21), (1996) 3601-3623. [2] N. Moes, J. Dolbow, T. Belytschko, A finite element method for crack growth without remeshing. Int. J. Num. Meth. Eng., Vol. 46:1, (1999) 131–150. [3] J. Oliver, A. Huespe, and P. Sanchez, A comparative study on finite elements for capturing strong discontinuities: E-FEM vs X-FEM. Computer methods in applied mechanics and engineering, 195(37), (2006) 4732-4752. [4] T. Rabczuk, S. Bordas, and G. Zi, A three-dimensional meshfree method for continuous multiple-crack initiation, propagation and junction in statics and dynamics. Comput. Mech., 40(3), (2007) 473-495. [5] S. Bordas, T. Rabczuk, and G. Zi, Three-dimensional crack initiation, propagation, branching and junction in non-linear materials by an extended meshfree method without asymptotic enrichment. Eng. Fract. Mech., 75(5), (2008) 943-960. [6] F. Stan, Discontinuous Galerkin method for interface crack propagation. Int. J. Mater. Forming 1, (2008) 1127-1130. [7] N. Sukumar, B. Moran, T. Black, and T. Belytschko, An element-free Galerkin method for three-dimensional fracture mechanics. Comput. Mech., 20(1), (1997) 170-175. [8] M. Hori, K. Oguni, and H. Sakaguchi, Proposal of FEM implemented with particle discretization for analysis of failure phenomena. J. Mech. Phys. Solids: 53(3), (2005) 681-703.
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