Monte-Carlo simulation of failure phenomena with heterogenety of material

In order to analyze failure phenomena, it is important to use heterogeneous models instead of an ideally homogeneous one since crack path is strongly influenced by the presence of local heterogeneities in the real deformable bodies. Numerical Monte-Carlo simulation is not feasible for such heterogeneous models if each simulation is computationally expensive. The authors are proposing FEM-β to solve this problem. The present paper provides two examples of Monte-Carlo simulation of analyzing crack path in heterogeneous models. The probability density functions of the crack paths are obtained, and they are compared with the path of the ideally homogeneous model. The usefulness of the Monte-Carlo simulation of heterogeneous models for failure analysis is discussed.