A non-local probabilistic method for modeling of crack propagation

Damage process in engineering systems is strongly affected by spatial heterogeneity and local discontinuities in the materials, which are significantly influencing the reliability and integrity of the systems. In this paper, we present a new stochastic approach as a tool for performing uncertainty quantification in simulating damage evolution in heterogeneous brittle materials. One of the advantages of the proposed method is its ability to capture the influence of uncertainty in the mechanical properties of whole simulation domain, not just the properties of the immediate neighbourhood around the crack tip, on direction of crack propagation. In fact, through this approach the direction of crack propagation at a specified point of localised damage can be probabilistically determined based on nonlocal mechanics theory, in which the influence of local discontinuities and weak points located at further distances from the crack tip, in addition to those located at the immediate neighbourhood of the local damage, are incorporated into the model. The reliability and performance of the methodology are examined through simulation of numerical examples and comparison with analytical results and experimental data. The case studies show how the crack initiation angle can be reasonably estimated with this methodology and how this approach provides realistic values of fracture toughness KIC and fracture energy Gf.