On robustness of stochastic finite element analysis of damage and fracture of heterogeneous materials

Stochastic finite element (SFE) analysis is anchored by the knowledge of spatial randomness of material properties, which are often represented by random fields. These fields are typically generated over sampling grids that are able to capture the spatial correlation of the random material properties. Since the grids of random fields rarely coincide with the FE mesh, a mapping procedure is required to transfer material properties from the sampling grids to the Gauss points of the FE mesh. The challenge becomes pronounced for heterogeneous materials, which often display complex failure processes such as damage localization, distributed damage, and transitions between them. These mechanisms could produce strongly inhomogeneous deformation within the finite elements, complicating the mapping of random fields. This study examines how different mapping strategies affect the robustness of SFE analysis for heterogeneous materials, using bending beam and cavity expansion tests on Dunnville sandstone specimens that exhibit diverse failure patterns. Three mapping methods, namely the local mapping method, the local averaging method, and the mechanism-based adaptive mapping method, are considered. The comparison between the experimental and simulation results shows the critical importance of linking the mapping algorithm to the evolving mechanical behavior of each finite element in order to ensure model robustness. The analysis further clarifies the influence of different length scales including the FE mesh size, correlation length of the random fields, and width of fracture process zone on the performance of the mapping method. The study offers new insights into the experimental calibration and validation of SFE models.