On mapping algorithms for material random fields in stochastic FE analysis of quasibrittle structures

This study investigates the algorithms for mapping the random fields of material properties onto finite element (FE) meshes and examines their consequences for stochastic FE analysis of damage and fracture in quasibrittle materials. A continuum damage constitutive modeling framework is adopted, in which the constitutive law of each finite element is regularized to ensure correct energy dissipation for different mesh sizes. Three mapping methods for random fields are considered: (1) local mapping, where the constitutive property of an element is directly sampled from the random field at a specific point (e.g., element centroid or integration point); (2) local averaging, where the property is obtained by averaging the random field over the element domain; and (3) mechanism-based mapping, where the projection of the random field onto the FE mesh is governed by the prevailing damage mechanism within the element. These methods are implemented in stochastic FE simulations of recent bending beam tests on Dunnville sandstone. Comparison between experimental and simulated results demonstrates the critical role of linking the mapping algorithm to the evolving damage behavior of individual finite elements. The analysis further elucidates the influence of multiple characteristic length scales—including FE mesh size, correlation length, and fracture process zone width—on the choice of mapping method.