Objective Stochastic Modeling of Quasibrittle Damage and Failure Through Mechanistic Mapping of Random Fields

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Understanding stochastic structural response is central to reliability-based engineering designs and stochastic finite element (FE) modeling has become a widely used simulation tool to investigate the probabilistic behavior of structures. Major research interest has recently been directed towards brittle heterogenous (a.k.a. quasibrittle) materials, such as concrete, rock, composites, etc., which are highly relevant to many modern engineering structures. Quasibrittle structures can exhibit complicated failure mechanisms, ranging from diffused damage to localized damage, which are governed by different material length scales. Recent studies have shown that, without considering these length scales in modeling the random constitutive properties, stochastic FE simulations suffer strong spurious mesh sensitivity. This severely limits the prediction capacity of the simulation. The goal of this award is to develop a new computational framework for stochastic analysis of quasibrittle damage and fracture. The framework is anchored by a mechanism-based projection of random fields of constitutive properties onto the finite elements. The model will be validated through a unique set of experimental data focusing on the effects of specimen size and geometry on the probabilistic failure of a porous rock. The research will be tightly integrated with educational activities for high-school, undergraduate, and graduate students. The educational plan includes participation in a high-school summer program, recruitment of female and minority research students, organization of workshops and sessions at conferences, and development of new courses. It has long been known that, due to strain-softening material behavior, FE simulations of quasibrittle structures exhibit a strong mesh dependence. Though various localization limiters have been suggested to address this issue, the focus has been limited to deterministic analysis. This research will investigate the issue of mesh dependence in stochastic FE simulations, and resolve it through a novel computational framework. The project will develop a mechanism-based model for mapping of random fields of material properties onto the finite element mesh. The direct consequence of the model is that the probability distributions of the constitutive properties depend on the mesh size, and the dependence is influenced by the prevailing damage pattern. Experiments on a quasibrittle material using specimens with different sizes and geometries will provide valuable data for validation of the computational models. The model will be calibrated based on a new understanding of the effect of spatial cross-covariance features of constitutive properties on the scaling behavior of the structural failure statistics. This research will enhance our capability of stochastic modeling of quasibrittle fracture and failure by linking the underlying failure mechanisms with the stochastic constitutive model of the material.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.