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

了解随机结构响应是基于可靠性的工程设计的核心，随机有限元（FE）建模已成为一种广泛使用的模拟工具，以研究结构的概率行为。主要的研究兴趣最近已指向脆性非均质（a.k.a.）。准脆性）材料，例如混凝土、岩石、复合材料等，这与许多现代工程结构高度相关。准脆性结构可以表现出复杂的破坏机制，从扩散损伤到局部损伤，这取决于不同的材料长度尺度。最近的研究表明，如果不考虑这些长度尺度的随机本构特性建模，随机有限元模拟遭受强大的虚假网格敏感性。这严重限制了模拟的预测能力。该奖项的目标是开发一个新的计算框架，用于准脆性损伤和断裂的随机分析。该框架是锚定的本构特性的随机场的有限元基于机制的投影。该模型将通过一组独特的实验数据进行验证，重点是试样尺寸和几何形状对多孔岩石的概率破坏的影响。这项研究将与高中、本科和研究生的教育活动紧密结合。教育计划包括参加一个高中暑期方案，招募女性和少数民族研究生，组织讲习班和会议，以及开发新课程。人们早就知道，由于应变软化材料的行为，准脆性结构的有限元模拟表现出很强的网格依赖性。虽然已经提出了各种本地化限制器来解决这个问题，但重点仅限于确定性分析。本研究将探讨随机有限元模拟中的网格依赖性问题，并通过一种新的计算框架来解决。该项目将开发一个基于机制的模型，用于将材料特性的随机场映射到有限元网格上。该模型的直接结果是，本构特性的概率分布依赖于网格尺寸，并且依赖性受占主导地位的损伤模式。在准脆性材料上进行的不同尺寸和几何形状试样的实验将为计算模型的验证提供有价值的数据。该模型将根据对本构特性的空间互协方差特征对结构失效统计的标度行为的影响的新理解来校准。这项研究将通过将潜在的失效机制与材料的随机本构模型联系起来，提高我们对准脆性断裂和失效的随机建模能力。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

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.