A Stochastic and Computational Approach for Fracture Modeling of Quasi-Brittle Materials

越来越需要从材料的微观结构组成来预测材料在宏观尺度上的响应和失效行为。在脆性和准脆性材料中，如玻璃、混凝土、岩石和陶瓷，失效对微观结构特别敏感，导致失效载荷的大分散。大多数现有的裂缝模型不能可靠地预测这种分散。该奖项支持开发脆性和准脆性材料断裂的理论和计算工具的基础研究，这些工具将其微观结构与失效载荷和观察到的分散直接联系起来。脆性和准脆性断裂力学在各种材料和结构设计中得到应用，并在许多其他领域中发挥核心作用。例如，陶瓷与金属一起用于开发用于装甲设计和航空航天工业的高强度和轻质材料。 岩石破裂，无论是自然发生的地震或人为的提高石油采收率和二氧化碳封存是另一个例子。最后，获得更准确的断裂概率减少了当前设计实践中的不确定性，并有助于评估现有基础设施系统的结构完整性。教育目标集中在随机模型和计算工具的短期课程工具包的开发，以吸引高中生到STEM领域，和软件模块，将与科学界共享。随机偏微分方程领域提供了系统的方法，传播随机性的分析一般。然而，目前还没有办法将材料的微观结构与这些随机模型所需的初始随机场描述联系起来。这项研究填补了知识空白，推导连续模型，直接翻译微观结构分布的初始材料场的描述。与一般的均匀化格式不同，随机代表体元仍然保持了材料的空间变异性和随机性。这使得脆性和准脆性断裂的真实建模成为可能。为了确保准确渲染这个理论模型的先进的有限元模型制定，可以有效地捕捉复杂的断裂模式，将散装和界面失效机制。此外，一种新的自适应计算方案消除了对初始网格离散化的故障负载的敏感性，并保证在用户指定的误差范围内的故障概率的估计。基于微观结构的概率断裂模型方法的目的是解释各种现象，不能很好地捕捉与常用的确定性模型。例如脆性和准脆性材料的尺寸效应、破坏载荷的分散性以及均匀载荷下复杂断裂模式的形成等。

There is an increasing need to predict materials response and failure behavior at macroscopic scale from its microstructural composition. In brittle and quasi-brittle materials, such as glass, concrete, rocks, and ceramics, failure is particularly sensitive to the microstructure leading to a large scatter in failure loads. Most existing fracture models fail to reliably predict this scatter. This award supports fundamental research in developing theoretical and computational tools for fracture of brittle and quasi-brittle materials that directly link their microstructure to failure loads and the scatter observed. Brittle and quasi-brittle fracture mechanics finds applications in a variety of material and structural designs and plays a central role in many other fields. For example, ceramics are used with metals to develop high-strength and light-weight materials for armor designs and aerospace industry. Rock fracture, whether occurring naturally as in earthquake or manmade for enhanced oil recovery and CO2 sequestration is another example. Finally, obtaining more accurate probabilities of fracture reduces uncertainties in current design practices and can aid in the assessment of the structural integrity of existing infrastructure systems. Educational goals focus on development of short course toolkits on random models and computational tools to attract high school students to STEM fields, and software modules that will be shared with scientific community.The field of stochastic partial differential equations provides systematic approaches for the propagation of randomness in an analysis in general. However, there is currently no means to relate material microstructures to initial random field description needed for these stochastic models. This research fills the knowledge gap by deriving continuum models that directly translate microstructure distribution to the initial material field description. Unlike common homogenization schemes, stochastic representative volume elements still preserve the spatial variability and randomness of material. This enables realistic modeling of brittle and quasi-brittle fracture. To ensure accurate rendering of this theoretical model an advanced finite element model is formulated that can efficiently capture complicated fracture patterns by incorporating both bulk and interfacial failure mechanisms. Moreover, a novel adaptive computational scheme eliminates the sensitivity of the failure load on initial mesh discretization and guarantees the estimation of probability of failure within the user-specified error bounds. The microstructure-based probabilistic fracture model approach aims to explain a variety of phenomena that are not well captured with commonly used deterministic models. Some examples are size effect in brittle and quasi-brittle materials, scatter in failure load, and formation of complex fracture patterns even under uniform loads.