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成分来预测材料在宏观尺度上的响应和失效行为。在玻璃、混凝土、岩石和陶瓷等脆性和准脆性材料中，破坏对导致破坏载荷大分散的微观结构特别敏感。大多数现有的裂缝模型不能可靠地预测这种分散。该奖项支持为脆性和准脆性材料的断裂开发理论和计算工具的基础研究，这些工具直接将它们的微观结构与破坏载荷和观察到的分散度联系起来。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，并在许多其他领域发挥着核心作用。例如，陶瓷与金属一起被用来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，无论是在地震中自然发生的，还是为了提高石油采收率和二氧化碳封存而人为造成的，都是另一个例子。最后，获得更准确的断裂概率可以减少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。教育目标集中于开发关于随机模型和计算工具的短期课程工具包，以吸引高中生进入STEM领域，以及将与科学界共享的软件模块。随机偏微分方程领域为一般分析中的随机性传播提供了系统的方法。然而，目前还没有将材料微结构与这些随机模型所需的初始随机场描述联系起来的方法。这项研究通过推导连续介质模型来填补这一知识空白，该模型直接将微观结构分布转换为初始材料场描述。与常用的均匀化方案不同，随机代表性体积单元仍然保持了材料的空间变异性和随机性。这使得能够对脆性和准脆性断裂进行逼真的建模。为了确保理论模型的准确再现，建立了一种先进的有限元模型，该模型通过结合整体和界面破坏机制来有效地捕捉复杂的断裂模式。此外，一种新的自适应计算方案消除了失效载荷对初始网格离散化的敏感性，并保证在用户指定的误差范围内估计失效概率。基于微观结构的概率断裂模型方法旨在解释通常使用的确定性模型不能很好地描述的各种现象。一些例子包括脆性和准脆性材料的尺寸效应，在破坏载荷中分散，以及即使在均匀载荷下也形成复杂的断裂模式。

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.