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

准脆性材料断裂建模的随机计算方法

• 批准号: 1538332
• 负责人: Reza Abedi
• 金额: $ 26.41万
• 依托单位: University of Tennessee Space Institute
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2015
• 资助国家: 美国
• 起止时间: 2015-09-01 至 2019-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1538332&HistoricalAwards=false
• 关键词: Stochastic; Computational; Approach; Fracture; Modeling

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.

人们越来越需要根据其微观结构成分来预测宏观尺度的材料响应和失效行为。在脆性和准脆性材料中，例如玻璃、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。大多数现有的断裂模型无法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，这些工具直接将其微观结构与失效载荷和观察到的散射联系起来。脆性和准脆性断裂力学在各种材料和结构设计中都有应用，并在许多其他领域发挥着核心作用。例如，陶瓷与金属一起使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。 另一个例子是岩石破裂，无论是在地震中自然发生还是为提高石油采收率和二氧化碳封存而人为发生的。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。教育目标侧重于开发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，以及与科学界共享的软件模块。随机偏微分方程领域为随机性的传播提供系统方法在一般分析中。然而，目前还没有办法将材料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。这项研究通过推导连续体模型填补了知识空白，该模型直接将微观结构分布转化为初始材料场描述。与常见的均质化方案不同，随机代表体积单元仍然保留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真实的建模。为了确保准确渲染该理论模型，制定了先进的有限元模型，该模型可以通过结合体和界面失效机制来有效捕获复杂的断裂模式。此外，一种新颖的自适应计算方案消除了故障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故障概率。基于微观结构的概率断裂模型方法旨在解释常用的确定性模型无法很好地捕获的各种现象。一些例子包括脆性和准脆性材料的尺寸效应、失效载荷的分散以及即使在均匀载荷下也会形成复杂的断裂模式。