Mesoscale Computational Modeling and Analysis of Materials Microstructure

在各种应用中使用的大多数金属和陶瓷材料，包括飞机，汽车和计算机等设备都是多晶的，即由许多微观晶体（晶粒）通过边界保持在一起。晶界有一种特性叫做？晶界能，这决定了颗粒之间的连接强度取决于能量，多晶结构可以具有非常不同的性质。关于这种能量及其对边界的晶体学性质的依赖性，我们知之甚少。这项工作的主要目标是建立有效的数学模型和数值算法，通过量化粗化过程的动力学和理解晶界能对微观结构演变的影响，预测和控制材料的微观结构。所提出的方法的新奇在于把重点放在理解统计效应的拓扑重构过程中的晶界网络的演变。该项目将允许开发一个新的随机框架，用于材料的介观分析，部分基于最近发现的演化方程和对晶粒消失率的深入研究。这项研究将链接粗化过程常见的几乎所有材料与潜在的随机过程，通过准确和验证的计算建模的基础上随机游走理论，调制泊松过程和分布式玻尔兹曼方程的具体微观结构的特点。显著的努力将致力于优化性能的数值算法，如数值方案求解分数积分微分方程的非局部内核和方法的参数估计随机过程。该项目中开发和分析的模型和算法将为传统上用于研究复杂材料界面特性的大规模模拟和其他数值技术提供准确且低成本的替代方案。这项工作将导致控制晶粒生长动力学，材料科学应用的主要问题，并更深入地了解材料参数及其在不同尺度上的相互作用。这将通过推进小说的综合而对许多具有实际意义的领域产生直接影响。聪明吗材料-高度复杂的材料，具有非常特定的属性，以满足社会在巨大的经济和环境挑战时代日益增长的需求。例如，能够可靠地承受极端热和压力环境的功能材料对于解决与能源相关的问题（如提高发电厂效率）是必不可少的，而设计新一代车辆时需要更轻的重量高强度部件以降低燃料消耗。研究人员和合作者开发的模型将用于构建一套能够模拟和分析微观结构的算法，这些微观结构可以在外部刺激下倾向于某种类型的行为。这些方法将允许更快，更可靠的分析，控制和优化材料特性，并将为工程师提供强大的预测工具，这些工具可以很容易地转移到工业中，用于模拟商品材料的加工过程。

Most metallic and ceramic materials used in a variety of applications, including aircraft, automobiles, and devices such as computers are polycrystalline, i.e. are made up of many microscopic crystals (grains) held together by boundaries. Grain boundaries have a property called ?grain boundary energy?, which is responsible for how strong the grains are connected to each other. Depending on the energy, polycrystalline structures may have very different properties. Very little is known about this energy and its dependence on the crystallographic nature of the boundary. The main objective of this work is to create efficient mathematical models and numerical algorithms for predicting and controlling materials microstructure by quantifying the kinetics of the coarsening processes and understanding the influence of grain boundary energy on microstructural evolution. The novelty of the proposed approach lies in placing focus on understanding statistical effects of the topological reconfigurations during the grain boundary network evolution. This project will allow to develop a new stochastic framework for mesoscopic analysis of materials based in part on recently discovered evolution equations and an in-depth study of grain disappearance rates. This research will link coarsening processes common to nearly all materials with underlying stochastic processes that characterize specific microstructures by means of accurate and validated computational modeling based on random walk theory, modulated Poisson processes and distributed Boltzmann equations. Significant effort will be dedicated to optimizing performance of numerical algorithms, such as numerical schemes for solving fractional integro-differential equations with nonlocal kernels and methods for parameter estimation in stochastic processes. The models and algorithms developed and analyzed in this project will offer an accurate and low cost alternative to large-scale simulations and other numerical techniques traditionally used in studying interfacial properties of complex materials. This work will lead to control over grain growth kinetics, a primary issue for materials science applications, and to a deeper understanding of the materials parameters and their interaction across different scales. This will have a direct impact on many practically important areas by advancing the synthesis of novel ?smart? materials - highly sophisticated materials, possessing very specific set of properties to target particular applications necessary to meet increasing demands of the society in the era of tremendous economic and environmental challenges. For instance, functional materials that can reliably withstand extreme thermal and pressure environments are indispensable for solving energy-related problems such as improving power plant efficiency, while lighter weight high strength components are required for designing new generation vehicles with reduced fuel consumption. The models developed by the investigator and collaborators will be used to build a suite of algorithms capable of simulating and analyzing microstructures that can be predisposed to certain type of behavior under external stimuli. These methods will allow for faster and more reliable analysis, control and optimization of materials properties and will equip engineers with powerful predictive tools that can be readily transferred to industry for modeling the processing of commodity materials.