Plasticity and Avalanches: Connections Between Systems Ranging from Metals to Granular Materials

该奖项支持理论研究和教育，结合统计物理学，材料科学，固体力学，工程，颗粒力学和冶金学的联合收割机概念，以提高和统一材料对外部应力的响应的理解。最近对小金属或冰晶的剪切响应的实验表明，通过一系列跨越广泛尺寸范围的位错滑动事件，变形不是平滑的，而是急动的。同样地，密集堆积的颗粒物质对剪切力的反应是一系列的滑动雪崩。在这两种情况下，分布的滑移事件的大小是由幂律在几十年来描述。相关的幂律指数对于一大类不同的材料是相同的;它们是“通用的”。这些系统的模拟是有用的，但不同系统之间的联系往往可以更容易地识别使用分析方法。基于最近的分析，可以评估具有雪崩并在长尺度上显示相同行为的系统类的大小。 在这个项目中，PI将分析计算滑动雪崩统计对一系列重要实验调谐参数（如应变率、应力率、无序度和温度）的依赖性的预测。 该方法也将被用来调查驱动动力学在低温和松弛动力学在较高的温度下，在没有驾驶之间的连接。一个主要目标是扩展和测试最近的分析方法，以统一以前被认为是无关的非平衡现象的理解。 这些方法包括相变理论，重整化群，无序系统理论，蒙特卡罗模拟和分子动力学模拟的技术。从这些研究的预测进行了比较与实验上的塑性变形，粒状材料，磁铁，从大规模的模拟结果。这项研究的高度跨学科性质促进了研究生和本科生在这个项目上工作的不同群体的理想学习环境。将促进与国家和国际理论家、实验学家、材料科学家、工程师和地震学家的合作。模拟代码将与研究界共享。这项工作的潜在应用包括：从纳米器件到散装材料的广泛尺度上的材料失效预测和控制，无损材料测试，对冶金学中通常不期望的Portevin-Le Chatelier效应的更好理解，在加工过程中增加的材料稳定性，对颗粒材料（例如筒仓中的粉末和颗粒）的堵塞和雪崩的更好理解，非技术性总结该奖项支持理论研究和教育，将统计物理学、材料科学、固体力学、工程学、颗粒力学和冶金学的联合收割机概念结合起来，以促进和统一对材料如何响应外部应力的理解。许多系统在缓慢推动时会发出噼啪声：木材在缓慢弯曲时会发出噼啪声。类似地，小的金属或冰晶以相当不稳定的方式变形，通过一系列跨越大范围尺寸的局部滑动事件。在这些滑动事件中，薄弱点响应于缓慢增加的所施加的剪切应力而失效。在更大的范围内，当缓慢的构造运动触发地壳薄弱点的滑动时，大致相同的现象会引起地震。许多其他系统表现出类似的故障雪崩，从颗粒材料到磁铁。该项目开发了这些系统的雪崩统计的相似性的定量理解，其中许多是以前单独研究。目标是预测结果和理解可以在多大程度上从一个系统转移到另一个系统。最近，强大的数学工具已经开发出来回答这些问题。这些方法将与金属、合金、颗粒材料和磁体的塑性变形的计算模拟和实验比较相结合。结果是相关的一些应用程序，包括：材料故障预测和控制从纳米器件到散装材料，无损材料检测，在处理过程中增加材料的稳定性，提高对颗粒材料的干扰和雪崩的理解，以及磁信息存储的长期安全性。参与该项目的研究生和本科生的多元化群体将接受广泛的跨学科培训，并将学习使用统计物理，材料科学，机械工程和数学的现代工具。将促进与国家和国际理论家、实验学家、材料科学家、工程师和地震学家的合作。模拟代码将与更广泛的研究社区共享。

TECHNICAL SUMMARYThis award supports theoretical research and education to combine concepts from statistical physics, materials science, solid mechanics, engineering, granular mechanics, and metallurgy to advance and unify understanding of the response of materials to external stresses. Recent experiments on the shear response of small metal or ice crystals reveal that the deformation is not smooth, but rather jerky, through a sequence of dislocation-slip events that span a broad range of sizes. Similarly, densely packed granular materials respond to shear with a sequence of slip avalanches. In both cases, the distribution of slip event sizes is described by a power law over several decades. The associated power law exponents are the same for a large class of different materials; they are "universal". Simulations of these systems are useful, but connections between different systems can often more easily be recognized using analytic approaches. Building on recent analyses, the size of the class of systems having avalanches and showing the same behavior on long length scales, can be assessed. In this project, the PI will analytically compute predictions for the dependence of the slip-avalanche statistics on a series of important experimental tuning parameters, such as strain rate, stress rate, disorder, and temperature. The approach will also be used to investigate the connection between driven dynamics at low temperature and relaxation dynamics at higher temperature in the absence of driving. A main goal is to expand and test recent analytical approaches in order to unify the understanding of non-equilibrium phenomena that were previously thought to be unrelated. The methods include techniques from the theory of phase transitions, the renormalization group, disordered-systems theory, Monte Carlo simulations and molecular dynamics simulations. Predictions from these studies are compared with experiments on plastic deformation, granular materials, magnets, and results from large-scale simulations. The highly interdisciplinary nature of this research promotes an ideal learning environment for the diverse group of graduate and undergraduate students working on this project. Collaborations with a network of national and international theorists, experimentalists, materials scientists, engineers, and seismologists will be fostered. Simulation codes will be shared with the research community. Potential applications of this work include: materials-failure prediction and control on a broad range of scales, from nanodevices to bulk materials, nondestructive materials testing, improved understanding of the often undesirable Portevin-Le Chatelier effect in metallurgy, increased materials stability during processing, improved understanding of jamming and avalanches of granular materials such as powders and grains in silos, and long-term security of magnetic information storage.NONTECHNICAL SUMMARYThis award supports theoretical research and education to combine concepts from statistical physics, materials science, solid mechanics, engineering, granular mechanics, and metallurgy to advance and unify understanding of how materials respond to external stresses. Many systems crackle when they are pushed slowly: Wood can crackle when it is slowly bent. Similarly, small metal or ice crystals deform in a rather jerky way, through a sequence of local slip events that span a broad range of size. In these slip events, weak spots fail in response to the slowly increasing applied shear stress. On a much larger scale roughly the same phenomenon gives rise to earthquakes, when the slow tectonic motion triggers slips of weak spots in the earth's crust. Many other systems exhibit similar failure avalanches, ranging from granular materials to magnets. This project develops a quantitative understanding of the similarities of the avalanche statistics of these systems, many of which were previously studied separately. The goal is to predict to what extent the results and understanding can be transferred from one system to another. Recently, powerful mathematical tools have been developed to answer these questions. These methods will be coupled with computational simulations and comparisons with experiments on plastic deformation of metals, alloys, granular materials, and magnets. The results are relevant for a number of applications, including: materials failure predictions and control from nanodevices to bulk materials, nondestructive materials testing, increased materials stability during processing, improved understanding of jamming and avalanches of granular materials, and long-term security of magnetic information storage. The diverse group of graduate and undergraduate students involved in this project will receive broad interdisciplinary training, and will learn to use modern tools from statistical physics, materials science, mechanical engineering, and mathematics. Collaborations with a network of national and international theorists, experimentalists, materials scientists, engineers, and seismologists will be fostered. Simulation codes will be shared with the broader research community.