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Instabilities in Materials Science

材料科学中的不稳定性

基本信息

批准号：
1714287
负责人：
Yury Grabovsky
金额：
$ 32.04万
依托单位：
Temple University
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2017
资助国家：
美国
起止时间：
2017-08-15 至 2020-07-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1714287&HistoricalAwards=false
关键词：
Instabilities Materials Science

项目摘要

1714287Grabovsky The investigator and his collaborators study several important phenomena where the main underlying feature is instability, or extreme sensitivity to measurement errors, imperfections of shape, or load. Three projects, unified by the general idea of instability, are pursued. One of them deals with understanding instabilities in nonlinear elasticity associated with martensitic phase transitions, whereby sharp phase boundaries are observed experimentally. Such phase transitions are responsible for shape memory effects in alloys, and for a giant magnetostrictive effect exhibited by some materials, to name just a few examples. Another project applies new tools to analyze the extreme sensitivity to imperfections of the buckling stress of axially compressed circular cylindrical shells -- an essential structural component in a vast variety of structures, from grain silos to airplanes and space ships. The third project focuses on quantitative understanding of a well-known confluence of rigidity and flexibility -- a seemingly contradictory combination of properties -- of Herglotz functions that are ubiquitous in applications from materials science to nuclear physics. For example, the investigator's research quantifies the uncertainty due to experimental errors in the estimates of complex electromagnetic permittivity, which describes how a material interacts with electromagnetic waves of various frequencies from radio waves through visible light to gamma rays. This project constitutes Ph.D. research of a graduate student working under the investigator's guidance. The most salient feature in martensitic shape transformations, which in particular is responsible for shape memory effect, is the presence of phase boundaries -- sharp interfaces separating different martensitic variants. Stability of such phase boundaries can be completely characterized in terms of the concept of quasiconvexity. With the understanding that characterization of quasiconvexity is often regarded as unachievable, the investigator and his collaborators focus on eminently computable algebraic conditions of stability of phase boundaries and assess their "strength" through specific examples that show how far off algebraic conditions are from true answers, which could be computed either analytically or numerically. Another project deals with buckling of cylindrical shells -- one of the extensively studied, yet poorly understood problems in mechanics, where the classical formula cannot be used to predict buckling stress observed in experiments due to initial imperfections of load and shape. This project creates a mathematically rigorous theory of the buckling of slender bodies that is capable of explaining why initial imperfections of shape and load have strong influence on the buckling stress in some structures, while having negligible effect in others. The third project studies the somewhat paradoxical behavior of Herglotz functions, that are at the same time extremely rigid and surprisingly flexible. Its understanding contributes to several areas of mathematics and physics and answers many important questions. The problems of data validation, and extrapolation are addressed. This project constitutes Ph.D. research of the investigator's graduate student.

小行星1714287 研究人员和他的合作者研究了几个重要的现象，其中主要的基本特征是不稳定性，或对测量误差，形状缺陷或负载的极端敏感性。三个项目，统一的不稳定性的一般思想，进行。其中之一涉及理解与马氏体相变相关的非线性弹性的不稳定性，从而通过实验观察到尖锐的相边界。这样的相变是合金中的形状记忆效应的原因，并且是一些材料所表现出的超磁致伸缩效应的原因，仅举几个例子。另一个项目应用新的工具来分析轴向压缩圆柱壳的屈曲应力对缺陷的极端敏感性-这是从粮仓到飞机和宇宙飞船的各种结构中的重要结构部件。第三个项目的重点是定量理解一个众所周知的刚性和柔性的汇合-一个看似矛盾的属性组合-从材料科学到核物理的应用中无处不在的Herglotz函数。例如，研究人员的研究量化了由于复电磁介电常数估计中的实验误差而导致的不确定性，复电磁介电常数描述了材料如何与各种频率的电磁波相互作用，从无线电波到可见光再到伽马射线。该项目是Ph.D.研究生在研究者的指导下进行的研究。马氏体形状转变中最显著的特征，特别是形状记忆效应，是相边界的存在-分离不同马氏体变体的尖锐界面。这种相界的稳定性可以完全用拟凸性的概念来描述。由于了解到拟凸性的表征通常被认为是无法实现的，研究者和他的合作者专注于相边界稳定性的显著可计算代数条件，并通过具体的例子来评估它们的“强度”，这些例子表明代数条件离真实答案有多远，可以通过解析或数值计算来计算。另一个项目涉及圆柱壳的屈曲--这是力学中广泛研究但了解甚少的问题之一，由于载荷和形状的初始缺陷，经典公式不能用于预测实验中观察到的屈曲应力。该项目创建了一个数学上严格的细长体屈曲理论，能够解释为什么形状和载荷的初始缺陷对某些结构的屈曲应力有很大的影响，而对其他结构的影响可以忽略不计。第三个项目研究了Herglotz函数的一些自相矛盾的行为，这些函数同时非常刚性和惊人的灵活性。对它的理解有助于数学和物理的多个领域，并回答了许多重要问题。数据验证和外推的问题得到解决。该项目是Ph.D.研究员的研究生的研究。