Kinetics of lattice phase transitions

本项目侧重于马氏体相变材料的物理驱动模型的开发和分析，马氏体相变是一种晶体从高对称的母奥氏体相到低对称的马氏体相的无扩散变形，可以存在于几种对称相关的孪晶变体中。在机械或热载荷下，这些材料形成精细层状孪晶微结构。马氏体的独特性质，如它们适应大变形的能力和在循环载荷下表现出的明显的滞后，是由相和孪晶边界动力学决定的。了解界面的动力学如何取决于它们的取向、微观结构配置和晶体的性质，涉及到马氏体建模中具有挑战性的开放性问题。该项目旨在从介观晶格模型的角度推进对这些现象的理解。在她之前的工作的基础上，研究者专注于几个原型离散模型，目标是捕捉界面动力学和微观结构演化的基本特征，并强调高维现象和速率效应。模型的主要成分是允许存在两个稳定的均匀状态的最近邻之间的非凸相互作用和远程相互作用。该项目的成果包括预测有核的微观结构模式和推导可用于解决涉及时间和空间不均匀性问题的界面动爪。结果与实验观察和分子动力学模拟结果进行了比较。通过关注界面动力学，该项目有助于确定马氏体和相关活性材料的耗散特性如何取决于材料结构和加载条件。这在需要大量被动阻尼的新兴民用、航空航天和工业应用中非常重要，例如复合结构的损伤和振动控制，以及建筑物和桥梁中地震和风致振动的衰减。该项目的结果也可能有助于设计具有理想性能的新材料。该项目开发的数学方法可用于解决位错理论、断裂力学、DNA建模、图像识别和数值分析中遇到的类似问题。通过跨学科研究项目对研究生和本科生的培训，以及教育和高中推广活动，该计划的更广泛影响也得以实现。

VainchteinDMS-1007908 This project focuses on development and analysis ofphysically-motivated models of materials undergoing martensiticphase transition, a diffusionless deformation of a crystallattice from the high-symmetry parent austenite phase to thelow-symmetry martensite phase, which can exist in severalsymmetry-related twin variants. Under mechanical or thermalloading, these materials form finely layered twinningmicrostructures. The unique properties of martensites, such astheir ability to accommodate large deformations and the markedhysteresis they exhibit under cyclic loading, are determined bythe kinetics of phase and twin boundaries. Understanding howdynamics of the interfaces depends on their orientation,microstructural configuration, and properties of the crystallattice involves challenging open problems in modeling ofmartensites. The project seeks to advance the understanding ofthese phenomena from the perspective of mesoscopic latticemodels. Building on her prior work, the investigator focuses onseveral prototypical discrete models with the goal of capturingthe essential features of interface kinetics and microstructureevolution and an emphasis on higher-dimensional phenomena andrate effects. The main ingredients of the models are nonconvexinteractions between nearest neighbors allowing for the existenceof two stable homogeneous states and the long-range interactions. Among the outcomes of this project are prediction of nucleatedmicrostructural patterns and derivation of interfacial kineticlaws that can be used to solve problems involving temporal andspatial inhomogeneities. The results are compared toexperimental observations and molecular dynamics simulations. By focusing on the interface kinetics, this project helpsdetermine how the dissipative properties of martensites andrelated active materials depend on the material structure and theloading conditions. This is important in emerging civil,aerospace and industrial applications that require significantpassive damping, such as damage and vibration control incomposite structures and attenuation of earthquake- andwind-induced vibrations in buildings and bridges. Results ofthis project may also help design new materials with desiredproperties. Mathematical methods developed during the projectcan be used to solve similar problems encountered in dislocationtheory, fracture mechanics, DNA modeling, image recognition, andnumerical analysis. The broader impacts of this program are alsoachieved through training of graduate and undergraduate studentsin an interdisciplinary research program, as well as educationaland high-school outreach activities.