Thermomechanical Instabilities in M-Lattices with Application to Shape Memory Materials

M格点的热力学可调性及其在形状记忆合金中的应用肖里根大学航空航天工程系。形状记忆合金（SMA）具有形状记忆效应和伪弹性效应两大特点，是一种重要的高科技材料。它们有趣的热机械响应使得它们作为低频鲁棒致动器和无源器件在各种新颖的应用中具有吸引力。SMA的热机械行为是由于位移，一级相变（或马氏体相变），产生复杂的，精细的微观结构。这一特点是在这些材料的连续描述中遇到的建模困难的核心。现有的SMA连续介质模拟工作是基于有限热弹性理论，需要使用唯象应变能密度函数。基于这些函数的边值问题的解成功地预测了实验观察到的精细尺度微结构的许多特征。然而，这种方法留下了一系列的其他问题没有回答，如晶格水平的起源theinstabilities，共存相的数量和特征波长的bridgedmicrostructures.的新功能，拟议的调查是使用原子晶格模拟的SMA，特别是NiTi，在其类最有技术前途的材料。我们的目标是产生真实的能量密度，并模拟和理解纳米尺度下的稳定性现象。具体来说，我们打算找到所有的温度和应力的平衡相及其相应的微观结构（孪生和晶体界面），并研究其稳定性，最终目标是弥合纳米（晶格）现象和微观（单晶）行为之间的尺度。除了在纳米尺度上推进对SMA的基本理解外，这项工作有可能帮助回答为什么某些金属间合金表现出形状记忆现象，而其他合金则没有，这项工作最终可能用于指导新SMA的研究。研究团队由两名研究人员组成，Nicolas Triantafyllidis教授和JohnShaw教授，他们为该项目带来了互补的专业知识。所要求的资金将在三年内资助一名博士生，再加上瑞安埃利奥特先生一年的博士后任命，他正在与PI在这一领域合作。与洛斯阿拉莫斯国家实验室的理论物理组的合作正在进行中，通过在夏季接待研究生。这项研究的结果将被用于一个新的研究生水平，跨学科的课程原子建模在solid mechanism.broader影响的拟议工作：这项工作非常适合在当前nanomemechanicsinitiative在美国国家科学基金会，因为它涉及到从原子的考虑的基本晶格稳定现象的研究m-晶体。理解这些现象将最终有助于具有形状记忆效应的新型材料的概念。拟议的工作不仅解决了力学中的一个基本问题，而且还需要其他学科的投入，即凝聚态物理学和应用数学。与洛斯阿拉莫斯国家实验室的现有合作为与这些学科的互动和知识的传播提供了一个自然的框架。

THERMOMECHANICAL INSTABILITIES IN M-LATTICESWITH APPLICATIONS TO SHAPE MEMORY ALLOYSNicolas Triantafyllidis and John A. ShawDepartment of Aerospace EngineeringThe University of Michigan1. Project SummaryShape memory alloys (SMAs) are technologically important materials, because of twouseful features: the shape memory effect and the pseudoelastic effect. Their interesting thermomechanicalresponse makes them attractive as low frequency robust actuators and passive devicesfor a variety of novel applications. The thermo-mechanical behavior of SMAs is due to displacive,first-order phase transformations (or martensitic transformations), which produce complex, finescalemicrostructures. This feature is at the heart of modeling difficulties encountered in thecontinuum descriptions of these materials. Existing work on continuum modeling of SMAs isbased on finite thermoelasticity theory and requires the use of phenomenological strain energydensity functions. Solutions of boundary value problems based on these functions are successful inpredicting many features of the experimentally observed fine scale microstructures. This approach,however, leaves a host of other problems unanswered, such as the lattice-level origin of theinstabilities, the number of coexisting phases and the characteristic wavelengths of the observedmicrostructures.The novel feature of the proposed investigation is the use of atomic lattice simulations ofSMAs, and in particular for NiTi, the most technologically promising material in its class. Our goalis to generate realistic energy densities and to simulate and understand the stability phenomena atthe nanometer scale. Specifically, we intend to find all equilibrium phases for temperature and stressand their corresponding microstructures (twinning and crystal interfaces) and study their stabilitywith the ultimate objective to bridge the scales between the nano-(lattice) phenomena and micro-(single crystal) behavior. Besides advancing a fundamental understanding of SMAs at the nanoscale,the work has the potential to help answer why certain intermetallic alloys exhibit shapememory phenomena and other do not, and this work could eventually be used to guide the searchfor new SMAs.The research team consists of two investigators, Professors Nicolas Triantafyllidis and JohnShaw, who bring complementary expertise to the project. The requested funds will fund onedoctoral student over a period of three years plus a one year post-doctoral appointment for Mr.Ryan Elliott, who is working with the PI's on this area. Collaboration with the Theoretical Physicsgroup of Los Alamos National Labs is underway through hosting of the graduate students duringthe summers. Results of this research will be used in a new graduate level, cross-disciplinary courseon atomistic modeling in solid mechanics.Broader Impact of the proposed work: This work fits well within the current nanomechanicsinitiative at NSF, since it pertains to the study of underlying lattice stability phenomenaof m-crystals from atomistic considerations. Understanding these phenomena will eventually beuseful in the conception of novel materials with shape memory effects. The proposed work not onlyaddresses a fundamental problem in mechanics, but it also requires input from other disciplines, i.e.condensed matter physics and applied mathematics. The existing collaboration with Los AlamosNational Labs provides a natural framework for the interaction with these disciplines and for thedissemination of the knowledge to be created.