EAGER: Network Sparsification for Atomistic to Continuum Scale Solid Mechanics

这一早期概念探索性研究(AGER)奖支持使用网络科学工具来预测材料的特性。固体材料中的微小缺陷(例如缺陷)会对其材料性能产生重大影响。由于解决此类问题所需的物理复杂性和计算机资源，预测这些特性的模型可能非常具有挑战性。为了克服这一挑战并促进对缺陷力学的理解，该奖项将提供初步支持，以制定和验证利用网络科学的新数学工具的新建模方法。虽然网络科学已经被成功地用于理解与友谊、疾病传播和互联网上的信息相关的系统的全球性质，但它还没有被考虑用于预测固体的复杂材料性质。通过揭示固体中最重要的局部相互作用，PI有望提供对考虑材料缺陷的全球材料特性的新见解。这对设计新的电子材料、用于机器人的智能致动器和传感器材料以及用于能源应用的材料具有重要意义。网络科学工具还将通过研究经验和课程介绍给研究生和本科生。应用图论方法预测固体的本构模型，以弥合原子结构计算和固体连续体场理论之间的差距。如果成功，这种方法将在固体力学中提供独特的机会，利用新的工具来提供对集体原子行为的更深层次的了解，作为一个具有高级预测能力的连续体，由底层网络的属性支持。PI计划利用这些概念来理解局部原子力如何通过将材料物理投影到不同稀疏性的图形上来控制中尺度本构行为。基于离散图形的变形的随机估计将在连续统框架内用于支持对固体中缺陷附近的应力进行量化。利用贝叶斯不确定性量化将被用来提供用于判断网络结构(例如，缺陷结构)的变化如何引起中尺度本构行为变化的有效性的度量。一维Lennard-Jones势的原子计算将扩展到二维和三维分子动力学模拟。网络结构将从这些模型中表达出来，然后用于变形的中尺度连续统均化，以评估基于网络的材料缺陷表征的有效性。

This EArly-concept Grant for Exploratory Research (EAGER) award supports the use of network science tools to predict characteristics of materials. Small imperfections (e.g., defects) in solid materials can have a dramatic impact on their material properties. Models that predict these properties can be extraordinarily challenging due to the physical complexity and computer resources required to solve such problems. To overcome this challenge and advance the understanding of defect mechanics, this award will provide the initial support to formulate and validate a new modeling methodology that leverages novel mathematical tools from network science. While network science has been successfully used to understand global properties of systems associated with friendships, spread of diseases, and information over the Internet, it has not been considered for predicting complex material properties of solids. By uncovering the most important local interactions within a solid, the PIs expect to provide new insights into global material characteristics that take material defects into consideration. This has implications on designing new electronic materials, smart actuator and sensor materials for robotics, and materials for energy applications. The network science tools will also be introduced to graduate and undergraduate students through research experiences and courses.A graph theoretic approach to constitutive model predictions of solids will be applied to bridge the gap between atomic structure calculations and continuum field theory of solids. If successful, this approach will provide unique opportunities in solid mechanics to utilize new tools to provide deeper insight of collective atomic behavior as a continuum with advanced predictive power supported by the properties of the underlying network. The PIs plan to utilize such concepts to understand how local atomic forces govern mesoscale constitutive behavior by projecting material physics onto graphs of varying sparsity. Stochastic estimations of deformation based on the discrete graphs will be utilized within a continuum framework to support quantification of stresses near defects in solids. Utilization of Bayesian uncertainty quantification will be used to provide metrics for judging the efficacy of how changes in the network structure (e.g., defects structures) give rise to changes in mesoscale constitutive behavior. Atomistic calculations of a Lennard-Jones potential in one dimension will be extended to two and three dimensional molecular dynamic simulations. Network structures will be formulated from these models and then used for mesoscale continuum homogenization of deformation to assess validity of the network-based characterization of material defects.