ERI: Learning the Constitutive Equations of Chemo-Mechanics from Atomistic Simulations

该奖项的全部或部分资金来自《2021年美国救援计划法案》(公法117-2)。在这个工程研究启动(ERI)项目中，研究了描述材料力学响应外力的支配定律。这些力学定律也称为本构关系。传统上，本构关系是通过实验或基于守恒关系来测量的。随着材料科学的发展，实现多功能的新材料层出不穷。因此，本构关系变得更加复杂。例如，材料需要在电场或化学势下工作。我们需要知道材料如何对不同的外部刺激做出反应。建立结构性关系的传统方式将不再奏效。该项目旨在开发一种通过从模拟数据中学习来建立本构关系的新方法。在这里，我们将构建锂离子电池硅阳极的本构关系。这项研究将帮助我们更好地了解电极材料及其失效原因。这种本构模型的新方法可能会发现材料中的新知识。这将是迈向大容量充电电池设计的重要一步。因此，该项目的成果将有助于国民经济的发展和可持续发展。该项目将支持本科生和研究生，特别是鼓励代表不足的学生加入。被资助的学生将获得力学、计算、数据科学和能源方面的研究经验。在这个项目中，将使用稀疏回归方法来学习锂离子电池硅阳极化学力学的控制方程。稀疏回归可以完全基于蒙特卡罗分子动力学模拟获得的时空数据来识别本构方程的函数形式。这项研究包括三项任务：(I)学习整体扩散的化学力学方程，以与现有的实验和模型进行比较，以进行验证；(Ii)学习表面扩散的化学力学方程，以获得对表面扩散和力学的耦合关系的新理解；(Iii)学习概率化学力学方程，以展示数据驱动方法在量化材料行为不确定性方面的能力。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

This award is funded in whole or in part under the American Rescue Plan Act of 2021 (Public Law 117-2).In this Engineering Research Initiation (ERI) project, the governing laws to describe the mechanics of materials in response to applied force is studied. These laws of mechanics are also known as constitutive relations. Traditionally, the constitutive relations are measured from experiments or based on conservation relations. With the development of materials science, new materials are emerging to achieve multiple functionalities. As a result, the constitutive relations are becoming more complicated. For example, materials need to work under electrical fields or chemical potentials. We need to know how materials respond to different external stimuli. The traditional ways of building constitutive relations would no longer work. This project is to develop a new way to build constitutive relations by learning from simulation data. Here, the constitutive relations for silicon anodes in lithium-ion batteries will be constructed. The study will help us better understand electrode materials and how they fail. The new approach for constitutive modeling can potentially uncover new knowledge in materials. It will be an important step towards the design of high-capacity rechargeable batteries. Therefore, results from this project will contribute to the development of the national economy and sustainability. This project will support undergraduate and graduate students, and particularly encourage underrepresented students to join. The supported students will gain research experience across mechanics, computations, data science, and energies. In this project, the sparse regression method will be used to learn the governing differential equations of chemo-mechanics for the silicon anodes in lithium-ion batteries. Sparse regression can identify the functional forms of the constitutive equations entirely based on spatiotemporal data which are obtained from Monte Carlo molecular dynamics simulations. This research includes three tasks: (i) learning the chemo-mechanics equations for bulk diffusion to compare with existing experiments and models for validation purposes; (ii) learning the chemo-mechanics equations for surface diffusion to gain new understandings of the coupling relations of surface diffusion and mechanics; (iii) learning the probabilistic chemo-mechanics equations to demonstrate the capabilities of the data-driven method in quantifying the uncertainties of material behavior.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.