CAREER: Nanomechanics from First principles: A Symmetry-Adapted Methodology

这项学院早期发展计划(Career)拨款将为开发一种新的多尺度方法提供资金，该方法将直接从纳米对象的第一原理原子描述中推导出实用的连续统模型。在目前的周期性边界条件下，建立这样的模型所需的纳米机械原子计算是不可能的，但在所提出的螺旋边界条件下是可能的。因此，通过用螺旋边界条件扩充现有的第一原理密度泛函理论求解器，将创建一个对称性适应的原子建模工具。与对称性适应的柯西·伯恩规则相结合，该工具将允许将精确的原子级物理引入大规模连续介质模型。以纳米管和纳米带为试验台，建立各向同性单原子厚度碳纳米管、各向异性/压电少原子厚度SiGe/Si和ZnO纳米带的纳米力学模型。在这项研究中，将进行第一性原理计算，以获得对石墨烯、SiGe/Si和ZnO超薄薄膜对拉伸、轧制和扭转的响应的前所未有的了解。将进行传统的有限元和离散元建模，以验证和测试所创建模型的实用性。如果成功，这项研究将带来一种通用的多尺度方法，可以应用于其他重要的纳米对象以及生物系统。为纳米管和纳米带创建的模型可以在旨在提高性能和产量的持续设计和工艺建模工作的背景下立即进行开发。拟议的研究有助于将纳米力学纳入工程课程，以及推广和指导活动：对纳米力学的兴趣日益增长，以及缺乏合适的教科书，这是计算纳米力学书籍将受到欢迎的强烈迹象。基于技术的教育工具。参与和交流，使用广泛可用的技术(PC/Mac和互联网)。这将使学生和教职员工更容易参与科学和工程活动，包括高中生和来自不同大学的代表不足的群体的成员。

This Faculty Early Development Program (CAREER) grant provides funding for developing a novel multiscale methodology that will derive practical continuum models for nano-objects directly from their first-principles atomistic description. The nanomechanical atomistic computations needed for building such models are prohibitive under the current periodic boundary condition but possible under the proposed helical boundary conditions. Thus, a symmetry-adapted atomistic modeling tool will be created by augmenting an existing first-principles density functional theory solver with helical boundary conditions. In conjunction with a symmetry adapted Cauchy Born rule, this tool will allow for importing the accurate atomic-level physics into the large-scale continuum models. Using nanotubes and nanobelts as test beds, nanomechanical models will be established for isotropic one atom thick carbon nanotubes, and anisotropic/piezoelectric few atoms thick SiGe/Si and ZnO nanobelts. During this research, first-principles calculations will be performed in order to obtain an unprecedented understanding of the response of graphene, SiGe/Si, and ZnO ultra thin layers to stretching, rolling, and torsion. Traditional finite and discrete element modeling will be carried out to validate and test the utility of the created models. If successful, this research will lead to a versatile multiscale methodology that can be applied for other important nano-objects as well as for biological systems. The models created for nanotubes and nanobelts are viable for immediate exploitation in the context of the ongoing design and process modeling efforts directed toward increasing performance and yield. The proposed research facilitates the incorporation of nanomechanics into the engineering curriculum, and outreach and mentoring activities: The growing interest in nanomechanics and the lack of a suitable textbook are strong indications that the Computational Nanomechanics book will be popular. The technology-based educational tool. Engage and Communicate, uses widely available technology (PC/Mac and Internet). This will make it easier to engage students and faculty, including high school students and members of underrepresented groups from various universities, in science and engineering activities.