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

该学院早期发展计划（CAREER）拨款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物体的第一原理原子描述中获得实用的连续模型。在目前的周期性边界条件下，建立这样的模型所需的纳米力学原子计算是禁止的，但可能在建议的螺旋边界条件下。因此，一个灵活的原子建模工具，将通过增加现有的第一性原理密度泛函理论求解器与螺旋边界条件。 结合对称性适应的柯西玻恩规则，该工具将允许将精确的原子级物理导入大尺度连续模型。以纳米管和纳米带为实验平台，建立了各向同性单原子厚碳纳米管和各向异性/压电少原子厚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，以获得石墨烯，SiGe/Si和ZnO超薄层对拉伸，滚动和扭转的响应的前所未有的理解。将进行传统的有限元和离散元建模，以验证和测试所创建的模型的效用。 如果成功，这项研究将导致一个多功能的多尺度方法，可以应用于其他重要的纳米物体以及生物系统。为纳米管和纳米带创建的模型在针对提高性能和产量的正在进行的设计和工艺建模工作的背景下是可行的。拟议的研究促进了将纳米力学纳入工程课程，以及推广和指导活动：对纳米力学日益增长的兴趣和缺乏合适的教科书是计算纳米力学书将受欢迎的强烈迹象。基于技术的教育工具。 参与和沟通，使用广泛可用的技术（PC/Mac和互联网）。这将使学生和教师，包括高中生和各大学代表性不足的群体的成员，更容易参与科学和工程活动。

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.