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.
Existing atomistic modeling tools can be used to simplify simulation of structures that have translational periodicity, such as a bulk crystal or a pristine NW. However, many nano- and bio-structures have rotational and/or helical symmetries instead – either inherent in their structure or imposed by a deformation such as torsion. The PI pioneered a symmetry-adapted MD technique termed objective molecular dynamics (OMD), which replaces the standard translational symmetry with the objective helical and/or rotational symmetries. This method gives significant reduction in the number of atoms that need to be simulated. The small number of atoms replicated with an arbitrary combination of rotation and translation operations, are representing an infinite helical structure that may not possess any pure translational periodicity. Moreover, the dynamics carried out on these domains under the objective boundary conditions represents a new dynamics, the OMD, which is distinct from the periodic MD. The computational savings created by reducing the number of atoms are used to apply accurate quantum treatments, which would otherwise be prohibitive. In the first stage, we have performed the coupling of OMD with the non-orthogonal tight-binding treatment of bonding. This advance opened up the possibility to simulate, based on density-functional based tight-binding, an important class of helical nanostructures. Examples include chiral carbon and MoS2 NTs, helical Si NWs containing an axial screw dislocation, and bent and twisted graphene structures. In the second stage, we have coupled OMD to the more complex self-consistent charge density functional theory-based tight binding. With the improved description of bonding, we can tackle a wide variety of helical nano- and bio-structures, some containing many chemical elements, like DNA. The objective MD method has the potential to transform the state-of-the-art in atomistic simulations. It enables the simulation studies described in this proposal. Twenty-three articles have been published, and one book, on multiscale modeling has been edited. Results that substantially advanced the field of nanomechanics were reported in five Physical Review Letters and one Nature Physics letter. Dumitrica has also developed lectures and homework modules based on this research for a graduate class titled Computational Nanomechanics. Three students (one female) received Ph.D. degrees based on this grant. This project also enabled five undergraduate students to work on atomistic and distinct element method simulations. Dumitric? also participated in the outreach activities of the UMN MRSEC center and interacted with local schools.
