Periodic Reporting for period 4 - COGRA (Decoding the Mechanics of Metals by Coarse-Grained Atomistics)
Reporting period: 2022-09-01 to 2024-08-31
Understanding why materials behave the way they do as well as creating novel materials with as-designed properties requires a careful investigation and a thorough understanding of the structure of materials. This challenge extends from understanding the strength and failure of metals to the diffusion and heat transport in ceramics (and beyond). Limited by computational resources, there is a significant gap between the length and time scales of typical engineering applications and those of predictive simulations at the atomic level and below. Bridging across scales, i.e. exporting atomic-scale accuracy to macroscopic simulations, has remained a holy grail of multiscale modeling. This project aimed for the seemingly impossible: the application of atomistic techniques to problems occurring over significantly larger time and length scales than what is commonly accessible by molecular dynamics. Instead of relying on computational power, the objective was to combine new scale-bridging methodology and computational science strategies to result in both new theory and an open-source computational toolset for long-term, large-scale simulations relying solely on atomic-scale input. Such simulation capabilities are of importance across science and technology, essentially everywhere where atomic-scale accuracy is needed but molecular dynamics simulations are too time-consuming or too expensive due to the sheer number of atoms and/or the time scales involved. Aside from developing the new simulation framework, this project also aimed to leverage the new modeling opportunities to study defects in metals and their impact on macroscopic material behavior. The project has been completed successfully, resulting in a new simulation framework for upscaled atomistics in 3D and at finite temperature, a new open-source code for such simulations, and new insight into the mechanics and physics of defects in crystalline solids at finite temperature.
A new and powerful numerical codebase has been generated, which serves as the basis for coarse-grained atomistic simulations in 3D (and which has been released publicly). Temporal upscaling has been achieved by separating the atomic mean motion (and their mean composition) from statistical variations, and to track those over time. Spatial upscaling has been achieved by coarse-graining, i.e. by simulating the physics of large assemblies of grains by tracking only a few representative atoms and using smart interpolation techniques for the remaining ones. Rather than relying on a static finite-element mesh, the new formulation operates in the current, deformed configuration (using a so-called updated-Lagrangian description). This allows us to more accurately refine the model where higher accuracy and resolution is needed, and it also lays the foundation for fully automatic adaptivity – allowing the code to autonomously maintain a high level of accuracy by introducing higher resolution where it is required within the simulation domain, while modeling other regions at low resolution to gain efficiency. In addition, the new simulation tool has been equipped with finite temperature and thermal effects, following the so-called hotQC approach of “thermalizing” atoms in a statistical-mechanics fashion. Rather than modeling temperature as lattice vibrations of high frequency (which usually dictate the small time steps of atomistic simulations), we separate their slow mean motion (which is of interest for the mechanical behavior of the material) from their statistical fluctuations (now represented by statistical measures rather than being fully resolved). The consequence is an efficient simulation technique, which enables us to simulate atomic ensembles at finite temperature at, in principle, arbitrary time scales. This new methodology has been applied to study the mechanics of crystalline solids with a focus on defects, providing new, accurate, and efficient avenues for determining, e.g. finite-temperature surface or grain boundary properties or defect interactions, which are essential for understanding and improving the mechanical performance of metals. Our simulations also revealed new data on the energetics of defects in metals over a range of temperatures. The new theory and code for mass transport further admit simulating atomic-level diffusion at previously inaccessible time scales, resulting in new insight into mechanisms such as the segregation of solute atoms to defects and interfaces across a wide range of temperature. Results have been widely disseminated through scientific publications in peer-reviewed journals, the public release of the codebase for its usage by the interested community, numerous conference presentations and invited seminars. The project further enabled the training of three talented doctoral students and two outstanding postdoctoral scholars.
Our simulation framework goes beyond existing techniques in various ways. It is the first coarse-grained-atomistics environment that allows for fully-nonlocal automatic adaptivity in 3D simulations. Without requiring any a-priori knowledge about where atomistic accuracy is required within a simulation domain, our method increases and/or decreases resolution adaptively throughout a simulation, thus aiming for an optimal balance between efficiency and accuracy. Providing this capability in 3D without the need for a Lagrangian background mesh is a further novelty, paired with a computational implementation that is massively parallel to exploit the use of high-performance computing infrastructure. Further, combining the aforementioned spatial coarsening with the implementation of finite temperature without having to resolve thermal fluctuations of individual atoms is a powerful new element. Finally, the extension to heat and mass transport has paved the road for unprecedented long-term simulations of thermal and diffusive effects and their impact on the mechanical behavior of materials. The new code has been released publicly and is at present the most powerful openly available 3D coarse-grained atomistics code, which is of tremendous value for both our own simulations (which have provided new understanding of defect and interface physics in metals) and for the scientific community at large (where it may be used for other applications as well).