Nano-Micro Scale Transition via Atomistic-Continuum Coupling by Homogenization

• Applicants: Professor Dr. Karsten Albe; Professor Dr.-Ing. Bernhard Eidel
• Subject Area: Mechanics
• Term: since 2020
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 440847672

Molecular computer simulations based on classical interatomic potentials enable the description of material properties and processes in high temporal and spatial resolution. They are, however, confined to small system sizes (typically < 1 billion atoms). Consequently, macroscopic length scales are out of reach. The goal of this research project is the development of a two-scale atomistic-continuum coupling method which realizes through homogenization a nano-micro transition for nanoheterogeneous solids. Thereby the simulation of material and structural behavior based on interatomic potentials shall be advanced to so far unmatched length scales.The proposed atomistic-continuum coupling method shall be realized by an effective combination of proof and tested, parallelized simulation tools. To reach that target the research project builds on existing theoretical and methodological concepts of the FE$^2$-method and the FE-HMM, which themselves are based on the equivalence of energy densities of both length scales referred to as Hill-Mandel condition. In contrast to micro-macro transitions in the framework of FE$^2$ and FE-HMM, the intended nano-micro scale transition can not rely on a continuum constitutive law on the level of representative volume elements. For that reason the use of analytical interatomic potentials is chosen. A molecular statics solver is used on the nanoscale, which is connected through an interface to the micro-FEM solver. The coupling quantities at the interface are, from micro to macro the microscopic deformation gradient, from nano to micro the first Piola-Kirchhoff stress tensor obtained from averaging over the representative volume element, as well as the effective tangent moduli. Accuracy, stability and convergence properties as well as the performance of this hybrid method shall be assessed for selected materials systems in the broad range of elastic up to large elastic-plastic deformations. Among the materials systems of interest there are in particular nanocrystalline polycrystals, single crystals having spatially distributed dislocations, and nanoporous structures. By means of this two-scale coupling method through homogenization the simulation of material and structural properties based on the accuracy of interatomic potentials is lifted to length scales that were seen as inaccessible till now.

• DFG Programme: Research Grants
• Co-Investigator: Dr. Alexander Stukowski