Coarse–grained modeling with hierarchical deformable and rigid assemblages (HiDRA)

One of the major challenges in computational mechanics of materials remains to bridge the length-scale and time-scale gaps between the computational and experimental methods to study the microstructure of materials. Traditional molecular dynamics is a powerful tool at the nanoscale, but it does not allow to simulate such mechanical experiments as AFM microscopy dealing with sub-micrometric lengths and microsecond times. Coarse-grained (CG) modeling is one of the possible solutions to fill these gaps. CG modeling does not consider all atoms in a system, but the “pseudo-atoms” or “grains”, approximating groups of these atoms. This allows a significant reduction in the number of considered interactions and degrees of freedom and, consequently, saves the computational resources. In this work, the unique method for CG modeling named “Hierarchical Deformable and Rigid Assemblages” (HiDRA) is proposed. The grains are chosen as assemblages of the atoms in the original crystal lattice. The method allows incorporating the grains’ elasticity so that the overall strain uniformly distributes in the lattice to avoid the unexpected stress concentrations in the bonds between the grains. Grains interact via forces acting to the surface atoms. Equations of motion for the grains are derived taking the uniform strain of the grain as an independent variable. In-house code is developed to perform the simulations with elastic grains. As an application, the HiDRA method is used to study the longitudinal vibrations and full 3D dynamics of chains of one-dimensional grains. Phonon spectra show to what extent large grains can correctly describe wave propagation in molecular chains.