A novel multiscale algorithm for concurrent coupling of atomistic and continuum scales with applications to tribological problems - Pandurangan, Venkataraman (2012)
Multiscale modeling approaches have attracted a lot of attention in the past decade due to the computationally efficient solutions offered by multiscale models for problems characterized by multiple length/time scales. Multiscale methods take advantage of the localized nature of physical problems and use more than one computational model for an accurate description of the system across different length/time scales. Typical examples would be nanoindentation and nanoscratching problems, where the region near the point of indentation or scratching is subject to large deformation gradients and therefore require Angstrom scale descriptions, while the region away from these points will experience significantly smaller strains and can be satisfactorily described using suitable continuum models. The logical approach for solving these problems would be to build a multiscale model that advantageously couples different computational models. In these cases, a multiscale model that uses both the molecular dynamics and the finite element/meshless approach could be used, with the molecular dynamics method providing an accurate solution in the region surrounding the crack tip, and the continuum model providing a reasonably accurate solution in the far-field. An atomistic or continuum model cannot in itself be used for these types of problems as it might be computationally prohibitive to simulate the entire problem using an atomistic model, whereas a continuum model may not be able to describe the entire problem accurately. Building a multiscale model thus ensures accurate results by using the most appropriate model to describe the physics at respective scales, and also substantially reduces the computational expense by restricting the method requiring a higher computational overhead to a small region of the problem domain, only where it is essential, thereby making it feasible to study problems over larger length/time scales. The major challenge involved in developing a multiscale model is to ensure a seamless interface between the constituent length/time scales. To address this issue, a novel concurrent multiscale numerical method is proposed in this work to provide a seamless coupling or handshaking between the atomistic and continuum scales. The novelty in this the proposed multiscale model is that it uses a strong-form meshless Hermite-cloud method, which approximates both the field variable and corresponding first-order derivative simultaneously, for continuum domain discretization. Therefore, the coupling between the atomistic and continuum scales is achieved by ensuring the compatibility of both the field variable and the first-order derivative, and also ensuring force equilibrium across the overlapping transition region. The use of a strong-form method further eliminates the need for any mesh generation. The proposed multiscale model is validated numerically by solving static and transient benchmark problems in one and two-dimensional domains, and the results are presented. In addition, nanoindentation and nanoscratching experiments on copper thin films are simulated using the developed multiscale model and compared with corresponding full atomistic simulations. The material properties obtained from the nanoindentation simulation include the load-displacement graph and the force/unit length values, obtained by dividing the maximum load on the indenter by its contact perimeter. The nanoscratching problem is solved using an adaptive node distribution scheme to maintain the size of the atomistic region constant. The normal and tangential forces, and the coefficient of friction obtained from the simulation are analyzed and compared with the values reported in literature.