The variable node multiscale approach: Coupling the atomistic and continuum scales

Abstract Linking atomistic and continuum zones in multiscale methods is a necessity in order to overcome the deficiencies of the conventional molecular and continuum-based methods. In this paper, a novel approach is presented to bind the atomistic and continuum zones together based on the combined concepts of the finite element method and the radial point interpolation meshfree method. This variable node multiscale method (VNMM) introduces a new way to couple the finite element method with the molecular solutions with nodes coinciding with the atoms. In contrast to QC methods, VNMM does not need a mesh refinement in the vicinity of the molecular zone, nor it requires an overlapping zone in the continuum/atomistic interface which is necessary in bridging schemes. In VNMM, the total displacement of each atom is decomposed into coarse and fine displacements, in which the coarse displacement is computed using the finite element solution over the whole domain, while the fine displacement is calculated just in a limited atomistic zone with the use of molecular statics. Integration of the finite element method within the VNMM formulation potentially allows for enrichment of any field over the entire domain. Conventional interatomic potentials could be employed at the atomistic zone. The results are compared with the fully atomistic simulation, conducted with the molecular statics, and the multiscale quasicontinuum method. A good agreement is observed with substantially reduced degrees of freedom and computational costs.