A concurrent multiscale method based on the meshfree method and molecular dynamics analysis
Y. T. Gu and L. C. Zhang
Multiscale Modeling & Simulation, 5, 1128–1155 (2006).


This paper presents a concurrent simulation technique for analyzing the deformation of systems that need the integration of material properties from nanoscopic to macroscopic dimensional scales. In the continuum subdomain, a weak-form based meshfree method using the radial basis function interpolation was employed, but in the atomic subdomain, molecular dynamics analysis was used. The transition from the atomic to continuum domains was realized by transition particles which are independent of either the nodes in the continuum subdomain or the atoms in the atomic subdomain. A simple penalty method was used to ensure the compatibility of displacements and their gradients in the transition. A virtual cell algorithm was developed using a local quasi-continuum approach to obtain the equivalent continuum strain energy density based on the atomic potentials and Cauchy-Born rule. Numerical examples showed that the present method is very accurate and stable, and has a promising potential to a wide class of multiscale systems.