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).

ABSTRACT
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.