A Concurrent Multiscale Method Based on the Meshfree Method and Molecular Dynamics Analysis

This paper presents a concurrent simulation technique for analysing the deformation of systems that need the integration of material properties from nanoscopic to macroscopic dimensional scales. In the continuum sub-domain, a weak-form meshfree based method using the radial basis function interpolation was employed, but in the atomic sub-domain, 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 sub-domain or the atoms in the atomic sub-domain. 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