Journal of Computational Physics 253 (2013) 64–85 Contents lists available at SciVerse ScienceDirect Journal of Computational Physics www.elsevier.com/locate/jcp A multiscale modeling technique for bridging molecular dynamics with finite element method Yongchang Lee ∗ , Cemal Basaran Electronic Packaging Laboratory, Department of Civil, Structural, and Environmental Engineering, State University of New York at Buffalo, United States article info abstract Article history: Received 1 March 2013 Accepted 30 June 2013 Available online 12 July 2013 Keywords: Multiscale modeling Weighted averaging momentum method Molecular dynamics Wave reflection In computational mechanics, molecular dynamics (MD) and finite element (FE) analysis are well developed and most popular on nanoscale and macroscale analysis, respectively. MD can very well simulate the atomistic behavior, but cannot simulate macroscale length and time due to computational limits. FE can very well simulate continuum mechanics (CM) problems, but has the limitation of the lack of atomistic level degrees of freedom. Multiscale modeling is an expedient methodology with a potential to connect different levels of modeling such as quantum mechanics, molecular dynamics, and continuum mechanics. This study proposes a new multiscale modeling technique to couple MD with FE. The proposed method relies on weighted average momentum principle. A wave propagation example has been used to illustrate the challenges in coupling MD with FE and to verify the proposed technique. Furthermore, 2-Dimensional problem has also been used to demonstrate how this method would translate into real world applications.  2013 Elsevier Inc. All rights reserved. 1. Introduction The insatiate demand for multiscale analysis is not only due to advances in nanotechnology, but also due to experimen- tal results proving that there is a need for connecting nanoscale physics and macroscale continuum analysis. Significant advancements in computational power make it feasible to link both powerful methods: molecular dynamics (MD) and finite element (FE) methods. MD and FE methods are well suited to a particular level of accuracy on atomistic and continuum simulations, respec- tively. In general, MD cannot be used for macroscale problems due to the restrictions on the number of atoms that can be simulated simultaneously, along with the time scale limit. On the other hand, usage of FE method for atomic scale problems is not accurate for many reasons mainly because continuum mechanics assumes that the substance of body is distributed continuously throughout the space of body and lacks atomic degrees of freedom. These inherent limitations make connect- ing these two methods essential but also challenging. Nevertheless, multiscale modeling will allow us to solve complicated problems with a greater accuracy than ever before. It should be pointed out that MD does not have electronic degrees of freedom. However, it is expected that methods like the one proposed here will allow us to connect FE, MD, and quantum mechanics, which has electronic degrees of freedom. * Corresponding author. E-mail address: yl83@buffalo.edu (Y. Lee). 0021-9991/$ – see front matter  2013 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.jcp.2013.06.039