The bridging scale for two-dimensional atomistic/continuum coupling

Abstract

In this paper, we present all necessary generalisations to extend the bridging scale, a finite-temperature multiple scale method which couples molecular dynamics (MD) and finite element (FE) simulations, to two dimensions. The crucial development is a numerical treatment of the boundary condition acting upon the reduced atomistic system, as such boundary conditions are analytically intractable beyond simple one-dimension systems. The approach presented in this paper offers distinct advantages compared to previous works, specifically the compact size of the resulting time history kernel, and the fact that the time history kernel can be calculated using an automated numerical procedure for arbitrary multi-dimensional lattice structures and interatomic potentials. We demonstrate the truly two-way nature of the coupled FE and reduced MD equations of motion via two example problems, wave propagation and dynamic crack propagation. Finally, we compare both problems to benchmark full MD simulations to validate the accuracy and efficiency of the proposed method.

Acknowledgements

We would like to thank the National Science Foundation (NSF) and the NSF-IGERT program for their support. We would also like to thank the NSF Summer Institute on Nano Mechanics and Materials and the Army Research Office (ARO) for supporting this work. HSP expresses his grateful thanks to the Engineering Sciences Summer Institute (ESSI) at Sandia National Laboratories. Sandia National Laboratories is supported by the U.S. Department of Energy under contract DE-AC04-94AL85000. The authors would like to acknowledge Dr. Gregory Wagner, Dr. Hiroshi Kadowaki and Professor Ted Belytschko for their kind assistance and helpful discussions on the bridging scale, and also Dr. Jonathan Zimmerman for his guidance and discussion on the dynamic fracture problem. Finally, we would like to thank Dr. Thao D. Nguyen for sharing her insights into dynamic fracture analysis.