“Bridging Scale Space-Time Finite Element Method:
A New Paradigm for Concurrently Coupled Atomistic/Continuum Simulation”
Dong Qian, Associate Professor of Mechanical Engineering
School of Dynamic Systems, University of Cincinnati
Many engineering problems are characterized by a multitude of spatial and temporal scale features that span from the atomistic to continuum scales. Developing numerical methods for studying these classes of problems with the aim of linking the atomistic with continuum representations has been a constant interest in the field of computational mechanics. Single scale approach such as the traditional finite element method (FEM) is not well suited for these types of analysis as it lacks the flexibility in establishing multiscale approximations in both the spatial and temporal domains. In addition, use of a specific semi-discrete scheme limits the temporal resolution and may also bring up the issues of stability and convergence. In this talk, I will present a multiscale simulation framework based on a bridging scale approach and the enriched space-time finite element method. Coupled atomistic/continuum representations are introduced with the use of enrichment functions based on the concept of partition of unity. The established space-time framework allows for a flexible choice of the time step sizes in different regions of interest thereby circumventing the limitation associated with the critical time step size in the traditional explicit time integration scheme. Concurrent coupling between the fine and coarse scale simulations is achieved with the introduction of projection operators and bridging scale treatment, which leads to a seamless interface between the continuum and atomistic representations. An important feature of the method is that the time evolution of the fine scale phenomena can be adaptively tracked with the multi-temporal scale characteristic of the approximation. After an outline of the formulation, the robustness of the method will be demonstrated in the cases of simulating lattice dynamics in one spatial dimension and dynamic fracture in two dimensional lattices.
Dr. Dong Qian is an associate professor of mechanical engineering and the director of the graduate studies in the school of dynamic systems at the University of Cincinnati. He received his B.S. degree in Bridge Engineering from Tongji University in China in 1994, his M.S. degree in Civil Engineering from the University of Missouri in 1998 and Ph.D. degree in Mechanical Engineering from Northwestern University in 2002. Shortly after his graduation, He was hired as an assistant professor of mechanical engineering in the University of Cincinnati and promoted to the rank of associate professor with tenure in 2008. Dr. Qian has conducted research in the general areas of computational mechanics of materials and is an author/co-author of over 40 published/accepted journal papers and book chapters with ~1500 citations. His research has been funded by NSF, AFOSR, AFRL, State of Ohio and industries such as P&G and General Electric. He is currently the assistant editor for the Journal of Computational Mechanics. Dr. Qian received a Young Investigator Award at the 3rd International Symposium on Computational Mechanics in 2011, the Distinguished Researcher award in 2010 and the Junior Faculty Research Award in 2008 by the college of Engineering at UC. He is an active member of ASME and USACM.