Events Calendar

Physics Colloquium, "A Comparative Study of General Finite Element Techniques in Atomistic-to-Continuum Coupling" by Dr. Peter W. Chung, U.S. Army Research Laboratory Monday, 9/15/2008, 4:00 AM-5:00 AM
It is well known that continuum based techniques such as Lagrangian or Eulerian numerical methods, which use constitutive relations that do not account for the atomistic structure, are invalid beyond the scope of their calibration. In regions containing dislocations, mobile defects, or nonlinear material, these numerical methods have to be modified to capture important phenomena. Yet they remain useful for dealing with field variations that occur slowly relative to atomic spacings. Molecular dynamics (MD), on the other hand, is an excellent means for modeling interactions on an atomic scale as well as predicting the response when sub-micron scale phenomena occur. However, MD can be computationally expensive beyond relatively small sample sizes. Therefore, to alleviate these problems multiscale methods have been developed in recent years to couple the continuum and atomistic scales together. After a brief introduction of motivational problems currently being considered at the U. S. Army Research Laboratory, we show a comparative study of the quality of interpolation that best suits continuum methods in regions at and near the interface with a molecular dynamics region. We specifically examine interpolation functions prominent in general finite element methods and meshless methods - Bubnov-Galerkin, partition of unity, and moving least squares - and assess their ability to capture a travelling wave through a discrete/continuum interface and a graded finite element mesh (increasing element size away from the MD region). Within the interface region, where the continuum and atomistic scales overlap, the displacements on the continuum are dictated by the atomistic results generated from MD. The results of our study show that using simple changes to the interpolation quality of fields in the continuum, namely using partition of unity interpolation functions, produces accurate results compared to finite elements and moving least squares interpolation functions. For example, we demonstrate the effectiveness of partition of unity shape functions by simulating a Gaussian wave propagating throughout a 1D domain with a harmonic potential between neighbouring atoms. As the wave moves through the atomistic-continuum interface and through the graded mesh, the effectiveness of the partition of unity shape functions are clearly seen. In spite of the higher computational costs, the improvement in accuracy appears beneficial in practice. The presentation will conclude with a discussion of open issues related to the problem from the point of view of phonon transport and the on-going development of numerical methods that can adequately represent the physics through modeling methods representing multiple scales. Sponsored by: WPI Physics Department, Izabela Stroe

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