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Multiple Scale Methods for the Design and Analysis of Solids

Monday, April 5, 2004
1:15–2:30 PM
216 Randolph
Harold S. Park
Northwestern University

The design process for materials has entered a new phase in which it is desirable to include relevant data from smaller length scales. One common difficulty that arises in the coupling of disparate length scales is that the continuum assumption may lose validity at the micro or nano-scale; conversely, it is currently infeasible to use atomistic methods to study a fully three-dimensional macro-scale structure. Therefore, multiple scale methods have evolved in order to combine the salient features of continuum and atomistic methods. This talk will present and discuss a recently developed multiple scale method, the bridging scale. This talk will also describe the method by which the bridging scale handles one crucial aspect of multiple scale methods: spurious wave reflection at the atomistic/continuum interface. Numerical examples in one and two-dimensions, including dynamic crack propagation, will demonstrate the efficiency and accuracy of the bridging scale when compared to full atomistic simulations. Concluding remarks will address future avenues of research in multiple scale analysis, both in terms of method development, and also in terms of application to concurrent material design.