Accurate and Efficient Atomistic-to-Continuum Coupling Methods

Many materials problems require the accuracy of atomistic modeling in small regions, such as the neighborhood of a crack tip. However, these localized defects typically interact with a much larger region through long-ranged elastic fields. These regions are too large to be computed atomistically. Materials scientists have proposed many methods to compute solutions to these multiscale problems by coupling atomistic models near a localized defect with continuum models where the deformation is nearly uniform.

The development of coupling methods for crystalline materials that are reliable and accurate for configurations near the onset of lattice instabilities such as dislocation formation has been particularly challenging. I will present theory developed with Mathew Dobson and Christoph Ortner to assess currently utilized methods and to propose more reliable, accurate, and efficient methods.

Mitchell Luskin, University of Minnesota

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