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Theory-Based Development and Benchmarking of Atomistic-to-Continuum Coupling Methods

Banff International Research Station for Mathematical Innovation and Discovery

The building blocks of micromechanics are the nucleation and movement of point, line, and surface defects and their long-range elastic interactions. Computational micromechanics has begun to extend the predictive scope of theoretical micromechanics, but mathematical theory able to assess the accuracy and efficiency of multiscale methods is needed for computational micromechanics to reach its full potential.\\r\\nMany 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 through long range elastic fields with a much larger region that cannot 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 on the atomistic scale.\\r\\nDuring the past several years, a theoretical structure has been given to the description and formulation of atomistic-to-continuum coupling methods, and corresponding numerical analysis and benchmark computational experiments have clarified the relation between the various methods and their sources of error. Our theoretical foundation has enabled the development of more accurate and efficient coupling methods.

Mathematics; Mechanics of deformable solids; Calculus of variations and optimal control; optimization; Applied analysis / inverse problems

video/mp4

Author affiliation: University of Minnesota

2014-08-06

Attribution-NonCommercial-NoDerivs 2.5 Canada

http://hdl.handle.net/2429/49255

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/2.5/ca/