The 48th SNP Meeting

Invited Lecture

Numerical Analysis of Quasicontinuum Methods

MITCHELL LUSKIN
School of Mathematics
University of Minnesota,
Minneapolis, Minnesota 55424, USA

Abstract. 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 through long ranged 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.

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.

Acknowledgement. This lecture was made possible through financial support from Ministry of Science and Technology (MCT), Coordination for the Improvement of Higher Education Personnel (CAPES), and National Council for Scientific and Technological Development (CNPq).