Theory-Based Benchmarking OF The Blended Force-based Quasicontinuum Method
Xingjie Li (Brown University), Mitchell Luskin (University of Minnesota), Christoph Ortner (University of Warwick), Alexander Shapeev (University of Minnesota)
From Atomistics to Reality: Spanning Scales in Simulations and Experiments Symposium B
Wed 3:10 - 4:30
CIT 165
The development of consistent and stable atomistic-to-continuum coupling models for multi-dimensional crystalline solids remains a challenge. For example, proving stability of the force-based quasicontinuum (QCF) model remains an open problem. In 1D and 2D, we show that by blending atomistic and Cauchy-- Born continuum forces (instead of a sharp transition as in the QCF method), one obtains positive-definite blended force-based quasicontinuum (B-QCF) models. We establish sharp conditions on the required blending width and also conduct numerical experiments to verify our theoretical conclusions.