We give computational results to study the accuracy of several quasicontinuum methods for two benchmark problems – the stability of a Lomer dislocation pair under shear and the stability of a lattice to plastic slip under tensile loading. We find that our theoretical analysis of the accuracy near instabilities for onedimensional model problems can successfully explain most of the computational results for these multi-dimensional benchmark problems. However, we also observe some clear discrepancies, which suggest the need for additional theoretical analysis and benchmark problems to more thoroughly understand the accuracy of quasicontinuum methods.
|Original language||English (US)|
|Title of host publication||Numerical Analysis of Multiscale Problems|
|Editors||Thomas Y. Hou, Omar Lakkis, Ivan G. Graham, Robert Scheichl|
|Number of pages||30|
|State||Published - 2012|
|Event||91st LMS Durham Symposium on Numerical Analysis of Multiscale Problems, 2010 - Durham, United Kingdom|
Duration: Jul 5 2010 → Jul 15 2010
|Name||Lecture Notes in Computational Science and Engineering|
|Other||91st LMS Durham Symposium on Numerical Analysis of Multiscale Problems, 2010|
|Period||7/5/10 → 7/15/10|
Bibliographical noteFunding Information:
Acknowledgements This work was supported in part by the National Science Foundation under DMS-0757355, DMS-0811039, the PIRE Grant OISE-0967140, the Institute for Mathematics and Its Applications, and the University of Minnesota Supercomputing Institute. This work was also supported by the Department of Energy under Award Number DE-SC0002085. CO was supported by the EPSRC grant EP/H003096/1 “Analysis of Atomistic-to-Continuum Coupling Methods.” We wish to thank Ellad Tadmor for helpful discussions.
© Springer-Verlag Berlin Heidelberg 2012.