Name
Abstract | ||
|---|---|---|
The development of consistent and stable quasicontinuum models for multidimensional crystalline solids remains a challenge. For example, proving the stability of the force-based quasicontinuum (QCF) model [M. Dobson and M. Luskin, M2AN Math. Model. Numer. Anal., 42 (2008), pp. 113-139] remains an open problem. In one and two dimensions, 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. |
Year | DOI | Venue |
|---|---|---|
2012 | 10.1137/110859270 | MULTISCALE MODELING & SIMULATION |
Keywords | Field | DocType |
quasicontinuum,atomistic-to-continuum,blending,stability | Open problem,Mathematical analysis,Continuum (design consultancy),Positive definiteness,Mathematics | Journal |
Volume | Issue | ISSN |
10 | 3 | 1540-3459 |
Citations | PageRank | References |
7 | 0.81 | 7 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Xingjie Helen Li | 1 | 8 | 1.17 |
| Mitchell Luskin | 2 | 124 | 23.89 |
| Christoph Ortner | 3 | 74 | 16.77 |