POSITIVE DEFINITENESS OF THE BLENDED FORCE-BASED QUASICONTINUUM METHOD

被引：16

作者：

Li, Xingjie Helen ^{[1
]}

Luskin, Mitchell ^{[1
]}

Ortner, Christoph ^{[2
]}

机构：

[1] Univ Minnesota, Sch Math, Minneapolis, MN 55455 USA

[2] Univ Warwick, Math Inst, Coventry CV4 7AL, W Midlands, England

来源：

MULTISCALE MODELING & SIMULATION | 2012年 / 10卷 / 03期

基金：

英国工程与自然科学研究理事会;

关键词：

quasicontinuum; atomistic-to-continuum; blending; stability; APPROXIMATION; MODEL; MECHANICS; PARTICLE; ERROR;

D O I：

10.1137/110859270

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：1023 / 1045

页数：23

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