Convergence of a Force‐Based Hybrid Method in Three Dimensions. Issue 1 (23rd October 2012)

• Record Type: Journal Article
• Authors: Lu, Jianfeng; Ming, Pingbing
• Is Part Of: Communications on pure and applied mathematics. Volume 66:Issue 1(2013:Jan.)
• Page Start: 83
• Page End: 108
• Publication Date: 2012-10-23
• Subjects: Mathematics -- Periodicals; Mechanics -- Periodicals; Mathématiques -- Périodiques; Mécanique -- Périodiques; 510.5
• DOI: 10.1002/cpa.21429
• Languages: English
• ISSNs: 0010-3640

Abstract

<abstract abstract-type="main" xml:lang="en"> <title>Abstract</title> <p>We study a force‐based hybrid method that couples an atomistic model with the Cauchy‐Born elasticity model. We show that the proposed scheme converges to the solution of the atomistic model with second‐order accuracy, since the ratio between lattice parameter and the characteristic length scale of the deformation tends to 0. Convergence is established for the three‐dimensional system without defects, with general finite‐range atomistic potential and simple lattice structure. The proof is based on consistency and stability analysis. General tools for stability analysis are developed in the framework opseudodifference operators in arbitrary dimensions. © 2012 Wiley Periodicals, Inc.</p> </abstract>