2011/12/03 by Kavinda Jayawardana, Christelle Mordacq, Jayawardana, K. +5
Computer Science · Materials Science · Physics and Astronomy · #65N12 #65N30 #70-08 #70C20 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Microstructure and mechanical properties #Numerical Analysis (math.NA) #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.1112.0683
openalex publication_date 2011/12/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Surface Cauchy-Born (SCB) method is a computational multi-scale method for the simulation of surface-dominated crystalline materials. We present an error analysis of the SCB method, focused on the role of surface relaxation. In a linearized 1D model we show that the error committed by the SCB method is O(1) in the mesh size; however, we are able to identify an alternative "approximation parameter" - the stiffness of the interaction potential - with respect to which the error in the mean strain is exponentially small. Our analysis naturally suggests an improvement of the SCB model by enforcing atomistic mesh spacing in the normal direction at the free boundary.