Analysis of an atomistic model for anti-plane fracture

2018/10/12 by Buze, Maciej, Hudson, Thomas, Ortner, Christoph
#65L20 #70C20 #74A45 #74G20 #74G40 #74G65 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1810.05501

Abstract

We develop a model for an anti-plane crack defect posed on a square lattice under an interatomic pair-potential with nearest-neighbour interactions. In particular, we establish existence, local uniqueness and stability of solutions for small loading parameters and further prove qualitatively sharp far-field decay estimates. The latter requires establishing decay estimates for the corresponding lattice Green's function, which are of independent interest.

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