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A stochastic framework for atomistic fracture

Buze, MacIej, Woolley, Thomas E. and Mihai, L. Angela 2022. A stochastic framework for atomistic fracture. SIAM Journal on Applied Mathematics 82 (2) , pp. 526-548. 10.1137/21M1416436

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Abstract

We present a stochastic modeling framework for atomistic propagation of a Mode I surface crack, with atoms interacting according to the Lennard--Jones interatomic potential at zero temperature. Specifically, we invoke the Cauchy--Born rule and the maximum entropy principle to infer probability distributions for the parameters of the interatomic potential. We then study how uncertainties in the parameters propagate to the quantities of interest relevant to crack propagation, namely, the critical stress intensity factor and the lattice trapping range. For our numerical investigation, we rely on an automated version of the so-called numerical-continuation enhanced flexible boundary NCFlex algorithm.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Mathematics
Publisher: Society for Industrial and Applied Mathematics
ISSN: 0036-1399
Date of First Compliant Deposit: 18 October 2021
Date of Acceptance: 18 October 2021
Last Modified: 11 May 2022 22:25
URI: https://orca.cardiff.ac.uk/id/eprint/144924

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