A stochastic framework for atomistic fracture

TL;DR

This paper introduces a stochastic modeling framework for atomistic crack propagation that accounts for uncertainties in interatomic potential parameters, using probabilistic inference and numerical methods to analyze their impact on fracture properties.

Contribution

It develops a novel stochastic framework combining the maximum entropy principle and numerical continuation to quantify uncertainty propagation in atomistic fracture modeling.

Findings

Uncertainty in interatomic potential parameters affects critical stress intensity factors.

The framework quantifies how parameter variability influences lattice trapping range.

Numerical results demonstrate the impact of parameter uncertainties on crack propagation predictions.

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.