Existence of quasi-static crack evolution for atomistic systems

TL;DR

This paper proves the existence of quasi-static crack evolution in atomistic systems with time-dependent boundary conditions, modeling atomic bond breaking and providing numerical tests for crack growth prediction.

Contribution

It introduces a mathematical framework for atomistic crack evolution with irreversibility and delay effects, and proves solution existence.

Findings

Existence of solutions for the crack evolution model.

Numerical validation of crack growth predictions.

Model captures delay effects in atomic bond breaking.

Abstract

We consider atomistic systems consisting of interacting particles arranged in atomic lattices whose quasi-static evolution is driven by time-dependent boundary conditions. The interaction of the particles is modeled by classical interaction potentials where we implement a suitable irreversibility condition modeling the breaking of atomic bonding. This leads to a delay differential equation depending on the complete history of the deformation at previous times. We prove existence of solutions and provide numerical tests for the prediction of quasi-static crack growth in particle systems.