Existence of quasi-static crack evolution for atomistic systems
Analysis of PDEs
2022-11-01 v2 Classical Analysis and ODEs
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.
Cite
@article{arxiv.2207.14505,
title = {Existence of quasi-static crack evolution for atomistic systems},
author = {Rufat Badal and Manuel Friedrich and Joscha Seutter},
journal= {arXiv preprint arXiv:2207.14505},
year = {2022}
}