Calculus of Variations and Geometric Measure Theory

R. Badal - M. Friedrich - J. Seutter

Existence of quasi-static crack evolution for atomistic systems

created by seutter on 06 Feb 2024


Published Paper

Inserted: 6 feb 2024
Last Updated: 6 feb 2024

Journal: Forces in Mechanics
Volume: 9
Number: 100138
Year: 2022

ArXiv: 2207.14505 PDF


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.