A continuum model for brittle nanowires derived from an atomistic description by Γ-convergence

2022/08/08 by Bernd Schmidt, Schmidt, Bernd, Jiří Zeman +1
Computer Science · Engineering · Materials Science · #49J45 #70G75 #74K10 #74R10 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Composite Material Mechanics #FOS: Mathematics #FOS: Physical sciences #Materials Science (cond-mat.mtrl-sci) #Mathematical Physics (math-ph) #Mesoscale and Nanoscale Physics (cond-mat.mes-hall) #Microstructure and mechanical properties

paper · pdf · doi:10.48550/arxiv.2208.04195

openalex publication_date 2022/08/08 · openalex created_date 2022/10/05 · openalex updated_date 2026/08/01

Abstract

Starting from a particle system with short-range interactions, we derive a continuum model for the bending, torsion, and brittle fracture of inextensible rods moving in three-dimensional space. As the number of particles tends to infinity, it is assumed that the rod's thickness is of the same order as the interatomic distance. Fracture energy in the Γ-limit is expressed by an implicit cell formula, which covers different modes of fracture, including (complete) cracks, folds and torsional cracks. In special cases, the cell formula can be significantly simplified. Our approach applies e.g. to atomistic systems with Lennard-Jones-type potentials and is motivated by the research of ceramic nanowires.

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