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. For this reason, discrete terms and energy contributions from the ultrathin rod’s lateral surface appear in the limiting functional. Fracture energy in the Gamma -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—we illustrate this by the example of a full crack and also show that the energy of a mere fold is strictly lower for a class of models. Our approach applies e.g. to atomistic systems with Lennard–Jones-type potentials and is motivated by the research of ceramic nanowires.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Calculus of Variations and Partial Differential Equations
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
