Bending-torsion theories for elastic and brittle nanowires as Gamma-limits of atomistic models

Abstract: Nanotechnology has ranked among paradigm-shifting and the fastest growing research areas over the last 30 years. To benefit from the wide application prospects of engineered nanoworld objects, it is important to study their mechanical response, which often differs from that of macroscopic bodies, though (because of size or structure effects for example). In particular, there exist rod-like structures in nanoengineering which are long enough in one direction for continuum theories to be applicable, but in the perpendicular direction, they have a diameter on the scale of tens to hundreds of atoms. In this talk, derivation of nonlinear continuum models for thin and ultrathin rods will be presented. We start from a 3D crystalline lattice with short-range interactions and study simultaneous limits of vanishing rod thickness and interatomic distance. Gamma-convergence especially yields a novel theory for inextensible rods that undergo bending, torsion, and brittle fracture. New discrete and surface terms appear in the limiting energy functional, whose fracture part is expressed by an implicit cell formula that covers different modes of fracture, including (complete) cracks, folds and torsional cracks. Joint work with Bernd Schmidt (Augsburg).

MathematicsPhysics

Audience: researchers in the topic

Nečas Seminar on Continuum Mechanics

Series comments: This seminar was founded on December 14, 1966.

Faculty of Mathematics and Physics, Charles University, Sokolovská 83, Prague 8. If not written otherwise, we will meet on Mondays at 15:40 in lecture hall K3 (2nd floor)