BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Jiří Zeman (Faculty of Mathematics and Physics\, Charles Univers ity) DTSTART:20231106T144000Z DTEND:20231106T161000Z DTSTAMP:20260405T175313Z UID:NSCM/119 DESCRIPTION:Title: B ending-torsion theories for elastic and brittle nanowires as Gamma-limits of atomistic models\nby Jiří Zeman (Faculty of Mathematics and Physi cs\, Charles University) as part of Nečas Seminar on Continuum Mechanics\ n\nLecture held in Room K3\, Faculty of Mathematics and Physics\, Charles University\, Sokolovská 83 Prague 8..\n\nAbstract\nNanotechnology has r anked among paradigm-shifting and the fastest growing research areas over the last 30 years. To benefit from the wide application prospects of engin eered nanoworld objects\, it is important to study their mechanical respon se\, which often differs from that of macroscopic bodies\, though (because of size or structure effects for example). In particular\, there exist ro d-like structures in nanoengineering which are long enough in one directio n for continuum theories to be applicable\, but in the perpendicular direc tion\, they have a diameter on the scale of tens to hundreds of atoms. In this talk\, derivation of nonlinear continuum models for thin and ultrathi n rods will be presented. We start from a 3D crystalline lattice with shor t-range interactions and study simultaneous limits of vanishing rod thickn ess 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 fun ctional\, whose fracture part is expressed by an implicit cell formula tha t covers different modes of fracture\, including (complete) cracks\, folds and torsional cracks. Joint work with Bernd Schmidt (Augsburg).\n LOCATION:https://researchseminars.org/talk/NSCM/119/ END:VEVENT END:VCALENDAR