BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Miroslav Kolář (Faculty of Nuclear Sciences and Physical Enginee ring Czech Technical University in Prague) DTSTART:20250929T134000Z DTEND:20250929T151000Z DTSTAMP:20260405T175311Z UID:NSCM/189 DESCRIPTION:Title: M odeling of discrete dislocation dynamics by means of the mathematical theo ry of evolving curves\nby Miroslav Kolář (Faculty of Nuclear Science s and Physical Engineering Czech Technical University in Prague) as part o f Nečas Seminar on Continuum Mechanics\n\nLecture held in Room K3\, Facu lty of Mathematics and Physics\, Charles University\, Sokolovská 83 Prag ue 8..\n\nAbstract\nDislocation dynamics (DD) has become a standard tool f or analyzing\ndeformation microstructures. Fundamentals of dislocation the ory have been\nestablished in 1930s and later verified by first TEM experi ments in 1950s.\nThe ultimate objective of DD is to fill the gap between f ully continuous\nmodels in the macroscopic scale based on crystal plastici ty\, and atomistic\nmodels in nanoscale usually treated by the molecular d ynamics methods. \n\nIn crystalline solids\, dislocations represent irreg ularities or defects in\nthe crystal structure. Such defects are usually o f the line character and\nthe characteristic unit of length of such defect s is microns. These line\ndefects are the subject of both external forces applied on the crystal as\nwell as various internal mechanisms\, and they evolve in the so-called slip\nplanes given by particular crystallographic orientation. \n\nOur research interest is in the detailed and precise mode ling of fundamental\nmechanisms involving single or very few dislocations. Such a topic is\ntypically referred to as a discrete dislocation dynamics (DDD). \n\nIn our approach to DDD\, a single dislocation carrying the pla stic flow in\nits respective slip plane is represented as an evolving plan ar curve. The\nexperimentally observed mechanism how dislocations evolve i s of a\nnon-Newtonian type and can be schematically described as\n\nnormal velocity = curvature + external force\, \n\nwhere the curvature term appr oximates the self-stress of the dislocation\ngenerated by a line tension. We treat this kind of evolution equation by the\ndirect (Lagrangian) appro ach resulting in the system of two degenerate\nparabolic equations for par ametrization of the single dislocation curve. We\nsolve this problem numer ically by means of the flowing finite-volume method\,\nand we improve the stability of the numerical scheme by the suitable choice\nof the external tangential velocity which helps to redistribute the\ndiscretization points along the dislocation in an appropriate way.\n\nWe demonstrate our approa ch in several computational examples covering the\nfundamental dislocation mechanisms and then we focus on the dislocation\ncross-slip\, which is co nsidered as one of the key mechanisms of\nmicroplasticity and still an ope n problem in general. We show how we modify\nour method by the geodesic de scription of curves to treat the cross-slip\nwithin our framework.\n LOCATION:https://researchseminars.org/talk/NSCM/189/ END:VEVENT END:VCALENDAR