BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Ivan Gudoshnikov (Institute of Mathematics\, Czech Academy of Scie nces) DTSTART:20230220T144000Z DTEND:20230220T161000Z DTSTAMP:20260405T175114Z UID:NSCM/99 DESCRIPTION:Title: El astoplasticity with softening in spring network models: a state-dependent sweeping process approach\nby Ivan Gudoshnikov (Institute of Mathemat ics\, Czech Academy of Sciences) as part of Nečas Seminar on Continuum Me chanics\n\nLecture held in Room K3\, Faculty of Mathematics and Physics\, Charles University\, Sokolovská 83 Prague 8..\n\nAbstract\nSoftening pl asticity and Gurson model of damage in particular lead to ill-posed mathem atical\nproblems due to the loss of monotonicity. Multiple co-existing sol utions are possible when softening\nelements are coupled together\, and so lutions cannot be continued beyond the point of complete\nfailure of a mat erial. Moreover\, spatially continuous models with softening suffer from l ocalization\nof strains and stresses to measure-zero submanifolds.\nWe for mulate a problem of quasistatic evolution of elasto-plastic spring network s (Lattice Spring\nModels) with a plastic flow rule which describes linear hardening\, linear softening and perfectly\nplastic springs in a uniform manner. The fundamental kinematic and static characteristics of the\nnetwo rk are described by the rigidity theory and structural mechanics.\nTo solv e the evolution problem we convert it to a type of a differential quasi-va riational inequality known as the state-dependent sweeping process. We pro ve the existence of solution to the\nassociated time-stepping problem (imp licit catch-up algorithm)\, and the estimates we obtain imply\nthe existen ce of a solution to the (time-continuous) sweeping process.\nUsing numeric al simulations of regular grid-shaped networks with softening we demonstra te\nthe development of non-symmetric shear bands. At the same time\, in to y examples it is easy to\nanalytically derive multiple co-existing solutio ns\, appearing in a bifurcation which happens when\nthe parameters of the networks continuously change from hardening through perfect plasticity to\ nsoftening.\n LOCATION:https://researchseminars.org/talk/NSCM/99/ END:VEVENT END:VCALENDAR