BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Franco Tomarelli (Politecnico di Milano) DTSTART:20230424T134000Z DTEND:20230424T151000Z DTSTAMP:20260405T175326Z UID:NSCM/105 DESCRIPTION:Title: P ure traction and Signorini problem between linear and finite elasticity\nby Franco Tomarelli (Politecnico di Milano) as part of Nečas Seminar o n Continuum Mechanics\n\nLecture held in Room K3\, Faculty of Mathematics and Physics\, Charles University\, Sokolovská 83 Prague 8..\n\nAbstract \nA limit elastic energy for pure traction problem is derived from re-scal ed nonlinear energies of a\nhyper-elastic material body subject to an equi librated force field.\nWe show that the strains of minimizing sequences as sociated to re-scaled nonlinear energies weakly\nconverge\, up to subseque nces\, to the strains of minimizers of a limit energy.\nThe limit energy f unctional exhibits a gap that makes it different from the classical linear elasticity\nfunctional. Nevertheless a suitable compatibility condition e ntails the coincidence of related minima\nand minimizers\, hence the rigor ous validation of linear elasticity. Strong violation of this condition\np rovides a limit energy which is unbounded from below\, while a mild violat ion may produce\nunboundedness of strains and a limit energy which has inf initely many extra minimizers which are\nnot minimizers of standard linear elastic energy. As a consequence\, a rigorous validation of linear\nelast icity fails for compressive force fields that infringe such a compatibilit y condition.\nThis phenomenon has relevant consequences also on the valida tion of the Signorini problem in\nlinear elasticity: there are loads pushi ng the body against the obstacle\, but unfit for the geometry of\nthe whol e system body-obstacle\, so that the corresponding variational limit turns out to be different\nfrom the classical Signorini problem. However\, if t he force field acting on the body fulfils an\nappropriate geometric admiss ibility condition\, we can show coincidence of related solutions.\nThe asy mptotic analysis provides a sharp and rigorous variational justification o f the unilateral\nproblem in linear elasticity\, together with an accurate analysis of the unilateral constraint.\nThese results were obtained in a joint research with Francesco Maddalena (Politecnico di Bari) and\nDanilo Percivale (Università di Genova).\n LOCATION:https://researchseminars.org/talk/NSCM/105/ END:VEVENT END:VCALENDAR