BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Giulio Giusteri DTSTART:20260128T080000Z DTEND:20260128T090000Z DTSTAMP:20260422T121917Z UID:MathMAC/49 DESCRIPTION:Title: Mathematical modeling of viscoelastic fluids\nby Giulio Giusteri as p art of Modelling of materials - theory\, model reduction and efficient num erical methods (UNCE MathMAC)\n\n\nAbstract\nA class of continuum mechanic al models aimed at describing the behaviorof viscoelastic materials will b e presented. These models are obtained by incorporating concepts originate d in the theory of solid plasticity in a fluid mechanics context [1]. With in this class\, even a simple model with constant material parameters is a ble to qualitatively reproduce a number of experimental observations in bo th simple shear and extensional flows\, including linear viscoelastic prop erties\, the rate dependence of steady-state material functions\, the stre ss overshoot in incipient shear flows\, and the difference in shear and ex tensional rheological curves.\n\nThese constitutive models are based on a logarithmic relation between the elastic strain measure and the stress ten sor and on evolution equations for a local representative of the elastical ly-relaxed strain state. Importantly\, it can be shown that classical mode ls are recovered by expanding the evolution equation for the elastic stres s around the null solution. The mathematical analysis of such tensorial tr ansport equations leads to the definition of the notion of charted weak so lutions [2]. These are based on non-standard a priori estimates that invol ve both viscous and plastic energy dissipation. The main aspects and open problems of the theoretical analysis of the evolution equations will be pr esented.\n\n[1] M. A. H Alrashdi\, G. G. Giusteri\, Evolution of local rel axed states and the modeling of viscoelastic fluids\, Phys. Fluids\, 36\, 093129\, 2024.\n[2] G. Ciampa\, G. G. Giusteri\, A. G. Soggiu\, Viscoelast icity\, logarithmic stresses\, and tensorial transport equations\, Math. M eth. Appl. Sci. 48\, 2934--2953\, 2025.\n LOCATION:https://researchseminars.org/talk/MathMAC/49/ END:VEVENT END:VCALENDAR