BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Petr Pelech (WIAS Berlin) DTSTART:20220307T144000Z DTEND:20220307T161000Z DTSTAMP:20260405T174811Z UID:NSCM/56 DESCRIPTION:Title: Pe nrose-Fife model with activated phase transformation - Existence and effec tive model for slow-loading regimes.\nby Petr Pelech (WIAS Berlin) as part of Nečas Seminar on Continuum Mechanics\n\n\nAbstract\nWe study a no n-autonomous system of two evolutionary PDEs\, an enhanced version of the Penrose-Fife model introduced in 1990\, which first in history coupled the Allen-Cahn phase-field equation with thermal effects in a thermodynamical ly consistent way. In our work we consider an activated phase transformati on which makes the phase-field equation non-linear in time derivative\; it contains an additional term that describes also the Coulomb dry friction and whose analogues appear in rate-independent models of plasticity or dam age. Apart from proving the existence of solutions of the system\, we inve stigate its effective behavior for the so-called slow-loading regimes. The re the internal time-scale introduced by phase-field viscosity and thermal conductivity is much smaller than the time-scale of the loading\, an exte rnal force acting on the system. Hence the system stays almost in its equi librium described by the static solution. However\, the limit of solutions (as the ratio of the time scales tends to zero) may not be characterized by the corresponding rate-independent model where the viscous-like terms h ave been dropped. The reason is that the phase transformation is driven by a non-convex thermodynamic potential and hence the solutions may develop jumps in the limit. In order to resolve the jump's detailed trajectory\, a long which the viscous effects play a crucial role\, we use the so-called Balanced-Viscosity (BV) solutions introduced by Efendiev and Mielke in 200 6. This work is a collaboration with Matthias Liero and Alexander Mielke f rom WIAS Berlin.\n\nPenrose O.\, Fife P. C. - Thermodynamically Consistent Models of Phase-Field Type for the Kinetics of Phase Transitions (1990)\n \nSprekels J.\, Zheng S. M. - Global smooth solutions to a thermodynamical ly consistent model of phase-field type in higher space dimensions (1993)\ n\nEfendiev M.\, Mielke A. - On the rate-independent limit of systems wit h dry friction and small viscosity (2006)\n\nMielke A.\, Roubicek T. - Rat e-independent Systems Theory and Application (2015)\n LOCATION:https://researchseminars.org/talk/NSCM/56/ END:VEVENT END:VCALENDAR