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SUMMARY:Matteo Negri (University of Pavia)
DTSTART:20241021T134000Z
DTEND:20241021T151000Z
DTSTAMP:20260405T175200Z
UID:NSCM/146
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NSCM/146/">R
 ate-independent evolutions in phase-field fracture generated by equilibriu
 m configurations</a>\nby Matteo Negri (University of Pavia) as part of Ne
 čas Seminar on Continuum Mechanics\n\nLecture held in Room K3\,  Faculty 
 of Mathematics and Physics\, Charles University\, Sokolovská 83  Prague 8
 ..\n\nAbstract\nIn the phase-field approach\, and in other regularized fra
 cture models\, rate-independent (quasi-static) evolutions are usually obta
 ined by means of time-discrete schemes\, providing at each time an equilib
 rium configuration of the system.  Numerically\, equilibria are computed b
 y descent methods for the free energy (e.g. staggered\, monolithic etc.) e
 ndowed with a suitable irreversibility constraint on phase-field parameter
  (e.g. monotonicity in time).  The time-continuous limit evolution is char
 acterized in terms of evolutionary variational inequalities and in terms o
 f Griffith's criterion. The study of the limit evolution reveals a couple 
 of propagation regimes: stable (or steady state) and unstable (or catastro
 phic). In the stable regime the evolution is simultaneous (in displacement
  and phase field parameter) and satisfies Griffith's criterion in terms of
  toughness and phase field energy release rate. In the unstable regime the
  evolution is not necessarily simultaneous and may not satisfy Griffith's 
 criterion. Energy identity holds in general with an instantaneous drop of 
 energy in unstable times. The monotonicity constraint turns out to be full
 y thermodynamically consistent along the whole evolution. Technically\, th
 e proof relies on: (a) the strong convergence of the phase field parameter
 \, (b) Kuratowski convergence of parametrized discrete times\, (c) the lim
 it of the power identity. The result is very general since it works indepe
 ndently of the scheme employed in the incremental problem\, it holds for i
 nstance for AT1 and AT2 energies\, in plane strain and plane stress settin
 gs. Numerically\, we compare energies\, energy release rates and evolution
 s computed in the sharp crack and in the phase field setting for a couple 
 of reference benchmarks: the double cantilever beam (for steady state prop
 agation) and the single edge notch under tension (for unstable propagation
 ).\n
LOCATION:https://researchseminars.org/talk/NSCM/146/
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