BEGIN:VCALENDAR VERSION:2.0 PRODID:-//Sabre//Sabre VObject 4.6.1//EN CALSCALE:GREGORIAN BEGIN:VTIMEZONE TZID:Europe/Zurich X-LIC-LOCATION:Europe/Zurich TZURL:http://tzurl.org/zoneinfo/Europe/Zurich BEGIN:DAYLIGHT TZOFFSETFROM:+0100 TZOFFSETTO:+0200 TZNAME:CEST DTSTART:19810329T020000 RRULE:FREQ=YEARLY;BYMONTH=3;BYDAY=-1SU END:DAYLIGHT BEGIN:STANDARD TZOFFSETFROM:+0200 TZOFFSETTO:+0100 TZNAME:CET DTSTART:19961027T030000 RRULE:FREQ=YEARLY;BYMONTH=10;BYDAY=-1SU END:STANDARD END:VTIMEZONE BEGIN:VEVENT UID:news2096@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20261026T173736 DTSTART;TZID=Europe/Zurich:20261113T110000 SUMMARY:Seminar in Numerical Analysis: Andrey Latyshev (University of Luxem bourg & Sorbonne University) DESCRIPTION:Geometric uncertainty can significantly affect the stability of solutions to variational problems in mechanics. We investigate fracture n ucleation using a variational phase-field model posed on a domain whose bo undary is represented by a stationary Gaussian random field with Matérn c ovariance. This formulation allows us to study how stochastic boundary mor phology influences the predicted failure strength.\\r\\nThe problem involv es an interaction between the local geometry of the random boundary and th e internal phase-field length scale. We identify two distinct nucleation r egimes: a stress-based regime\, in which the failure load is governed by t he local stress concentration\, and a notch-based regime associated with s teep boundary defects that progressively behave like sharp notches.\\r\\nO ur results show that the largest reduction in strength does not occur at e ither limiting geometry. Instead\, it occurs for an intermediate defect ge ometry marking the transition from the stress-based regime to the notch-ba sed regime. This transition is governed by the ratio between the local roo t radius of curvature of the boundary defect and the phase-field length sc ale.\\r\\nThe resulting dimensionless description establishes a connection between local boundary geometry and variational fracture nucleation. It a lso provides a basis for studying failure on statistically defined rough d omains.\\r\\nFor further information about the seminar\, please visit this webpage [https://dmi.unibas.ch/de/forschung/mathematik/seminar-in-numeric al-analysis/]. X-ALT-DESC:

Geometric uncertainty can significantly affect the stability of solutions to variational problems in mechanics. We investigate fracture nucleation using a variational phase-field model posed on a domain whose boundary is represented by a stationary Gaussian random field with Matérn covariance. This formulation allows us to study how stochastic boundary m orphology influences the predicted failure strength.

\n

The problem i nvolves an interaction between the local geometry of the random boundary a nd the internal phase-field length scale. We identify two distinct nucleat ion regimes: a stress-based regime\, in which the failure load is governed by the local stress concentration\, and a notch-based regime associated w ith steep boundary defects that progressively behave like sharp notches.\n

Our results show that the largest reduction in strength does not oc cur at either limiting geometry. Instead\, it occurs for an intermediate d efect geometry marking the transition from the stress-based regime to the notch-based regime. This transition is governed by the ratio between the l ocal root radius of curvature of the boundary defect and the phase-field l ength scale.

\n

The resulting dimensionless description establishes a connection between local boundary geometry and variational fracture nucle ation. It also provides a basis for studying failure on statistically defi ned rough domains.

\n

For further information about the seminar\, ple ase visit this webpage.

DTEND;TZID=Europe/Zurich:20261113T123000 END:VEVENT END:VCALENDAR