Kolloquium zur Masterarbeit: Valentin Hölker

Studentischer Vortrag (Kolloquium zur Masterarbeit/Master's thesis defense)
Vortragender/Speaker: Valentin Gregor Hölker
Ansprechpartner/Contact: Prof. Dr. Stefan Neukamm

Titel/Title: Reducing the dissipative component for rate-independent systems
Zusammenfassung/Abstract:
We investigate dimension reduction for dissipative components in rate-independent systems. Building on the 2024 result of Stefan Neukamm and Kai Richter, who derived an effective bending model for elastoplastic rods with dimension reduction only in the non-dissipative part, we establish existence of energetic solutions for the limiting model via incremental minimization. We analyse the dissipative component in a simpler convex setting and obtain a limiting model in the asymptotic regimes where the quadratic plastic energy vanishes or diverges. Furthermore, we present an abstract result showing that a subsequence of solutions to incremental minimization problems converges to a solution of the reduced problem. It remains open whether these reductions are applicable to the rod model.