Orientation-preserving homeomorphic deformations in nonlinear elasticity

Datum

16.04.2015

Zeit

15:15 - 16:15

Sprecher

Priv.-Doz. Dr. Martin Kruzík

Zugehörigkeit

The Czech Academy of Sciences

Serie

TUD Mathematik Oberseminar Analysis

Sprache

en

Hauptthema

Mathematik

Andere Themen

Mathematik

Host

Prof. Dr. St. Neukamm

Beschreibung

Dieser Vortrag findet im Rahmen des Forschungsseminars des Instituts für Wissenschaftliches Rechnen und des Oberseminars Analysis statt. In this talk we characterize necessary and sufficient conditions to ensure weak-*lower semicontinuity of the energy functional on the set of orientation-preserving bi-Lipschitz maps in the plane. This problem is motivated by variational problems in nonlinear hyperlasticity where the orientation preservation and injectivity of the admissible deformations are key requirements. Generally speaking, the main difficulty in finding such conditions is that the set of bi-Lipschitz functions is non-convex. Thus, standard cut-off techniques that modify the generating sequence to have the same boundary conditions as the limit generally fail; however, the standard proofs in the calculus of variations rely on such methods. We obtain a new cut-off strategy employing bi-Lipschitz extension theorems.

Links

• Oberseminar Analysis
• Seminar des Instituts für Wissenschaftliches Rechnen

Letztmalig verändert: 25.03.2015, 16:31:48