Numerical Approaches for Investigating Quasiconvexity in the Context of Morrey’s Conjecture

Publikation: Beitrag in FachzeitschriftForschungsartikelBeigetragenBegutachtung

Beitragende

  • Jendrik Voss - , Universität Duisburg-Essen, Technische Universität (TU) Dortmund (Autor:in)
  • Robert J. Martin - , Universität Duisburg-Essen (Autor:in)
  • Oliver Sander - , Professur für Numerik partieller Differentialgleichungen (Autor:in)
  • Siddhant Kumar - , Technische Universität Delft (Autor:in)
  • Dennis M. Kochmann - , ETH Zurich (Autor:in)
  • Patrizio Neff - , Universität Duisburg-Essen (Autor:in)

Abstract

Deciding whether a given function is quasiconvex is generally a difficult task. Here, we discuss a number of numerical approaches that can be used in the search for a counterexample to the quasiconvexity of a given function W. We will demonstrate these methods using a particular planar isotropic rank-one convex function, as our main example. In a previous contribution, we have shown that quasiconvexity of this function would imply quasiconvexity for all rank-one convex isotropic planar energies in two-dimensional elasticity with an additive volumetric-isochoric split of a particular form. This example is therefore of particular interest with regard to Morrey’s open question whether or not rank-one convexity implies quasiconvexity in the planar case.

Details

OriginalspracheEnglisch
Aufsatznummer77
Seitenumfang41
FachzeitschriftJournal of Nonlinear Science
Jahrgang32
Ausgabenummer77
PublikationsstatusVeröffentlicht - 2 Sept. 2022
Peer-Review-StatusJa

Externe IDs

ORCID /0000-0003-1093-6374/work/146166887
Scopus 85137586555

Schlagworte

Bibliotheksschlagworte