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

Research output: Contribution to journalResearch articleContributedpeer-review


  • Jendrik Voss - , University of Duisburg-Essen, Dortmund University of Technology (Author)
  • Robert J. Martin - , University of Duisburg-Essen (Author)
  • Oliver Sander - , Chair of Numerical Methods of Partial Differential Equations (Author)
  • Siddhant Kumar - , Delft University of Technology (Author)
  • Dennis M. Kochmann - , ETH Zurich (Author)
  • Patrizio Neff - , University of Duisburg-Essen (Author)


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.


Original languageEnglish
Article number77
Number of pages41
JournalJournal of Nonlinear Science
Issue number77
Publication statusPublished - 2 Sept 2022

External IDs

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


Library keywords