Numerical Approaches for Investigating Quasiconvexity in the Context of Morrey’s Conjecture
Publikation: Beitrag in Fachzeitschrift › Forschungsartikel › Beigetragen › Begutachtung
Beitragende
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
Originalsprache | Englisch |
---|---|
Aufsatznummer | 77 |
Seitenumfang | 41 |
Fachzeitschrift | Journal of Nonlinear Science |
Jahrgang | 32 |
Ausgabenummer | 77 |
Publikationsstatus | Veröffentlicht - 2 Sept. 2022 |
Peer-Review-Status | Ja |
Externe IDs
ORCID | /0000-0003-1093-6374/work/146166887 |
---|---|
Scopus | 85137586555 |