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Rank‐one convexity and polyconvexity of Hencky‐type energies
Author(s) -
Neff Patrizio,
Ghiba IonelDumitrel,
Lankeit Johannes,
Martin Robert
Publication year - 2014
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201410350
Subject(s) - rank (graph theory) , convexity , isotropy , logarithm , conjecture , regular polygon , tensor (intrinsic definition) , type (biology) , mathematics , strain (injury) , combinatorics , mathematical analysis , geometry , physics , geology , quantum mechanics , biology , paleontology , financial economics , economics , anatomy
We investigate a family of isotropic volumetric‐isochorically decoupled strain energies based on the Hencky‐logarithmic (true, natural) strain tensor log U . The main result of this note is that for n = 2 the considered energies are rank‐one convex for suitable values of two material parameters. We also conjecture that there are values of the material parameters such that the corresponding energies are polyconvex. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)