Rank‐one convexity and polyconvexity of Hencky‐type energies

Abstract

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.

Euromech 563 Cisterna di Latina 17–21 March 2014 Generalized continua and their applications to the design of composites and metamaterials: A review of presentations and discussions

“…As a second candidate, a logarithmic defect energy is investigated. Polyconvexity of the exponentiated Hencky strain energy in plane elastostatics is analyzed in the talk by Patrizio Neff [72].…”