Characterization of polyconvex isotropic functions

2023/04/17 by Wiedemann, David, Peter, Malte A. · 2 citations
#49J10 #74B20 #74G65 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2304.08385

Abstract

Polyconvexity is an important concept in the analysis of energies related to elasticity. A function f \colon \R^{d× d} → \R is called polyconvex if it can be written as a convex function in the minors of the argument. We show that for isotropic functions it suffices to consider diagonal matrices. For d=3, this leads to a dimension reduction for the convex representative of f from \R¹⁹ to \R⁷. Moreover, we present a new result for the polyconvexity of functions formulated in the principal invariant of the left or right stretch tensor.

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