Abstract Polyconvexity is an important concept in the analysis of energies related to elasticity. A function W: R^d d R W: 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 d = 3, this leads to a dimension reduction for the convex representative of W from R^19 R 19 to R⁷ R 7. Moreover, we present a new result for the polyconvexity of functions formulated in the principal invariant of the left or right stretch tensor.
Wiedemann et al. (Sat,) studied this question.