Characterization of polyconvex isotropic functions

Polyconvexity is an important concept in the analysis of energies related to elasticity. A function W :Rd× 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 R¹⁹ 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.