Rank 1 convex hulls of isotropic functions in dimension 2 by 2

summary:Let $f$ be a rotationally invariant (with respect to the proper orthogonal group) function defined on the set $\text{M}^{2\times 2}$ of all $2$ by $2$ matrices. Based on conditions for the rank 1 convexity of $f$ in terms of signed invariants of $\mathbb{A}$ (to be defined below), an iterative procedure is given for calculating the rank 1 convex hull of a rotationally invariant function. A special case in which the procedure terminates after the second step is determined and examples of the actual calculations are given