Polyconvexity

Summary

A function of an $m \times n$ matrix is polyconvex if it is a convex function of the matrix together with all its minors. For $3 \times 3$ matrices the minors are the entries, the entries of the cofactor matrix and the determinant. Polyconvexity implies Morrey quasiconvexity, and it is much easier to check. It allows energies that blow up as the determinant tends to $0$, so it is the standard hypothesis on stored energies in nonlinear elasticity.