On the equivalence between rank-one convexity and polyconvexity for isotripic sets of R-2x2

We prove the equivalence between rank-one convexity and polyconvexity for i sotropic sets of R-2X2, and characterize rank-one convex isotropic sets. Th ese results allow to compute the weak closure of some sets of constraints u sed in elasticity theory. (C) 2000 Academie des sciences/Editions scientifi ques et medicales Elsevier SAS.