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We present a sufficient condition under which a weak solution of theEuler-Lagrange equations in nonlinear elasticity is already a global minimizerof the corresponding elastic energy functional. This criterion is applicable toenergies $W(F)=\widehat{W}(F^TF)=\widehat{W}(C)$ which are convex with respectto the right Cauchy-Green tensor $C=F^TF$, where $F$ denotes the gradient ofdeformation. Examples of such energies exhibiting a blow up for $\det F\to0$are given.

On the convexity of nonlinear elastic energies in the right Cauchy-Green tensor