Abstract
In this note we formulate a sufficient condition for the quasiconvexity at $x ____mapsto ____l x$ of certain functionals $I(u)$ which model the stored-energy of elastic materials subject to a deformation $u$. The materials we consider may cavitate, and so we impose the well-known technical condition (INV), due to M'{u}ller and Spector, on admissible deformations. Deformations obey the condition $u(x)= ____lambda x$ whenever $x$ belongs to the boundary of the domain initially occupied by the material. In terms of the parameters of the models, our analysis provides an explicit $____lambda_0>0$ such that for every $____lambda____in (0,____lambda_0]$ it holds that $I(u) ____geq I(u_{____lambda})$ for all admissible $u$, where $u_{____lambda}$ is the linear map $x ____mapsto ____lambda x$ applied across the entire domain. This is the quasiconvexity condition referred to above.