  In this note we formulate a sufficient condition for the quasiconvexity at $x
\mapsto \lambda x$ 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 upper bound on those $\lambda>0$ such 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.
