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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-energyof elastic materials subject to a deformation $u$. The materials we considermay cavitate, and so we impose the well-known technical condition (INV), due toM\"{u}ller and Spector, on admissible deformations. Deformations obey thecondition $u(x)= \lambda x$ whenever $x$ belongs to the boundary of the domaininitially 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 thelinear map $x \mapsto \lambda x$ applied across the entire domain. This is thequasiconvexity condition referred to above.

A simple sufficient condition for the quasiconvexity of elastic stored-energy functions in spaces which allow for cavitation