Quasiconvexity is a mathematical notion introduced by Morrey (1952) as the appropriate convexity notion for variational integrals depending on a gradient, such as for example elasticity (for details, see S. Müller, Variational models for microstructure and phase transitions). Quasiconvex energy densities are those for which affine deformations are minimizers with respect to their own boundary conditions, i.e.

for any with y(x) = Fx on . It can be shown that this property of W does not depend on the domain . Non-quasiconvex energy densities instead spontaneously generate fine-scale oscillations. Their macroscopic behavior is captured by the quasiconvex envelope.