Convergence of equilibria of thin elastic plates under physical growth conditions for the energy density

The asymptotic behaviour of the equilibrium configurations of a thin elastic plate is studied, as the thickness h of the plate goes to zero. More precisely, it is shown that critical points of the nonlinear elastic functional E^h, whose energies (per unit thickness) are of order h^4, converge to critical points of the Gamma-limit of h^{−4}E^h. This is proved under the physical assumption that the energy density blows up as the determinant of the deformation gradient tends to zero.