On the Kirchhoff-Love Hypothesis (Revised and Vindicated)

Abstract The Kirchhoff-Love hypothesis expresses a kinematic constraint that is assumed to be valid for the deformations of three-dimensional body when one its dimensions much smaller than other two, as case plates. This has long history checkered with vicissitudes life: even paternity been questioned, and recent rigorous dimension-reduction tools (based on standard $\varGamma $ Γ -convergence) have proven incompatible it. We find an appropriately revised version valuable means derive two-dimensional variational model elastic plates from nonlinear free-energy functional. bending energies thus obtained number materials also show contain measures stretching plate’s mid surface (alongside expected bending). incompatibility -convergence appears removed in cases where contact method ours can made.