The strain-energy function for combined bending and stretching of incompressible isotropic elastic plates∗

Abstract

The strain-energy function of a thin plate composed of an incompressible isotropic elastic
material is derived. In contrast to conventional models developed for applications involving large
plate deformations with small midplane strains, the present model accommodates large deformations
accompanied by finite midplane strains. An extended Kirchhoff-Love hypothesis underpinning prior
work on the topic is here justified on energetic grounds. The model, specialized to certain generalized
neo-Hookean materials, exhibits bending-stretching coupling and reduces to the classical pure-bending
energy in the absence of midplane strain.