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.