Elements of the Theory of Elastic Surfaces

I present a development of the modern theories of elastic shells, regarded as mathematical surfaces endowed with kinematical and constitutive structures deemed sufficient to represent many of the features of the response of thin shell-like bodies. The emphasis is on Cosserat theory, specialized to obtain a model of the Kirchhoff-Love type through the introduction of appropriate constraints. Noll's concept of material symmetry, adapted to surface theory by Cohen and Murdoch, is used to derive new constitutive equations for elastic surfaces having hemitropic, isotropic and unimodular symmetries. The last of these furnishes a model for fluid films with local bending resistance, which may be used to describe the response of certain fluid microstructures and biological cell membranes.