Elastic moduli for strongly curved monoplayers. Position of the neutral surface

(Received 25 March 1991, revised 3 June 1991, accepted 10 June 1991)

Abstract
The existing approaches to interface mechanics describe almost flat interfaces and use two elastic moduli corresponding to extension and bending deformations. Recently these theories have been applied to systems with a strong curvature and hereby the finite thicknesses of interfaces come into play. We show that for such systems the elastic moduli considerably depend on the choice of the dividing surface. For an arbitrary dividing surface one has to take into account the coupling between the extension and bending deformations and therefore to use a third elastic modulus corresponding to mixed deformation. We give the expressions relating the set of elastic moduli defined for one dividing surface to the corresponding set for another arbitrary dividing surface. The dividing surface with vanishing modulus of mixed deformation is defined as the neutral surface. We find the position of the neutral surface in terms of elastic moduli for any arbitrary dividing surface.