Oriented Thermomechanics for Isothermal Planar Elastic Surfaces Under Small Deformation

Abstract

In the present paper, the issue of the thermomechanical definitions of intrinsic surface elastic properties is addressed in the context of infinitesimal elasticity, utilizing two fundamental ideas of Gibbs surface thermodynamics, i.e., the Gibbs dividing surface and the associated surface excesses. Firstly, we introduce a novel scalar yet implicitly oriented thermomechanical function, called the Reissner free energy, as a partial Legendre transformation of the conventional Helmholtz free energy function. It naturally facilitates the application of fundamental principles in classical Gibbs surface thermodynamics of fluids to purely elastic solids. In view of the diffusionless characteristic of elastic surfaces, surface elastic parameters that are invariant with altering the position of the Gibbs dividing surface are defined. Resorting to the construction of a fictitious elastic field in the comparison system, we obtain a fundamental thermodynamic identity, i.e., the isothermal surface Gibbs-Duhem type relation. Thereby the modified Shuttleworth-Herring equation as well as the generalized Nozières-Wolf equation, which could be regarded respectively as the defining equations for the intrinsic surface stress and surface strain, are derived. The oriented thermomechanics treatment of elastic surfaces presented here is expected to serve as an essential basis for further developments of an intrinsic surface elasticity theory.