Extensions Of Phenomenological Theories For Surface/Interface Elasticity And Elastic Surface Thermodynamics

Nano-materials and nano-structures are advanced science and technology withrapid developments. In this respect surface efects always play a key role. In thesolid mechanics community, several phenomenological theories including the clas-sical Gurtin-Murdoch (GM) surface elasticity are the most powerful and prevalentmethods to study the mechanical surface efects at present. Those theories have theability to reveal the size efects commonly observed at nanoscale. However, they areinconsistent with the thermodynamic principles. This fact was confirmed in this the-sis by a critical examination of the underlying basic concepts and the methodologyused by GM surface elasticity as well as its dipolar solutions. In order to developa thermodynamically-consistent surface elasticity theory, we should investigate thesurface thermodynamics of elastic surfaces.Within the realm of phenomenological theories:(1) The efect of interfacial slippage on the contact instability of an elastic thinfilm surface was studied using the shear-spring model, which is one of 'soft'interface models. A new potential strategy to control the morphology of surfaceinstability patterns was proposed based on theoretical analyses.(2) The concept of surface elasticity was extended to take into account of the linearelectromechanical coupling behaviors in nanodielectrics. A phenomenologicalcontinuum theory of surface piezoelectricity was proposed. New boundary con-ditions accounting for the superficial interplay between electricity and elasticityare derived. As an illustrative application, we calculated the residual mechani-cal and electrical fields of an infinite radially polarizable piezoelectric nanotube.The results predict a possible phenomenon of surface-induced polarity inversionfor thin enough nanotubes.(3) The basic problem of the surface displacement fields induced by a superficialdipolar force was resolved within the framework of two-dimensional GM sur-face elasticity. The analytical solutions showed that once either the residualsurface stress or the surface elastic modulus becomes negative, the displace-ment field will take on an unattenuated wave-like form. Obviously, it violates the Saint-Venant principle.On the other hand, the surface parameters calculated by atomistic calculations andmeasured by sophisticated experiments can definitely be negative. Those parameter-s should all be defined in a thermodynamic manner. Therefore, phenomenologicalsurface elasticity theories are inconsistent with the basic principles of Gibbs surfacethermodynamics.The key issue of this thesis is the elastic surface thermodynamics. Starting fromthe classical interface thermodynamics of fluids, we introduced basic concepts, sort-ed necessary contexts, refined basic methods, and then extended them to the case ofsolids. With respect to an arbitrarily given orientation in elastic solids, we identi-fied the in-plane strains and transverse stresses as the mechanical intensive quantitiescharacterizing the elastic equilibrium. A novel implicitly oriented thermomechanicalfunction called the Reissner free energy was introduced as a partial Legendre transfor-mation of the classical Helmholtz free energy. For elastic surfaces, the characteristicdividing surface was chosen in such a way that the surface excess of mass densityequals zero. A surface Gibbs-Duhem type relation was derived according to the prin-ciple of covariance of surface excesses. The modified and generalized Shuttleworth-Herring equation and the generalized Nozie`res-Wolf equation, which can be viewedrespectively as the thermodynamic definitions of surface stresses and surface strain-s followed naturally. Those surface constitutive relations are essential to the furtherdevelopment of a thermodynamically-consistent surface elasticity theory.