Thermodynamic restrictions on, and Eshelbian forms of Interfacial Stress under Mechanical, Thermal and Chemical Driving Forces

Abstract In this paper, the thermodynamic configurational force and velocity associated with a reaction-diffusion moving interface are studied to derive both Cauchy stress, its Eshelbian form, and their Piola transformations to the reference configuration. The driving force on the interface is mathematically connected to mechanical, thermal, and chemical fields both in the bulk and on the interface, including anisotropic and inhomogeneous interface stress. Systematically applying a general interface transport theorem, we derive the balance laws, the thermodynamic principles, and the consequent thermodynamic restrictions on the interface stress under the driving forces. These forms are shown to mirror their bulk versions. Next, the velocity-force Eshelbian forms of momentum balance in the bulk are reviewed followed by the derivation of Eshelbian forms for the analogous interface momentum balance equations. In general, the jump in surface Eshelby stress forms assure homogeneity on a planar surface, but additional curvature-dependent terms are required to ensure linear momentum balance on a curved surface.