Mass transport along a bimaterial interface

A mass transport process that can operate to change the system free energy is mass flow along a surface that is interior to the material. A grain boundary 

This separation 6n is a time-dependent field over S, and its history represents shape evolution associated with mass transport along the surface. It could be anticipated at this point that the corresponding work-conjugate force is the normal stress acting on the surface. This is borne out by the following calculation which establishes a chemical potential for this mass transport process. 

To derive an expression for the chemical potential, suppose that the loading conditions imposed on S are such that there is no exchange of energy between the material in R and its surroundings outside S . Furthermore, to avoid dissipative shear deformations across S which are not involved in mass transport, it is assumed either that the tangential displacement is continuous across S, which requires that uf — u n nf = u — u n n, or that the shear traction vanishes on S from either side, which requires that = 0. 

Because strain may be discontinuous across S, the rates of change of the free energies in the regions i2 and are calculated separately. Following the development in Section 8.2.1 for calculation of R t), it is found that 

If the tangential displacement across S is continuous, then there are scalar functions and u such that uf = u nf with Sn = — u + n)-Then, continuity of normal traction implies that = a, 

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