Two-dimensional chemo-elasticity under chemical equilibrium

The coupling between solid state diffusion and mechanical stress arises in a number of important technological applications. The theory that describes such coupling is termed chemo-elasticity. In this paper, a solution approach is developed for two-dimensional chemo-elasticity problems. First, a coupled system of nonlinear partial differential equations is derived in terms of an Airy stress function and the solute concentration. Then, this coupled system of nonlinear equations is solved asymptotically using a perturbation technique. Finally, based on this approach, asymptotic solutions are obtained for three fundamental problems in two-dimensional chemo-elasticity, namely, a circular hole in an infinite plate under uniaxial tension, a straight edge dislocation and a disclination.