Poor cyclic performance of electrodes in lithium-ion rechargeable cell batteries is calling for efforts to develop continuum models of diffusion under very large stresses and high solute concentrations. The present work is aimed to develop such a model based on input from atomistic simulations. We consider four fundamental features of highly nonlinear behavior associated with diffusion at high solute concentrations. First, the effect of solute-induced stresses on the activation energy of solute diffusion could be important. Second, the solute concentration may be subject to an upper limit if there exists a stoichiometric maximum concentration. Third, the strong influence of the change in local chemical environment on the interaction energy between solute and host atoms could play a significant role. Fourth, we include the effect of the solute concentration on the Young's modulus of the host material. A continuum model is developed and validated based on atomistic simulations of hydrogen diffusion in nickel. The influences of each feature above are clearly discussed through parametric studies. (C) 2010 Elsevier B.V. All rights reserved.