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.