Nonlinear diffusion-induced stresses in a long bar of square cross section

This paper is to investigate the nonlinear e}ect of the self!induced electric _eld on the di}usion!induced stresses in a long bar[ We _rst approximate the nonlinear concentration!dependent di}usivity as a series of third!degree polynomials by the least!squares curve!_tting techniques\ and then calculate the distributions of concentration by the Galerkin method[ Afterwards\ the di}usion!induced stresses inside the bar are determined analytically by introducing the Goodier displacement potential and Airy stress function[ It is found that the nonlinear self!induced electric _elds can depress both the concentration gradient and the maximum di}usion!induced stresses apparently\ and these e}ects are more signi_cant at short times than at long times[ 0887 Elsevier Science Ltd[ All rights reserved