THE CAUCHY AND CHARACTERISTIC BOUNDARY-VALUE-PROBLEMS OF RANDOM RIGID-PERFECTLY PLASTIC MEDIA

Effects of spatial random fluctuations in the yield condition of rigid -perfectly plastic continuous media are analysed in cases of Cauchy an d characteristic boundary value problems. A weakly random plastic micr ostructure is modeled, on a continuum mesoscale, by an isotropic yield condition with the yield limit taken as a locally averaged random fie ld. The solution method is based on a stochastic generalization of the method of slip-lines, whose significant feature is that the determini stic characteristics are replaced by the forward evolution cones conta ining random charac teristics. Comparisons of response of this random medium-and of a deterministic homogeneous medium, with a plastic limit equal to the average of the random one, are carried out numerically i n several specific examples of the two boundary value problems under s tudy. An application of the method is given to the limit analysis of a cylindrical tube under internal traction. The major conclusion is tha t weak material randomness always leads to a relatively stronger scatt er in the position and field variables, as well as to a larger size of the domain of dependence-effects which are amplified by both presence of shear traction and inhomogeneity in the boundary data. Additionall y, it is found that there is hardly any difference between stochastic slip-line fields due to either Gaussian or uniform noise in the plasti c limit.