Plasticity of random inhomogeneous media

Effects of spatial random fluctuations in the yield condition are analyzed in rigid-perfectly plastic media governed, generally, by a Mohr-Coulomb yield condition with cohesion. The solution method is based on a stochastic generalization of the method of slip-lines, whose significant feature is that the deterministic characteristics are replaced by the forward evolution cones containing random characteristics; the actual choice of spacing of a finite difference net of slip-lines defines the mesoscale approximation in any given problem. 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 in several examples of boundary value problems; finite difference methods appropriate for inhomogeneous materials are developed. The major conclusion is that weak material randomness may lead to a relatively stronger scatter 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.