The formulation and the solution of a nonlinear stochastic boundary-value problem of creep under the condition that the elastic deformations are small and can be neglected, is given. Defining relations for creep, taken in accordance with the nonlinear theory of viscous flow, were formulated in a stochastic form. Nonlinear stochastic problem is reduced to a system of linear differential equations in partial derivatives with respect to fluctuations of the stress tensor according to the perturbation method. The solution of the linearized problem is obtained as the sum of two series. The first series gives the solution away from the border the body without edge effects , the second one represents the solution of the boundary layer, members of this series are quickly exhausted on the distance from the boundary. Based on this decision, the statistical analysis of random stress field near the boundaries was carried out. It is shown that the spread of stress in the surface layer, whose width depends on the degree of heterogeneity of the material, may be much greater than for the deep layers.
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