COMPUTATIONAL APPROACHES TO INELASTIC MEDIA WITH UNCERTAIN PARAMETERS

In this paper we will consider inelastic material described with uncertain parameters like bulk and shear modulus as well as yield stress, described as lognormal random fields. Uncertainty also can appear on the right hand side of the equilibrium equation. These uncertainties define stochastic inelastic problem, computationally treated by Karhunen-Loève expansion and polynomial chaos expansion. We observed just one material point, where the random fields become lognormal random variables. Here, we are introducing a stochastic radial return mapping for one material point based on the well-known deterministic radial return mapping, assuming that the elastoplastic evaluation is independent of all other material points for the case of isotropic material. The reference solution is calculated using a Monte Carlo method and compared with the stochastic Galerkin method. The results show that both methods give almost the same results, while the Galerkin method is more effective than the Monte Carlo method.