COMPUTATIONAL APPROACHES TO INELASTIC MEDIA WITH UNCERTAIN PARAMETERS
B. Rosić, H. G. Matthies
Abstract
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.
