  Macroscopically heterogeneous materials, characterised mostly by comparable
heterogeneity lengthscale and structural sizes, can no longer be modelled by
deterministic approach instead. It is convenient to introduce stochastic
approach with uncertain material parameters quantified as random fields and/or
random variables. The present contribution is devoted to propagation of these
uncertainties in mechanical modelling of inelastic behaviour. In such case the
Monte Carlo method is the traditional approach for solving the proposed
problem. Nevertheless, convergence rate is relatively slow, thus new methods
(e.g. stochastic Galerkin method, stochastic collocation approach, etc.) have
been recently developed to offer fast convergence for sufficiently smooth
solution in the probability space. Our goal is to accelerate the uncertainty
propagation using a polynomial chaos expansion based on stochastic collocation
method. The whole concept is demonstrated on a simple numerical example of
uniaxial test at a material point where interesting phenomena can be clearly
understood.

Computational Engineering, Finance, and Science