Uncertainty quantification for random fields estimated from effective moduli of elasticity

The stochastic finite element method is a useful tool to calculate the response of systems subject to uncertain parameters and has been applied extensively to analyse structures composed of randomly heterogeneous materials. The methodology to estimate the parameters of the random field underlying a stochastic finite element model often utilises the midpoint approximation wherein material properties that are measured over a sample volume are treated as point observations of the random field at the centroid of the sample volume. This paper investigates the error induced by this approximation for the case of effective moduli of elasticity resulting from tensile loading as well as 3 and 4-point bending. A computer experiment has been performed consisting of the generation of synthetic stiffness profiles from a lognormal stochastic process, the calculation of effective properties as weighted harmonic averages and the estimation of random field parameters through the method of moments. The uncertainty in the parameter estimates is quantified and a recommendation is made as to which bending test is superior for obtaining random field parameter estimates with reference to the statistics of the base process and the tensile loading condition