Quantification of microstructure-related uncertainties in structural analysis based on artificial microstructures and the FE 2 $$ {\mathrm{FE}}^2 $$ -method

Abstract

The characteristics of microstructure morphology of micro-heterogeneous materials may vary over the macroscopic length scale and thus result in macroscopically distributed, uncertain material properties. Hence, multiscale approaches for the structural analysis of such materials, for example, in terms of the ${\text{FE}}^2$-method, should not be based on a single representative volume element. In this contribution a method is proposed, which considers different, artificial statistically similar volume elements at each macroscopic integration point which mimic the microstructure variability of the real material as a random field. For this purpose, the microstructure variation of the real material is quantified first in terms of the distribution of a scalar measure containing deviations of statistical measures of higher order, and then this distribution is used to construct a set of artificial microstructures to be used as volume elements within the multiscale simulation. To avoid manual discretization of the large amount of statistically similar volume elements, the finite cell method is combined with concurrent computational homogenization following the ${\text{FE}}^2$-method. The proposed method is demonstrated for two examples, a simpler tensile experiment for testing purposes and a simplified, idealized deep drawing process.