Analysis of uncertainty effects due to microstructural disorder in cellular or porous materials

Aim of the present study is an analysis of the effect of microstructural uncertainties on the scatter in the macroscopic material properties of highly porous materials consisting of metallic or other constituents. For the numerical analysis of the uncertainty effects, a probabilistic homogenization scheme is proposed. In contrast to direct Monte-Carlo approaches, the thermomechanical response of a limited number of pre-selected cases throughout the range of possible microstructures is analyzed. Their effective properties are determined by means of an energy based homogenization procedure. In a stochastic evaluation, the results of the individual computations are weighted with the probability of the occurrence of the underlying microstructures. As a result, the probability distributions for the effective properties are obtained. The basic uncertain microstructural properties considered in the investigation are the microstructural geometry and orientation, the local relative density and the local pore size distribution. In an application to an experimental data base from other sources, the approach proves to be accurate and numerically efficient compared to direct Monte-Carlo approaches. Parameter studies reveal that uncertainties in the local relative density are the most important factor leading to scatter in the macroscopic material properties of cellular materials.