Statistical volume element method for predicting microstructure–constitutive property relations

There is an inevitable need to establish multilength scale statistical microstructure–constitutive property relations in materials design. In this paper, we have developed a statistical volume element method to analyze, quantify, and calibrate such microstructure–constitutive property relations by statistical means. Statistical volume element simulations are adopted to predict material constitutive properties corresponding to various realizations of random microstructure configurations. A computing framework that links random configuration generators and finite element analysis has been developed. A statistical cause–effect analysis approach is proposed to study the influence of random material microstructure on material constitutive properties. Within the proposed approach, statistically significant microstructure parameters are first identified based on their linear impacts on material constitutive properties. Global sensitivity analysis is then employed to provide a more comprehensive importance ranking of these critical microstructure parameters considering both main and interaction effects. The uncertainties in material constitutive properties due to random microstructure configurations are quantified in terms of distributions, statistical moments, and correlations. The obtained probabilistic constitutive relations are used to calibrate the model parameters in a constitutive relation model following a statistical calibration process. The proposed approach is applied to examine a porous steel alloy material for demonstrative purposes.