Virtual model validation of complex multiscale systems: Applications to nonlinear elastostatics

• Published in: Computer methods in applied mechanics and engineering 2013-11, Vol.266, p.162-184
• Main Authors: Oden, J. Tinsley, Prudencio, Ernesto E., Bauman, Paul T.
• Format: Article
• Language: English
• Subjects: Bayesian inference; Calibration; Computer simulation; Consistency; Design of experiments; Gain; Information entropy; Kullback–Leibler divergence; Mathematical models; MATHEMATICS AND COMPUTING; Model validation; Model validation, information entropy, Kullback-Leibler divergence, mutual information, uncertainty quanti cation, Bayesian inference; Mutual information; Phases; Uncertainty; Uncertainty quantification
• ISSN: 0045-7825; 1879-2138
• DOI: 10.1016/j.cma.2013.07.011

We propose a virtual statistical validation process as an aid to the design of experiments for the validation of phenomenological models of the behavior of material bodies, with focus on those cases in which knowledge of the fabrication process used to manufacture the body can provide information on the micro-molecular-scale properties underlying macroscale behavior. One example is given by models of elastomeric solids fabricated using polymerization processes. We describe a framework for model validation that involves Bayesian updates of parameters in statistical calibration and validation phases. The process enables the quantification of uncertainty in quantities of interest (QoIs) and the determination of model consistency using tools of statistical information theory. We assert that microscale information drawn from molecular models of the fabrication of the body provides a valuable source of prior information on parameters as well as a means for estimating model bias and designing virtual validation experiments to provide information gain over calibration posteriors.