Los Alamos Report LA-UR-05-3935

Hierarchical Bayesian analysis and the Preston-Tonks-Wallace model

Michael Fugate, Brian Williams, David Higdon, Kenneth M. Hanson, James Gattiker, Shuh-Rong Chen, Cetin Unal
Los Alamos National Laboratory


We utilize data from Hopkinson-bar experiments and quasi-static compression experiments to characterize uncertainties for parameters governing the Preston-Tonks-Wallace (PTW) plastic deformation model for a variety of materials. This particular plastic deformation model is designed to be valid over a range of input conditions, which include strain, strain rate and temperature. However, because of variations between experimental samples, measurement variation, as well as slight inadequacies in the model, no single parameter setting gives a good match to all of the experimental data for a given material. These deficiencies need to be taken into account when assessing the uncertainties in the model parameters. In this paper, we use a Bayesian hierarchical model to account for the variations in the experimental data. This modeling approach results in parameter estimates for each material, along with uncertainty estimates, which are the main focus of this paper.

Keywords: plastic deformation model, Preston-Tonks-Wallace model, uncertainty analysis, Bayesian analysis, hierarchical model, model uncertainty, Hopkinson-bar experiments, quasi-static-compression experiments

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