This paper examines the variability of predicted responses when multiple stress-strain curves (reflecting variability from replicate material tests) are propagated through a finite element model of a ductile steel can being slowly crushed. Over 140 response quantities of interest (including displacements, stresses, strains, and calculated measures of material damage) are tracked in the simulations. Each response quantity’s behavior varies according to the particular stress-strain curves used for the materials in the model. We desire to estimate response variability when only a few stress-strain curve samples are available from material testing. Propagation of just a few samples will usually result in significantly underestimated response uncertainty relative to propagation of a much larger population that adequately samples the presiding random-function source. A simple classical statistical method, Tolerance Intervals, is tested for effectively treating sparse stress-strain curve data. The method is found to perform well on the highly nonlinear input-to-output response mappings and non-standard response distributions in the can-crush problem. The results and discussion in this paper support a proposition that the method will apply similarly well for other sparsely sampled random variable or function data, whether from experiments or models. Finally, the simple Tolerance Interval method is also demonstrated to be very economical.
This report describes the methods, results, and conclusions of the analysis of 11 scenarios defined to exercise various options available in the xLPR (Extremely Low Probability of Rupture) Version 2 .0 code. The scope of the scenario analysis is three - fold: (i) exercise the various options and components comprising xLPR v2.0 and defining each scenario; (ii) develop and exercise methods for analyzing and interpreting xLPR v2.0 outputs ; and (iii) exercise the various sampling options available in xLPR v2.0. The simulation workflow template developed during the course of this effort helps to form a basis for the application of the xLPR code to problems with similar inputs and probabilistic requirements and address in a systematic manner the three points covered by the scope.
