Publications

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This paper examines the variability of predicted responses when multiple stress-strain curves (reflecting variability from replicate material tests) are propagated through a transient dynamics finite element model of a ductile steel can being slowly crushed. An elastic-plastic constitutive model is employed in the large-deformation simulations. Over 70 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. The present work assigns the same material to all the can parts: lids, walls, and weld. We desire to estimate response variability due to variability of the input material curves. When only a few stress-strain curve samples are available from material testing, response variance will usually be significantly underestimated. This is undesirable for many engineering purposes. A simple classical statistical method, Tolerance Intervals, is tested for effectively compensating for 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, and further studies referenced, support a proposition that the method will apply similarly well for other sparsely sampled random functions.

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A discussion of the five responses to the 2014 Sandia Verification and Validation (V&V) Challenge Problem, presented within this special issue, is provided hereafter. Overviews of the challenge problem workshop, workshop participants, and the problem statement are also included. Brief summations of teams' responses to the challenge problem are provided. Issues that arose throughout the responses that are deemed applicable to the general verification, validation, and uncertainty quantification (VVUQ) community are the main focal point of this paper. The discussion is oriented and organized into big picture comparison of data and model usage, VVUQ activities, and differentiating conceptual themes behind the teams' VVUQ strategies. Significant differences are noted in the teams' approaches toward all VVUQ activities, and those deemed most relevant are discussed. Beyond the specific details of VVUQ implementations, thematic concepts are found to create differences among the approaches; some of the major themes are discussed. Lastly, an encapsulation of the key contributions, the lessons learned, and advice for the future are presented.

This work examines the variability of predicted responses when multiple stress-strain curves (reflecting variability from replicate material tests) are propagated through a transient dynamics finite element model of a ductile steel can being slowly crushed. An elastic-plastic constitutive model is employed in the large-deformation simulations. The present work assigns the same material to all the can parts: lids, walls, and weld. Time histories of 18 response quantities of interest (including displacements, stresses, strains, and calculated measures of material damage) at several locations on the can and various points in time are monitored in the simulations. Each response quantity's behavior varies according to the particular stressstrain curves used for the materials in the model. We estimate response variability due to variability of the input material curves. When only a few stress-strain curves are available from material testing, response variance will usually be significantly underestimated. This is undesirable for many engineering purposes. This paper describes the can-crush model and simulations used to evaluate a simple classical statistical method, Tolerance Intervals (TIs), for effectively compensating for sparse stress-strain curve data in the can-crush problem. Using the simulation results presented here, the accuracy and reliability of the TI method are being evaluated on the highly nonlinear inputto- output response mappings and non-standard response distributions in the can-crush UQ problem.