Epistemic Uncertainty Modeling of Johnson-Cook Plasticity Model Using Evidence Theory

Abstract

Principles of evidence theory are used to develop a methodology for quantifying epistemic uncertainty in constitutive models that are often used in nonlinear finite element analysis involving large plastic deformation at different strain rates and temperatures. The developed methodology is used for modeling epistemic uncertainty in Johnson-Cook plasticity model. All sources of uncertainty emanating from experimental stress-strain curves for different temperatures and strain rates, as well as expert opinions for method of fitting the model constants and the representation of homologous temperature in the model are considered. The five Johnson-Cook model constants are determined in interval form using two different fitting approaches and three sets of experimental data. Rules for identifying intervals that are in agreement, conflict, or ignorance are discussed. The presented methodology is used to find the basic belief assignment (BBA) for separate intervals of uncertainty, and the Yager rule is used for combining different sources of evidence and generating a consolidated BBA structure for each model constant. The represented uncertainty intervals with corresponding BBA are used to estimate belief and plausibility of precision intervals for a published set of Johnson-Cook constants for Al6061-T6. Results show that the constants of Johnson-Cook plasticity model are subject to considerable uncertainty.

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