An Evidence-Based Framework for Determination of Material Constants in Advanced Plasticity Models

The principles of evidence theory are used to develop a nondeterministic framework for determination of material constants in advanced plasticity models. Both epistemic and aleatory uncertainties rooted in material microstructure, choice of experimental approach to obtain stressstrain curves at high strain rates and temperatures, method of fitting the constants, and expert opinions for capturing the physics of dynamic material behavior are considered. A step-by-step methodology is presented for deriving the constants in interval form with corresponding assigned degree of belief that accounts for agreement, conflict, and ignorance relationship between different intervals. A formulation for the average belief structure is provided as a way to capture the characteristics of material considering all associated uncertainties. The developed framework is used to calculate the constants in the microstructure-based BCJ plasticity model for ductile heterogeneous metals. The results indicate that the calculated material constants can fairly accurately describe the macroscopic behavior of AL6061-T6 in various ranges of strain rates and temperatures.