Evidence-Based Uncertainty Modeling of Constitutive Models with Application in Design Optimization

Phenomenological material models such as Johnson-Cook plasticity are often used in finite element simulations of large deformation processes at different strain rates and temperatures. Since the material constants that appear in such models depend on the material, experimental data, fitting method, as well as the mathematical representation of strain rate and temperature effects, the predicted material behavior is subject to uncertainty. In this dissertation, evidence theory is used for modeling uncertainty in the material constants, which is represented by separate belief structures that are combined into a joint belief structure and propagated using impact loading simulation of structures. Yager’s rule is used for combining evidence obtained from more than one source. Uncertainty is quantified using belief, plausibility, and plausibility-decision functions. An evidence-based design optimization (EBDO) approach is presented where the nondeterministic response functions are expressed using evidential reasoning. The EBDO approach accommodates field material uncertainty in addition to the embedded uncertainty in the material constants. This approach is applied to EBDO of an externally stiffened circular tube under axial impact load with and without consideration of material field uncertainty caused by spatial variation of material uncertainties due to manufacturing effects. Surrogate models are developed for approximation of structural response functions and uncertainty propagation. The EBDO example problem is solved using genetic algorithms. The uncertainty modeling and EBDO results are presented and discussed

A new approach for determination of material constants of internal state variable based plasticity models and their uncertainty quantification

a b s t r a c t Physically-based plasticity models such as the BCJ model include internal state variables that represent the current state of the material and allow capturing strain rate and temperature history effects as well as the coupling of rate-and temperature-dependence with material hardening. However, the inclusion of internal state variables increases significantly the number of unknown material constants that need to be found through fitting of the model to experimental stress-strain data at different strain rates and temperatures. This makes the fitting process extremely challenging and increases the uncertainty in the material constants. The paper presents a physics-guided numerical fitting approach that reduces the associated difficulties and uncertainties involved in determining the material constants of the BCJ plasticity model. The approach uses experimental data from monotonic and reverse loading stress-strain curves at different temperatures and strain rates to determine the 18 material constants of the model. An evidential uncertainty quantification approach is used to determine uncertainties rooted in experimental data, selection of stress-strain curves at different loading conditions, variability of material properties, numerical aspects of the fitting method and mathematical formulations of the BCJ model. The represented uncertainty of the BCJ material constants based on mathematical tools of evidence theory is propagated through Taylor impact simulations of a 7075-T651 aluminum alloy cylinder. Uncertainty quantification results verify the presented numerical fitting approach for the BCJ model and its potential applicability to other similar material models

An Evidence-Based Software Engineering Evaluation Approach

model evaluation, decision making, project management, data collection, evidence theory Abstract � Evaluation of software project management is a crucial content for software development enterprise. However, the process of software project management is burdened by various sources of uncertainty due to the lake of information for object of evaluation, differences in knowledge and experience of participated experts, fuzzy reviews of experts and other reasons. A step-by-step algorithm for uncertainty reasoning of software project management using mathematical tools of evidence theory is presented. It is shown that the presented evidential uncertainty reasoning is very efficient for evaluating the successful level of software project management and helpful for software development enterprise to improve management. 1