Fuzzy logic enhancement of material hardening parameters obtained from tension\u2013compression test

Abstract

This paper presents the determination of material hardening parameters with the use of the fuzzy set theory. The hardening parameters were initially predicted from measurements taken in the cyclic tension–compression test. The experimental hysteresis loop was compared to numerical one obtained by the integration of the plastic flow rule. The nonlinear combined hardening model—Voce isotropic hardening and Frederick–Armstrong kinematic hardening—was considered here. After the initial selection, the hardening parameters were adjusted in the optimization problem using the least-squares method. An approximation error of the hysteresis loop was minimized. Finally, nonlinear isotropic and kinematic hardening parameters were assumed to be fuzzy variables. Hardening parameters obtained in the optimization problem were randomly scattered up to 20%, and the membership functions associated with them were computed. The approximation error of the hysteresis loop was found for each selection of the hardening parameters providing the output membership function associated with this error. The upalpha -level optimization method was used as the main numerical tool, while the extension principle was tested only as the reference solution. In the defuzzification process, the most reliable hardening parameters were found.