A. Skrzat∗ Fuzzy Logic Application to Strain-stress Analysis in Selected Elastic-plastic Material Models Zastosowanie Logiki Rozmytej Do Analizy Odkształceń I Naprężeń Dla Wybranych Modeli

The common engineering practice is the selection of certain physical factors such as geometry, loading, boundary conditions, and material properties. In reality these data are more or less uncertain. In many engineering problems this uncertainty should be taken into consideration. Fuzzy set theory allows to determine randomness model response to the external loading. Two methods extension principle and α-level optimization are presented and compared in this paper. Advantages and disadvantages of these approaches are discussed on example of mapping function. Next the extension principle and α-level optimization are applied to the analysis of stresses in the bar made of elastic-plastic material subjected to uniaxial tension. The yield stress and hardening modulus are fuzzy variables. The influence of fuzziness of numerical procedure (large integration step) to the result space is also discussed. The main part of this paper is the investigation of influence of selected fuzzy parameters of Bodner-Partom material model to stress analysis in the stretched bar. BP material model allows to take into consideration elastic and plastic material properties, isotropic and kinematic hardening, visco-plastic effects, as well as creep and relaxation. The proper response of the material to external loading requires the correct selection of fourteen material constants. The experimental determination of these data is problematic, and gives imprecise results. The increase of accuracy of BP material parameters may be achieved by application of optimization procedures or genetic algorithms. In this research for the first time the fuzzy sets theory is applied to accomplish this goal.