Identification of nonlinear membership function for failure of structural material and its application to structural optimization

Abstract The purpose of this paper is the identification and application of fuzzy membership function for material failure. The concept of evolutionary damage in continuum damage mechanics is related with the decision of material failure in fuzzy set theory. The failure phenomenon has a fuzzy nature and the internal state variable which indicates the degree of damage in continuum damage mechanics can be thought as a fuzzy membership function for failure in the structural design of machines such as automobiles, airplanes and ships. The results of the numerical analysis based on continuum damage mechanics, which are verified by the uniaxial tensile test, are introduced to obtain the evolution of the damage variable from which the fuzzy membership function for failure can be derived. An exponential type fuzzy membership function is proposed to represent the fuzziness of material failure from the results of the numerical analysis. In this study, an elastoviscoplastic isotropic damage model of an isotropic hardening material is introduced, and the three bar truss problem is revisited with the proposed fuzzy membership function which is applied to structural optimization.