Plasticity Theory Based on Fuzzy Sets

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Abstract
This paper presents a general theory that describes the cyclic loading behavior of different materials. It is mathematically based on the theory of fuzzy sets. From the constitutive modeling point of view it is closely related to many previous cyclic plasticity models. Instead of utilizing two or more yield or bounding surfaces one more general surface is introduced in the space spanned by the stress and a membership function. This concept allows us to define many different models within the same mathematical framework. Several possibilities of the theory are examined with the aid of one‐dimensional examples. The paper considers constitutive models with and without memory, as well as models with fading memory, with isotropic and kinematic hardening, as well as without hardening. The fuzzy‐sets formulation describes different phenomena during cyclic loading such as hysteresis loops, cyclic stabilization effects, smooth elastic‐plastic transition, and so on, which are illustrated with pertinent examples.