Research on Fuzzy Plastic Constitutive Model Based on Membership Function

Xigang Wang,Liling Jin,Mingfu Fu,Lei Hou

doi:10.1155/2021/9901948

Abstract

Soil has no obvious yield point, and the classical elastoplastic theory contradicts the uncertainty of the plastic yield point of the soil. Therefore, a fuzzy plastic Cambridge model based on the membership function was designed by combining the fuzzy mathematics with the Cambridge model. This model made the plastic membership function to correspond with the fuzzy yield function. The plastic strain at any stress state was calculated using the fuzzy Cambridge model and was compared with the indoor triaxial test results, and they were in good agreement. Therefore, it is appropriate to use fuzzy mathematics to express the unobvious soil yield property. The characteristics of soil yield in any stress state is reflected by the fuzzy plastic theory, which indicates that there is entirely no elasticity at any stress state. Moreover, the varying degrees of plasticity and the degree of plastic yield were uniquely determined by the plastic membership function. The fuzzy plastic model used the membership function change to replace the complex hardening. Additionally, the cyclic loading path was clear and appropriate for the cyclic loading and unloading calculations.

Highlights

E stress point, presented in Figure 1, produced only elastic strain. e plastic strain occurred in accordance with the hardening rule only when the stress point reached the yield line f(p, q, εpv ) 0. e technique to reflect the plastic strain at any point in the elastic region depicted in Figure 1 is a problem that needs to be solved. e stress state within the yield surface did not produce plastic strain to solve this problem Hashiguch [1] proposed a lower load surface concept
Dafalias [2,3,4] proposed a boundary surface model to calculate the plasticity in the initial yield surface
Jiang [6] analyzed the fuzzy factors in elastoplastic mechanics and explained the ambiguity of the yield and failure criterion of concrete materials

Summary

Critical state line Initial yield surface

Provided a general method for transforming the plastic model into a fuzzy plastic model. Based on the movable hardening criterion of the hardening center and boundary surface, Yao [20] described the anisotropy of soil caused by cyclic loading. He proposed a detailed plastic modulus interpolation method that enabled the model to accurately describe the cyclic stability of saturated clay under low stress levels. E fuzzy plastic Cambridge model is used to describe the fuzziness of the soil yield and solve the problems of cyclic loading and unloading. E continuous change in the plastic membership function can replace the complicated hardening law; the fuzzy plastic model is more suitable for cyclic loading and unloading problems. To make the stress points in the elastic region meet the corresponding q

Critical state line Initial yield surface Fuzzy yield surface

Findings

Fuzzy yield surface Fuzzy yield surface