Yield Function and Hardening Law

The yield function f( r,K) is classified into several hardening models depending on the history of loading  

We illustrate the isotropic and kinematic hardening models for the onedimensional problem in Fig. 2.18a, b, and for the two dimensional problem in Fig. 2.19. Note that the behavior shown in Fig. 2.18b is known as the Bauschinger effect. In geotechnical engineering practice the isotropic hardening model is widely used because, except in earthquake situations, it is rare that the loading direction is completely reversed. 

The stress-dependent part of the yield function has been widely investigated using experimental methods. We summarize the results for the case of the isotropic 

The original Cam clay model employs isotropic hardening with strain hardening such as 

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