Cam-Clay plasticity, part I: implicit integration of elastoplastic constitutive relations

Abstract Two stress integration algorithms based on implicit calculation of plastic strain are implemented and tested for the modified Cam-Clay plasticity model. The integration rules fall under the category of return mapping algorithms in which the return directions are computed by closest point projection for associative flow rule and by central return mapping for non-associative flow rule applied to the Cam-Clay ellipsoids. Stress updates take place at the Gauss points upon enforcement of the consistency condition in which the appropriate consistency parameters are determined iteratively on the scalar level. Numerical examples with geotechnical applications, which include an analysis of foundation bearing capacity and an investigation of deformations in vertical cuts, are discussed to demonstrate the global accuracy and stability of the numerical solution. The relationships among various return mapping schemes are discussed in the context of both associative and non-associative flow rule formulations.

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