Modified Сam-clay model. Theoretical foundations and numerical analysis

State equations and principle assumptions of a modified cam-clay model are analyzed. It is assumed that the modified cam-clay model is related to the plasticity models described by the isotropic hardening rules and closed yield surfaces. Equations of state in the elastic zone, along with models related to the hyperelastic equations of state with the exponential potential, are considered. Some generalizations of the modified cam-clay model for finite strains are performed. Works associated with the problems regarding calibration of theoretical modified cam-clay models with experimental data are reviewed. The first Clay-clay model with logarithmic surface plasticity in the critical zone was constructed in [1, 2]. Later on, the logarithmic surface plasticity was replaced by ellipsoidal one. This model is also called a modified Cam-clay model. The Cam-clay model and its modified variant belong to a class of the elastic-plastic models with isotropic hardening. It should be noted that there are also some modifications of the Cam-clay models, which take into account the possibility of modeling the Bauschinger effect by shifting surface plasticity using a combination of isotropic and kinematic hardening rules. There are a considerable number of works, in which the Cam-clay model and its modifications are used to study the behavior of various granular materials with low cohesion under monotonic or cyclic force loadings. Most of these works are devoted to uniaxial or triaxial force loading. This paper deals with analyzing the behavior of the modified Cam-Clay model under combined kinematic loadings.