Reconstruction of Cam-clay model based on multiplicative decomposition of the deformation gradient

Abstract

This study formulated the Cam-clay model, an elastoplastic constitutive model for fully remolded and normally consolidated clay, using the multiplicative decomposition of the deformation gradient and a hyperelastic body to correspond to the finite deformation theory. Finite deformation elastoplastic theory in this framework has been developed for metallic materials that do not yield plastic volume change. If this theory is directly applied to a model that yields plastic volume change, the Cauchy stress cannot be determined only from the current elastic deformation. Therefore, the existing multiplicative decomposition Cam-clay models cannot accurately reproduce the experimental facts underlying the core of critical-state soil mechanics. Through thermodynamic considerations that consider the volume changes occurring in the intermediate configuration, this study determined a common stress suitable for describing the elastic and plastic components, in addition to forms of hyperelastic body and plastic flow rule. Consequently, the proposed model can draw the state boundary surface in the Cauchy stress-specific volume space, which previous models could not achieve. In addition, an implicit stress-update algorithm for the proposed model was constructed, and a tangent modulus consistent with the algorithm was derived. The proposed model demonstrated the same numerical calculation convergence as that of existing models.