Modified cam clay bounding surface hyper-viscoplastic model

Abstract

Clays exhibit complex mechanical behaviour with significant viscous, nonlinear, and hysteric characteristics, beyond the prediction capacity of the well-known modified cam clay (MCC) model. This paper extends the MCC model to address these important limitations. The proposed family of models is constructed entirely within the hyperplasticity framework deduced from thermodynamic extremal principles. More specifically, the previously developed MCC hyper-viscoplastic model based on the isotache concept is extended to incorporate multiple internal variables and to capture recent loading history, hysteresis, and smooth response of the material. This is achieved by defining an inelastic free energy and an element that implements a bounding surface within hyperplasticity, resulting in pressure dependency in both reversible and irreversible processes with a unique critical state envelope, and only eight material parameters with a readily measurable viscous parameter. A kinematic hardening in the logistic differential form in stress space is derived that enables the proposed model to function effectively across a wide range of stresses. Based on this kinematic hardening rule, the current stress state acts as an asymptotic attractor for the back/shift stresses whose evolution rates are proportional to their current state.