Cam-Clay plasticity, Part IV: Implicit integration of anisotropic bounding surface model with nonlinear hyperelasticity and ellipsoidal loading function

Abstract

This paper describes a fully implicit stress-point integration algorithm for a class of anisotropic bounding surface plasticity models with ellipsoidal loading function. The plasticity model is coupled with a nonlinear hyperelastic model to ensure that the elastic component of the combined model is energy-conserving. A key feature of the integration algorithm for the combined model is a return mapping in strain space, which allows fully implicit integration and consistent linearization of the constitutive equations. For this class of bounding surface models the consistency condition on the bounding surface is shown to be mathematically equivalent to the consistency condition on the loading surface, thus allowing practically all attributes of the standard return mapping algorithm of classical plasticity theory to be carried over to the bounding surface theory with little modification. As a specific example, the infinitesimal version of modified Cam-Clay theory is used to represent the bounding surface model, and an exponential function is used to interpolate the plastic modulus on the loading surface. Isoerror maps are generated describing the accuracy of the integration algorithm on the stress-point level. Finally, a boundary-value problem involving a strip footing on lightly overconsolidated clay is analyzed to demonstrate the robustness of the algorithm in a finite element setting.