Numerical Methods for Implementing the Bounding Surface Plasticity Model for Clays.

Abstract

Abstract : Previous work on the development and numerical implementation of the bound surface plasticity model for clays is discussed. Modifications were made to the hardening relationship to improve the numerical performance in the tensile range. A rate equation for the loading surface was developed. Modifications were made to the invariant description of the bounding surface to avoid numerical difficulties in evaluating the derivatives. The closest point projection method is described for simple and general internal variable plasticity models. The method was developed within the classical plasticity framework and uses the Newton-Raphson method to satisfy the implicit integration of the rate equations and the consistency condition. An explicit treatment of the internal variables is discussed. Application of this method for the bounding surface plasticity model for clays was developed by adding an internal variable and using the rate equation for the loading surface. A new algorithm 'the reduced Newton method' was developed for the bounding surface plasticity model for clays. It involved mapping the stress rate equations, internal variable rate equations and the consistency condition into two nonlinear equations and integrating them with a backwards Euler formula using Newton-Raphson iteration. Comparisons of predictions for a number of sample problems was made using the trapezoidal integration, closest point and reduced Newton methods. 'Exact' solutions for stress points that start on the bounding surface were developed by assigning an arbitrary stress path and calculating the corresponding strains using numerical integration with a tight tolerance. The 'exact' solutions were used to evaluate the effectiveness of the proposed general numerical implementation of the bounding surface method. A standard effective stress interface is proposed for finite element programs that u