Nonlinear Solution Techniques and Load Stepping Schemes for Modified Cam Clay Model

Critical state models are developed from the application of plasticity to soil mechanics and they are the most widely used soil constitutive model. The model is highly nonlinear in nature and in finite element analysis, with a nonlinear material model; an iterative and incremental scheme is required to solve the resulting system of nonlinear equations. Variety of incremental and iterative schemes are developed in the past to integrate the load-displacement curve for nonlinear material models and each of them has advantages and limitations over other while using with a specific constitutive model. As critical state models are nonlinear in nature in the elastic as well as plastic parts of the constitutive relation, the performance of different load stepping schemes for finite element analysis particularly with critical state models is to be done and can be an active area of study.  In the present study the review of the literature on the use of various nonlinear solution techniques and load stepping schemes used for general plasticity models and critical state soil constitutive models are carried out. It is observed that very little literature is available which study the influence of the nonlinear solution techniques and load stepping schemes on the solution of nonlinear finite element problems with critical state models. From the available literature it can be concluded that critical state models are very sensitive to the load step size and iteration tolerance as well.  A comparative study on the performance of some of the mostly used nonlinear solution techniques and load stepping schemes with modified cam clay model is also carried out.  The solution schemes which are included in the study are: Newton-Raphson methos, Modified Newton-Raphson methos, Accelerated modified Newton-Raphson methods and Arclength method. The study reveals that the performance of Arclength method as compared to other methods is better while using them with modified cam clay model.