Object Oriented Nonlinear Finite Element analysis Framework for Implementing modified cam Clay Model

Abstract

Cam clay and modified Cam clay models are most widely used plasticity based constitutive models in soil mechanics. Finite element method is a powerful numerical tool which can model many complex conditions and popularly used to analyze geotechnical engineering problems. Traditionally procedure oriented programing, particularly in FORTRAN or C, has been used but recently object-oriented programming has gained wide attention and used by many investigators to develop finite element framework. In this present work an object-oriented finite element analysis framework for modified Cam clay model has been developed using C++ as programming language. In this framework, the whole finite element analysis class is divided into separate component classes to perform various tasks. Extensions to the design are presented in terms of inclusion of new integration algorithms for an existing constitutive model, inclusion of new constitutive models and inclusion of different nonlinear solution techniques and load stepping schemes with an existing integration algorithm of a constitutive model. In this study, firstly, an implicit integration algorithm for modified Cam clay model incorporating nonlinear elasticity is presented. The proposed implicit stress integration algorithm for the modified Cam clay model is based on the return mapping algorithm by making use of the both first order forward Euler scheme and the backward Euler scheme, considering associative flow rule. Secondly, some of the nonlinear solution techniques and load stepping schemes are presented and implemented with the modified Cam clay model. Their performances in some practical geomechanics problems are compared in terms of solution accuracy, number of global iteration and CPU time required to run the program. Thirdly, the context of interpreting the descretized form of the principle of virtual displacement and the ordinary differential equations of the constitutive model together as a system of differential. newline