Formulations for incremental elastic-plastic analysis and the consolidation of porous media

• Main Author: Bird, Wyndham Wadham
• Other Authors: Martin, JB
• Format: Doctoral Thesis
• Language: English
• Published: University of Cape Town 2014
• Subjects: Civil Engineering
• Online Access: http://hdl.handle.net/11427/7583

Includes bibliographical references. === The formulation and solution of the problem of an elastic-plastic body subject to successive increments of loading is a fundamental problem in plasticity. A variety of powerful iterative techniques are available for the solution of the problem, mostly based on Newton-Raphson methods using an explicit scheme for the integration of the constitutive relations. The procedures in current use can be criticised in that they are essentially heuristic, and they are not fully linked to the governing mechanical principles of the incremental plasticity problem. Recent work aimed at the improvement of the accuracy and stability of the numerical algorithms in plasticity explores the fundamental relationship between the nature of the forward integration algorithm and the mechanical principles of the problem. In this thesis we attempt to advance this understanding. Through the use of an internal variable formulation of the problem, we are able to explore links between a consistent mathematical programming formulation of the incremental problem in plasticity and the conventional Newton-Raphson iterative solution procedures.