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On accelerated symmetric stiffness techniques for non‐associated plasticity with application to soil problems

Xi Chen (Department of Geotechnical and Geoenvironmental Engineering, Beijing Jiaotong University, Beijing, China)
Yong‐Gang Cheng (College of Water Resources and Hydroelectric Engineering, Wuhan University, Wuhan, China)

Engineering Computations

ISSN: 0264-4401

Article publication date: 15 November 2011

Abstract

Purpose

The initial stiffness method has been extensively adopted for elasto‐plastic finite element analysis. The main problem associated with the initial stiffness method, however, is its slow convergence, even when it is used in conjunction with acceleration techniques. The Newton‐Raphson method has a rapid convergence rate, but its implementation resorts to non‐symmetric linear solvers, and hence the memory requirement may be high. The purpose of this paper is to develop more advanced solution techniques which may overcome the above problems associated with the initial stiffness method and the Newton‐Raphson method.

Design/methodology/approach

In this work, the accelerated symmetric stiffness matrix methods, which cover the accelerated initial stiffness methods as special cases, are proposed for non‐associated plasticity. Within the computational framework for the accelerated symmetric stiffness matrix techniques, some symmetric stiffness matrix candidates are investigated and evaluated.

Findings

Numerical results indicate that for the accelerated symmetric stiffness methods, the elasto‐plastic constitutive matrix, which is constructed by mapping the yield surface of the equivalent material to the plastic potential surface, appears to be appealing. Even when combined with the Krylov iterative solver using a loose convergence criterion, they may still provide good nonlinear convergence rates.

Originality/value

Compared to the work by Sloan et al., the novelty of this study is that a symmetric stiffness matrix is proposed to be used in conjunction with acceleration schemes and it is shown to be more appealing; it is assembled from the elasto‐plastic constitutive matrix by mapping the yield surface of the equivalent material to the plastic potential surface. The advantage of combining the proposed accelerated symmetric stiffness techniques with the Krylov subspace iterative methods for large‐scale applications is also emphasized.

Keywords

Citation

Chen, X. and Cheng, Y. (2011), "On accelerated symmetric stiffness techniques for non‐associated plasticity with application to soil problems", Engineering Computations, Vol. 28 No. 8, pp. 1044-1063. https://doi.org/10.1108/02644401111179027

Publisher

:

Emerald Group Publishing Limited

Copyright © 2011, Emerald Group Publishing Limited