An interior-point algorithm for elastoplasticity

authored by: Kristian Krabbenhoft, A. V. Lyamin, S. W. Sloan, Peter Wriggers
Abstract: The problem of small-deformation, rate-independent elastoplasticity is treated using convex programming theory and algorithms. A finite-step variational formulation is first derived after which the relevant potential is discretized in space and subsequently viewed as the Lagrangian associated with a convex mathematical program. Next, an algorithm, based on the classical primal-dual interior point method, is developed. Several key modifications to the conventional implementation of this algorithm are made to fully exploit the nature of the common elastoplastic boundary value problem. The resulting method is compared to state-of-the-art elastoplastic procedures for which both similarities and differences are found. Finally, a number of examples are solved, demonstrating the capabilities of the algorithm when applied to standard perfect plasticity, hardening multisurface plasticity, and problems involving softening.
Organisation(s): Institute of Mechanics and Computational Mechanics
External Organisation(s): University of Newcastle
Type: Article
Journal: International Journal for Numerical Methods in Engineering
Volume: 69
Pages: 592-626
No. of pages: 35
ISSN: 0029-5981
Publication date: 05.06.2006
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Numerical Analysis, Engineering(all), Applied Mathematics
Electronic version(s): https://doi.org/10.1002/nme.1771 (Access: Unknown)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{0fa7292a255849cba7fd65cc56e18316,
title = "An interior-point algorithm for elastoplasticity",
abstract = "The problem of small-deformation, rate-independent elastoplasticity is treated using convex programming theory and algorithms. A finite-step variational formulation is first derived after which the relevant potential is discretized in space and subsequently viewed as the Lagrangian associated with a convex mathematical program. Next, an algorithm, based on the classical primal-dual interior point method, is developed. Several key modifications to the conventional implementation of this algorithm are made to fully exploit the nature of the common elastoplastic boundary value problem. The resulting method is compared to state-of-the-art elastoplastic procedures for which both similarities and differences are found. Finally, a number of examples are solved, demonstrating the capabilities of the algorithm when applied to standard perfect plasticity, hardening multisurface plasticity, and problems involving softening.",
keywords = "Finite elements, Interior-point, Optimization, Plasticity",
author = "Kristian Krabbenhoft and Lyamin, {A. V.} and Sloan, {S. W.} and Peter Wriggers",
year = "2006",
month = jun,
day = "5",
doi = "10.1002/nme.1771",
language = "English",
volume = "69",
pages = "592--626",
journal = "International Journal for Numerical Methods in Engineering",
issn = "0029-5981",
publisher = "John Wiley and Sons Ltd",
number = "3",
}