An interior-point algorithm for elastoplasticity

• Published in: International journal for numerical methods in engineering 2007-01, Vol.69 (3), p.592-626
• Main Authors: Krabbenhoft, K., Lyamin, A. V., Sloan, S. W., Wriggers, P.
• Format: Article
• Language: English
• Subjects: Algorithms; Computational techniques; Elastoplasticity; Exact sciences and technology; finite elements; Fundamental areas of phenomenology (including applications); Inelasticity (thermoplasticity, viscoplasticity...); interior-point; Mathematical analysis; Mathematical methods in physics; Mathematical models; optimization; Physics; Plasticity; Programming; Softening; Solid mechanics; Structural and continuum mechanics
• ISSN: 0029-5981; 1097-0207
• DOI: 10.1002/nme.1771

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. Copyright © 2006 John Wiley & Sons, Ltd.