Application of Exponential-Based Methods in Integrating the Constitutive Equations with Multicomponent Nonlinear Kinematic Hardening
Publication: Journal of Engineering Mechanics
Volume 136, Issue 12
Abstract
The von-Mises plasticity model, in the small strain regime, along with a class of multicomponent nonlinear kinematic hardening rules is considered. The material is assumed to be stabilized after several load cycles and therefore, isotropic hardening will not be accounted for. Application of exponential-based methods in integrating plasticity equations is provided, which is based on defining an augmented stress vector and using exponential maps to solve a system of quasi-linear differential equations. The solutions obtained by this new technique give very accurate updated stress values that are consistent with the yield surface. The classical forward Euler method is reformulated in details and applied to the multicomponent form of the nonlinear kinematic hardening in order to provide a comparison for the suggested technique. Moreover, a consistent tangent operator for the exponential-based integration strategy and also for the classical forward Euler algorithm is presented. In order to show the robustness and performance of the proposed formulation, an extensive numerical investigation is carried out.
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Published In
Journal of Engineering Mechanics
Volume 136 • Issue 12 • December 2010
Pages: 1502 - 1518
Copyright
© 2010 ASCE.
History
Received: Jan 16, 2010
Accepted: May 24, 2010
Published online: Nov 15, 2010
Published in print: Dec 2010
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