Title: Tangent modulus in numerical integration of constitutive relations and its influence on convergence of N-R method
Authors: Halama, Radim
Poruba, Zdeněk
Citation: Applied and Computational Mechanics. 2009, vol. 3, no. 1, p. 27-38.
Issue Date: 2009
Publisher: University of West Bohemia
Document type: článek
URI: http://www.kme.zcu.cz/acm/old_acm/full_papers/acm_vol3no1_p03.pdf
ISSN: 1802-680X (Print)
2336-1182 (Online)
Keywords: plastická deformace;mechanické napětí;simulace a modelování;metoda konečných prvků
Keywords in different language: plastic deformation;mechanical stress;simulation and modelling;finite element method
Abstract: For the numerical solution of elasto-plastic problems with use of Newton-Raphson method in global equilibrium equation it is necessary to determine the tangent modulus in each integration point. To reach the parabolic convergence of Newton-Raphson method it is convenient to use so called algorithmic tangent modulus which is consistent with used integration scheme. For more simple models for example Chaboche combined hardening model it is possible to determine it in analytical way. In case of more robust macroscopic models it is in many cases necessary to use the approximation approach. This possibility is presented in this contribution for radial return method on Chaboche model. An example solved in software Ansys corresponds to line contact problem with assumption of Coulomb’s friction. The study shows at the end that the number of iteration of N-R method is higher in case of continuum tangent modulus and many times higher with use of modified N-R method, initial stiffness method.
Rights: © 2009 University of West Bohemia. All rights reserved.
Appears in Collections:Volume 3, number 1 (2009)
Volume 3, number 1 (2009)

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