A Newton-Krylov-based implicit integration algorithm for single and multisurface plasticity

•Development of a Jacobian-free Newton-Krylov algorithm for implicit plasticity model integration.•Smooth complementary functions implemented to enforce Karush-Kuhn-Tucker conditions.•Application to single and multisurface plasticity under various stress states.•Efficient scheme eliminating the need...

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Published in:Computers & structures Vol. 316; p. 107872
Main Authors: Abreu, Rafael, Mejia, Cristian, Roehl, Deane
Format: Journal Article
Language:English
Published: Elsevier Ltd 01.09.2025
Subjects:
Computational plasticity
Implicit integration
Jacobian-Free Newton-Krylov method
Multisurface plasticity
Smooth complementary functions
Smooth complementary functions
Computational plasticity
Implicit integration
Jacobian-Free Newton-Krylov method
Multisurface plasticity
ISSN:0045-7949
Online Access:Get full text
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Abstract •Development of a Jacobian-free Newton-Krylov algorithm for implicit plasticity model integration.•Smooth complementary functions implemented to enforce Karush-Kuhn-Tucker conditions.•Application to single and multisurface plasticity under various stress states.•Efficient scheme eliminating the need for Jacobian matrices in complex plasticity models. Robust integration schemes for plasticity models allow accurate and efficient numerical simulations of materials such as metals, concrete, soils, and rocks. The Newton-Raphson method is a popular choice for solving systems of nonlinear equations in the context of plasticity problems. However, this method requires calculating the Jacobian matrix of the system of equations defined by the flow rule, the hardening/softening law, and the Karush-Kuhn-Tucker conditions. This task can be cumbersome, especially for complex and multisurface plasticity models. Therefore, this work proposes a novel numerical implicit integration scheme for multisurface plasticity based on a Jacobian-free Newton-Krylov method. Notably, the Karush-Kuhn-Tucker conditions are implemented based on well-established smooth complementary functions to consider multiple yield surfaces properly. The proposed algorithm is vastly versatile since it can be easily applied to diverse single and multisurface models under different stress conditions, including the plane stress condition. The computational efficiency of the proposed method is compared to other common integration schemes, focusing on evaluating different smooth complementary functions. The results highlight the effectiveness of the Jacobian-free Newton-Krylov method for integrating multisurface plasticity equations and its ability to handle challenging finite element problems.
AbstractList •Development of a Jacobian-free Newton-Krylov algorithm for implicit plasticity model integration.•Smooth complementary functions implemented to enforce Karush-Kuhn-Tucker conditions.•Application to single and multisurface plasticity under various stress states.•Efficient scheme eliminating the need for Jacobian matrices in complex plasticity models. Robust integration schemes for plasticity models allow accurate and efficient numerical simulations of materials such as metals, concrete, soils, and rocks. The Newton-Raphson method is a popular choice for solving systems of nonlinear equations in the context of plasticity problems. However, this method requires calculating the Jacobian matrix of the system of equations defined by the flow rule, the hardening/softening law, and the Karush-Kuhn-Tucker conditions. This task can be cumbersome, especially for complex and multisurface plasticity models. Therefore, this work proposes a novel numerical implicit integration scheme for multisurface plasticity based on a Jacobian-free Newton-Krylov method. Notably, the Karush-Kuhn-Tucker conditions are implemented based on well-established smooth complementary functions to consider multiple yield surfaces properly. The proposed algorithm is vastly versatile since it can be easily applied to diverse single and multisurface models under different stress conditions, including the plane stress condition. The computational efficiency of the proposed method is compared to other common integration schemes, focusing on evaluating different smooth complementary functions. The results highlight the effectiveness of the Jacobian-free Newton-Krylov method for integrating multisurface plasticity equations and its ability to handle challenging finite element problems.
ArticleNumber 107872
Author Roehl, Deane
Mejia, Cristian
Abreu, Rafael
Author_xml – sequence: 1
  givenname: Rafael
  orcidid: 0000-0002-6885-2571
  surname: Abreu
  fullname: Abreu, Rafael
  email: rafaeloabreu@tecgraf.puc-rio.br
  organization: Department of Civil Engineering, State University of Maranhão, University City Paulo VI, 1000 Lourenço Vieira da Silva Avenue, Jardim São Cristóvão, 65055-310 São Luís, MA, Brazil
– sequence: 2
  givenname: Cristian
  orcidid: 0000-0002-3803-7592
  surname: Mejia
  fullname: Mejia, Cristian
  email: crisms@tecgraf.puc-rio.br
  organization: Tecgraf Institute/PUC-Rio, 225 Marquês de São Vicente Street, Gávea, 22451-900 Rio de Janeiro, RJ, Brazil
– sequence: 3
  givenname: Deane
  orcidid: 0000-0003-4644-120X
  surname: Roehl
  fullname: Roehl, Deane
  email: droehl@puc-rio.br
  organization: Department of Civil and Environmental Engineering, Pontifical Catholic University of Rio de Janeiro, 225 Marquês de São Vicente Street, Gávea, 22451-900 Rio de Janeiro, RJ, Brazil
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Keywords Smooth complementary functions
Computational plasticity
Implicit integration
Jacobian-Free Newton-Krylov method
Multisurface plasticity
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Snippet •Development of a Jacobian-free Newton-Krylov algorithm for implicit plasticity model integration.•Smooth complementary functions implemented to enforce...
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StartPage 107872
SubjectTerms Computational plasticity
Implicit integration
Jacobian-Free Newton-Krylov method
Multisurface plasticity
Smooth complementary functions
Title A Newton-Krylov-based implicit integration algorithm for single and multisurface plasticity
URI https://dx.doi.org/10.1016/j.compstruc.2025.107872
Volume 316
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