Semi-implicit finite strain constitutive integration of porous plasticity models

P. Areias, T. Rabczuk, J. César De Sá

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)


Abstract Two porous plasticity models, Rousselier and Gurson-Tvergaard-Needleman (GTN), are integrated with a new semi-implicit integration algorithm for finite strain plasticity. It consists of using relative Green-Lagrange during the iteration process and incremental frame updating corresponding to a polar decomposition. Lowdin's method of orthogonalization is adopted to ensure incremental frame-invariance. In addition, a smooth replacement of the complementarity condition is used. Since porous models are known to be difficult to integrate due to the combined effect of void fraction growth, stress and effective plastic strain evolution, we perform a complete assessment of our semi-implicit algorithm. Semi-implicit algorithms take advantage of different evolution rates to enhance the robustness in difficult to converge problems. A detailed description of the constitutive algorithm is performed, with the key components comprehensively exposed. In addition to the fully detailed constitutive algorithms, we use mixed finite strain elements based on Arnold's MINI formulation. This formulation passes the inf-sup test and allows a direct application with porous models. Isoerror maps for two common initial stress states are shown. In addition, we extensively test the two models with established benchmarks. Specifically, the cylindrical tension test as well as the butterfly shear specimen are adopted for validation. A 3D tension test is used to investigate mesh dependence and the effect of a length scale. Results show remarkable robustness.

Original languageEnglish
Article number2997
Pages (from-to)41-55
Number of pages15
JournalFinite Elements in Analysis and Design
Publication statusPublished - 2015 Jun 13
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2015 Elsevier B.V.

Copyright 2015 Elsevier B.V., All rights reserved.


  • Constitutive integration
  • Finite strains
  • Löwdin's method
  • Porous plasticity
  • Semi-implicit

ASJC Scopus subject areas

  • Analysis
  • General Engineering
  • Computer Graphics and Computer-Aided Design
  • Applied Mathematics


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