Three-dimensional Limit Analysis using the Extended-Matsuoka–Nakai yield criterion

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This paper investigates the implementation of the Extended-Matsuoka–Nakai yield criterion on a strict Limit Analysis finite element formulation. The current approach is based on a three-field mixed finite element model and the Alternating Direction Method of Multipliers optimization algorithm. With the support of duality principles two variants are derived, the lower bound and the upper bound element. The main novelty of this work is the development of an efficient iterative predictor–corrector scheme, customized for the Extended-Matsuoka–Nakai. This scheme is an indispensable requirement for this formulation. To conclude four numerical examples are presented to assess the effectiveness and efficiency of the numerical tool.
Original languageEnglish
Article number105526
Number of pages13
JournalComputers and Geotechnics
Publication statusPublished - Sept 2023


  • Alternating Direction Method of Multipliers (ADMM)
  • Extended-Matsuoka–Nakai criterion
  • Limit Analysis
  • Non-conventional finite elements


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