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Vicente da Silva, M., and A. N. Antão. "Three-dimensional Limit Analysis using the Extended-Matsuoka–Nakai yield criterion." Computers and Geotechnics. 161 (2023): 105526. AbstractWebsite

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.

Santana, T., Vicente M. da Silva, Nunes A. Antão, and N. M. C. Guerra Two dimensional upper and lower-bound numerical analysis of the basal stability of deep excavations in clay. Pro eedings of the 9 th European Conference on Numerical Methods in Geotechnical Engineering (NUMGE 2018). Porto, 2018.
Antão, A. N., and M. Vicente da Silva. "Three-dimensional Limit Analysis with Lade-Duncan criterion." Géotechnique Letters. 12 (2022): 1-21. AbstractWebsite

The paper describes the three-dimensional numerical implementation of the Lade-Duncan criterion in a finite element limit analysis (FELA) code. Validation is done using examples with a known solution. To conclude the proposed numerical tool is applied to the calculation of the ultimate bearing capacity of square footing.

Antão, Nunes A., T. Santana, Vicente M. da Silva, and Costa N. M. da Guerra. "Three-dimensional active earth pressure coefficients by upper bound numerical limit analysis." Computers and Geotechnics. 79 (2016): 96-104.