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Complete geometric representation of yield surfaces for porous ductile media by a 3D computational homogenization approach: an assessment of the Gurson yield criterion

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Abstract

The analytical criterion proposed by Gurson is an important reference for modeling the plastic behavior of porous ductile media. However, the Gurson model assumes a simplified representative porous cell, whose morphology is formed by a ductile spherical matrix with a centered spherical void. Other limitations of this model are related to: (i) the simplified trial velocity field adopted; (ii) the disregard of the Lode angle effect due to a linearization of the microscopic dissipation. In this context, the present article explores a 3D computational homogenization approach to fill a gap in the complete geometric representation of isotropic yield surfaces of porous ductile media, relaxing the previous mentioned simplifications. A large number of numerical simulations in finite elements were carefully performed aiming to create full yield surfaces. In particular, the influence of the void morphology inserted in the ductile matrix is addressed, considering two representative volume elements (RVEs): (i) cube with a spherical void; (ii) cube with a cubic void. Spherical and cubic voids are interesting because the yield surfaces may provide reference limits for other voids with similar morphology. It is worth mentioning that the strategy allows us to investigate in detail the effect of the Lode angle on the geometry of full yield surfaces. The kinematic field provided by the numerical simulations also allows a better description of the yield surfaces for low triaxialities compared to Gurson simplified trial velocity field. The ductile matrix is governed by the von Mises model with perfect elasto-plastic behavior. Small strain hypothesis is used in the numerical analyses. The main findings are as follows. The strength of the RVE with a cubic void is lower compared to the RVE with a spherical void, especially for intermediate/high triaxialities. The Lode angle has a strong influence on the geometry of yield surfaces for intermediate triaxialities. Furthermore, yield surfaces by computational homogenization have significant differences compared to the Gurson criterion.

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Acknowledgements

The authors would like to gratefully acknowledge Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) and Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES) for the research grants.

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  1. Department of Structural Engineering, Sao Carlos School of Engineering, University of Sao Paulo, Av. Trab. Sao Carlense, Sao Carlos, Sao Paulo, 13566-590, Brazil

    Wanderson Ferreira dos Santos, Ayrton Ribeiro Ferreira & Sergio Persival Baroncini Proença

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  1. Wanderson Ferreira dos Santos
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  2. Ayrton Ribeiro Ferreira
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  3. Sergio Persival Baroncini Proença
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Correspondence to Wanderson Ferreira dos Santos.

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Technical Editor: Joao Marciano Laredo dos Reis.

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dos Santos, W.F., Ferreira, A.R. & Proença, S.P.B. Complete geometric representation of yield surfaces for porous ductile media by a 3D computational homogenization approach: an assessment of the Gurson yield criterion. J Braz. Soc. Mech. Sci. Eng. 44, 163 (2022). https://doi.org/10.1007/s40430-022-03483-1

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