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Isotropic yield surfaces for porous ductile materials: complete geometric representation by a computational homogenisation procedure

Wanderson Ferreira dos Santos (Department of Structural Engineering, Sao Carlos School of Engineering, University of Sao Paulo, Sao Carlos, Brazil)
Ayrton Ribeiro Ferreira (Department of Structural Engineering, Sao Carlos School of Engineering, University of Sao Paulo, Sao Carlos, Brazil)
Sergio Persival Baroncini Proença (Department of Structural Engineering, Sao Carlos School of Engineering, University of Sao Paulo, Sao Carlos, Brazil)

Engineering Computations

ISSN: 0264-4401

Article publication date: 27 April 2023

Issue publication date: 15 June 2023

367

Abstract

Purpose

The present paper aims to explore a computational homogenisation procedure to investigate the full geometric representation of yield surfaces for isotropic porous ductile media. The effects of cell morphology and imposed boundary conditions are assessed. The sensitivity of the yield surfaces to the Lode angle is also investigated in detail.

Design/methodology/approach

The microscale of the material is modelled by the concept of Representative Volume Element (RVE) or unit cell, which is numerically simulated through three-dimensional finite element analyses. Numerous loading conditions are considered to create complete yield surfaces encompassing high, intermediate and low triaxialities. The influence of cell morphology on the yield surfaces is assessed considering a spherical cell with spherical void and a cubic RVE with spherical void, both under uniform strain boundary condition. The use of spherical cell is interesting as preferential directions in the effective behaviour are avoided. The periodic boundary condition, which favours strain localization, is imposed on the cubic RVE to compare the results. Small strains are assumed and the cell matrix is considered as a perfect elasto-plastic material following the von Mises yield criterion.

Findings

Different morphologies for the cell imply in different yield conditions for the same load situations. The yield surfaces in correspondence to periodic boundary condition show significant differences compared to those obtained by imposing uniform strain boundary condition. The stress Lode angle has a strong influence on the geometry of the yield surfaces considering low and intermediate triaxialities.

Originality/value

The exhaustive computational study of the effects of cell morphologies and imposed boundary conditions fills a gap in the full representation of the flow surfaces. The homogenisation-based strategy allows us to further investigate the influence of the Lode angle on the yield surfaces.

Keywords

Acknowledgements

The authors would like to gratefully acknowledge the Conselho Nacional de Desenvolvimento Científico e Tecnológico - Brasil (CNPq) for the research grants. This study was also financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES) - Finance Code 001.

Citation

Santos, W.F.d., Ferreira, A.R. and Proença, S.P.B. (2023), "Isotropic yield surfaces for porous ductile materials: complete geometric representation by a computational homogenisation procedure", Engineering Computations, Vol. 40 No. 4, pp. 737-771. https://doi.org/10.1108/EC-12-2021-0718

Publisher

:

Emerald Publishing Limited

Copyright © 2023, Emerald Publishing Limited

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