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The anisotropic elasto-plastic analysis using a natural neighbour RPIM version

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Abstract

In this work, the natural neighbour radial point interpolation method (NNRPIM), an advanced discretization meshless technique, is used to study several solid mechanics benchmark examples considering an elasto-plastic approach. The NNRPIM combines the radial point interpolators (RPI) with the natural neighbour geometric concept. The nodal connectivity and the background integration mesh depend entirely on the nodal discretization and are both achieved using mathematic concepts, such as the Voronoï diagram and the Delaunay tessellation. The obtained interpolation functions, used in the Galerkin weak form, are constructed with the RPI and possess the delta Kronecker property, which facilitates the imposition of the natural and essential boundary conditions. Due to the organic procedure employed to impose the nodal connectivity, the obtained displacement and the stress field are smooth and accurate. Since the scope of this work is to extend and validate the NNRPIM in the anisotropic elasto-plastic analysis, it is used as nonlinear solution algorithm, the modified Newton–Raphson initial stiffness method. The efficient “backward-Euler” procedure is considered to return the stress to the Hill anisotropic yield surface. The elasto-plastic algorithm of solution is described. Several benchmark two-dimensional problems are solved, considering anisotropic elasto-plastic materials with anisotropic hardening, and the obtained solutions are compared with finite-element solutions, showing that the meshless approach developed is efficient and accurate.

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Acknowledgments

The authors truly acknowledge the funding provided by Ministério da Educação e Ciência,—Fundação para a Ciência e a Tecnologia (Portugal), under Grant SFRH/BPD/75072/2010 and SFRH/BPD/111020/2015, and by project funding UID/EMS/50022/2013 (funding provided by the inter-institutional projects from LAETA). Additionally, the authors gratefully acknowledge the funding of Project NORTE-01-0145-FEDER-000022—SciTech—Science and Technology for Competitive and Sustainable Industries, co-financed by Programa Operacional Regional do Norte (NORTE2020), through Fundo Europeu de Desenvolvimento Regional (FEDER).

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Authors and Affiliations

  1. INEGI, Institute of Mechanical Engineering and Industrial Management, Rua Dr. Roberto Frias, 4200-465, Porto, Portugal

    S. F. Moreira & J. Belinha

  2. Faculty of Engineering of the University of Porto, FEUP, Rua Dr. Roberto Frias, 4200-465, Porto, Portugal

    L. M. J. S. Dinis & R. M. Natal Jorge

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  1. S. F. Moreira
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  2. J. Belinha
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  3. L. M. J. S. Dinis
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  4. R. M. Natal Jorge
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Correspondence to J. Belinha.

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Techniccal Editor: Eduardo Alberto Fancello.

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Moreira, S.F., Belinha, J., Dinis, L.M.J.S. et al. The anisotropic elasto-plastic analysis using a natural neighbour RPIM version. J Braz. Soc. Mech. Sci. Eng. 39, 1773–1795 (2017). https://doi.org/10.1007/s40430-016-0603-x

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