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Arbitrary order 2D virtual elements for polygonal meshes: part II, inelastic problem

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Abstract

The present paper is the second part of a twofold work, whose first part is reported in Artioli et al. (Comput Mech, 2017. doi:10.1007/s00466-017-1404-5), concerning a newly developed Virtual element method (VEM) for 2D continuum problems. The first part of the work proposed a study for linear elastic problem. The aim of this part is to explore the features of the VEM formulation when material nonlinearity is considered, showing that the accuracy and easiness of implementation discovered in the analysis inherent to the first part of the work are still retained. Three different nonlinear constitutive laws are considered in the VEM formulation. In particular, the generalized viscoelastic model, the classical Mises plasticity with isotropic/kinematic hardening and a shape memory alloy constitutive law are implemented. The versatility with respect to all the considered nonlinear material constitutive laws is demonstrated through several numerical examples, also remarking that the proposed 2D VEM formulation can be straightforwardly implemented as in a standard nonlinear structural finite element method framework.

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Notes

  1. In the following, the space of symmetric traceless second-order tensors is denoted by \({{\mathrm{\mathrm {SymDev}}}}\).

  2. Note that, in the case \(k=1\), a single Gauss point for the whole polygon (for instance at the centroid of the element) is sufficient, see [45].

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Acknowledgements

The first author gratefully acknowledges the partial financial support of the Italian Minister of University and Research, MIUR (Program: Consolidate the Foundations 2015; Project: BIOART; Grant no. (CUP): E82F16000850005). The second and third authors were partially supported by IMATI-CNR of Pavia, Italy. This support is gratefully acknowledged

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Authors and Affiliations

  1. Department of Civil Engineering and Computer Science, University of Rome Tor Vergata, Via del Politecnico 1, 00133, Rome, Italy

    E. Artioli

  2. Department of Mathematics and Applications, University of Milan Bicocca, Via Roberto Cozzi 55, 20125, Milan, Italy

    L. Beirão da Veiga

  3. Department of Mathematics, University of Milano, Via Cesare Saldini 50, 20133, Milano, Italy

    C. Lovadina

  4. Civil Engineering and Mechanical Engineering, University of Cassino and Southern Lazio, Via Di Biasio 43, 03043, Cassino, Italy

    E. Sacco

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  1. E. Artioli
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Correspondence to E. Artioli.

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Artioli, E., Beirão da Veiga, L., Lovadina, C. et al. Arbitrary order 2D virtual elements for polygonal meshes: part II, inelastic problem. Comput Mech 60, 643–657 (2017). https://doi.org/10.1007/s00466-017-1429-9

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