Extended virtual element method for elliptic problems with singularities and discontinuities in mechanics

Extended virtual element method for elliptic problems with singularities and discontinuities in mechanics

Andrea CHIOZZI, Elena BENVENUTI, Gianmarco MANZINI N. SUKUMAR

Abstract. Drawing inspiration from the extended finite element method (X-FEM), we propose for two-dimensional elastic fracture problems, an extended virtual element method (X-VEM). In the X-VEM, we extend the standard virtual element space with the product of vector-valued virtual nodal shape functions and suitable enrichment fields, which reproduce the singularities of the exact solution. We define an extended projection operator that maps functions in the extended virtual element space onto a set spanned by the space of linear polynomials augmented with the enrichment fields. Several numerical examples are adopted to illustrate the convergence and accuracy of the proposed method, for both quadrilateral and general polygonal meshes.

Keywords
Virtual Element Method, Extended Finite Element Method, Singularities, Discontinuities

Published online 3/17/2022, 6 pages
Copyright © 2023 by the author(s)
Published under license by Materials Research Forum LLC., Millersville PA, USA

Citation: Andrea CHIOZZI, Elena BENVENUTI, Gianmarco MANZINI N. SUKUMAR, Extended virtual element method for elliptic problems with singularities and discontinuities in mechanics, Materials Research Proceedings, Vol. 26, pp 239-244, 2023

DOI: https://doi.org/10.21741/9781644902431-39

The article was published as article 39 of the book Theoretical and Applied Mechanics

Content from this work may be used under the terms of the Creative Commons Attribution 3.0 license. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.

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