Extended virtual element method for elliptic problems with singularities and discontinuities in mechanics
Andrea CHIOZZI, Elena BENVENUTI, Gianmarco MANZINI N. SUKUMARdownload PDF
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.
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
The article was published as article 39 of the book Theoretical and Applied Mechanics
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