0202 Virtual Element and related polygonal methods in solid and fluid mechanics applica-tions

  • Peter Wriggers, Liebniz University Hannover
  • Edoardo Artioli
  • Lourenco Beirão da Veiga

The virtual element method was firstly developed by F. Brezzi, L. Beirao da Veiga and coworkers, see [1]. By avoiding the explicit integration of the shape functions that span the discrete space and introducing an innovative construction of the stiffness matrices, the VEM acquires very interesting properties and advantages with respect to more standard Galerkin methods, yet still keeping the same coding complexity.
In the last decade, a vivid development of this new approximation technology took place and it was applied to solid and fluid mechanics problems. The range of application includes prob-lems of mathematics and engineering and is constantly extended to new fields. Among those problems in elasticity for small and inelastic deformations, like elasto-plasticity, see [2], frac-ture mechanics in two and three dimensions. Extensions of the virtual element method to problems of compressible and incompressible nonlinear elasticity and finite plasticity, see [3], are recent as well as applications to contact mechanics, see [4], coupled and multi-scale problems.
Still, despite its rather recent introduction, different and interesting VEM formulations gain increasing interest within the computational mechanics community, for instance with numer-ous applications in the field of nonlinear solid mechanics and porous media flow.
The Invited Session aims at gathering researchers in the engineering and mathematics com-munities active in the VEM field, and welcomes contributions both from the theoretical, applic-ative and computational point of view, and is intended as a fruitful moment of interdisciplinary exchange of ideas.

[1] Beirao da Veiga, L. Brezzi, F., Cangiani, A., Manzini, G., Marini, L.D. & Russo, A.: Basic principles of virtual element methods, Mathematical Models and Methods in Applied Sci-ences 23, 199-214, 2013
[2] L. Beirão da Veiga, C. Lovadina, D. Mora, A virtual element method for elastic and inelastic problems on polytope meshes, Comp. Meth. Appl. Mech. Eng. 295, 327–346, 2015.
[3] P. Wriggers, B. Hudobivnik, A low order virtual element formulation for finite elasto-plastic deformations, Comp. Meth. Appl. Mech. Eng. 327, 459–477, 2017.
[4] F. Aldakheel, B. Hudobivnik, E. Artioli, L. Beirão da Veiga and P. Wriggers, Curvilinear Vir-tual Elements for Contact Mechanics, Comp. Meth. Appl. Mech. Eng. 372, 113394, 2020.

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