In the present work we generalize the curvilinear Virtual Element technology, introduced for a simple linear scalar problem in a previous work, to generic 2D solid mechanic problems in small deformations. Such generalization also includes the development of a novel Virtual Element space for displacements that contains rigid body motions. Our approach can accept a generic black-box (elastic or inelastic) constitutive algorithm and, in addition, can make use of curved edges thus leading to an exact approximation of the geometry. Rigorous theoretical interpolation properties for the new space on curvilinear elements are derived. We develop an extensive numerical test campaign, both on elastic and inelastic problems, to assess the behavior of the scheme. The results are very promising and underline the advantages of the curved VEM approach over the standard one in the presence of curved geometries.

Artioli, E., Beirao da Veiga, L., Dassi, F. (2020). Curvilinear Virtual Elements for 2D solid mechanics applications. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 359(1 February 2020) [10.1016/j.cma.2019.112667].

Curvilinear Virtual Elements for 2D solid mechanics applications

Beirao da Veiga, L
;
Dassi, F
2020

Abstract

In the present work we generalize the curvilinear Virtual Element technology, introduced for a simple linear scalar problem in a previous work, to generic 2D solid mechanic problems in small deformations. Such generalization also includes the development of a novel Virtual Element space for displacements that contains rigid body motions. Our approach can accept a generic black-box (elastic or inelastic) constitutive algorithm and, in addition, can make use of curved edges thus leading to an exact approximation of the geometry. Rigorous theoretical interpolation properties for the new space on curvilinear elements are derived. We develop an extensive numerical test campaign, both on elastic and inelastic problems, to assess the behavior of the scheme. The results are very promising and underline the advantages of the curved VEM approach over the standard one in the presence of curved geometries.
Articolo in rivista - Articolo scientifico
Curved edges; Inelasticity; Polygonal mesh; Solid mechanics; Virtual Element Method
English
2020
Artioli, E., Beirao da Veiga, L., Dassi, F. (2020). Curvilinear Virtual Elements for 2D solid mechanics applications. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 359(1 February 2020) [10.1016/j.cma.2019.112667].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/254301
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