We present a general virtual element method (VEM) framework for finite elasticity, which emphasizes two issues: element-level volume change (volume average of the determinant of the deformation gradient) and stabilization. To address the former issue, we provide exact evaluation of the average volume change in both 2D and 3D on properly constructed local displacement spaces. For the later issue, we provide a new stabilization scheme that is based on the trace of the material tangent modulus tensor, which captures highly heterogeneous and localized deformations. Two VEM formulations are presented: a two-field mixed and an equivalent displacement-based, which is free of volumetric locking. Convergence and accuracy of the VEM formulations are verified by means of numerical examples, and engineering applications are demonstrated.

Chi, H., BEIRAO DA VEIGA, L., Paulino, G. (2017). Some basic formulations of the virtual element method (VEM) for finite deformations. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 318, 148-192 [10.1016/j.cma.2016.12.020].

Some basic formulations of the virtual element method (VEM) for finite deformations

BEIRAO DA VEIGA, LOURENCO;
2017

Abstract

We present a general virtual element method (VEM) framework for finite elasticity, which emphasizes two issues: element-level volume change (volume average of the determinant of the deformation gradient) and stabilization. To address the former issue, we provide exact evaluation of the average volume change in both 2D and 3D on properly constructed local displacement spaces. For the later issue, we provide a new stabilization scheme that is based on the trace of the material tangent modulus tensor, which captures highly heterogeneous and localized deformations. Two VEM formulations are presented: a two-field mixed and an equivalent displacement-based, which is free of volumetric locking. Convergence and accuracy of the VEM formulations are verified by means of numerical examples, and engineering applications are demonstrated.
Articolo in rivista - Articolo scientifico
Filled elastomers; Finite elasticity; Mixed variational principle; Virtual element method (VEM); Computational Mechanics; Mechanics of Materials; Mechanical Engineering; Physics and Astronomy (all); Computer Science Applications1707 Computer Vision and Pattern Recognition
English
148
192
45
This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Chi, H., BEIRAO DA VEIGA, L., Paulino, G. (2017). Some basic formulations of the virtual element method (VEM) for finite deformations. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 318, 148-192 [10.1016/j.cma.2016.12.020].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/157694
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