A simple, stable, and accurate linear tetrahedral finite element for transient, nearly, and fully incompressible solid dynamics: a dynamic variational multiscale approach. (12th November 2015)

• Record Type: Journal Article
• Authors: Scovazzi, Guglielmo; Carnes, Brian; Zeng, Xianyi; Rossi, Simone
• Is Part Of: International journal for numerical methods in engineering. Volume 106:Number 10(2016)
• Page Start: 799
• Page End: 839
• Publication Date: 2015-11-12
• Subjects: tetrahedral finite element -- piecewise linear interpolation -- stabilized method -- transient dynamics -- nearly incompressible elasticity; Numerical analysis -- Periodicals; Engineering mathematics -- Periodicals; 620.001518
• DOI: 10.1002/nme.5138
• Languages: English
• ISSNs: 0029-5981

Abstract

Summary: We propose a new approach for the stabilization of linear tetrahedral finite elements in the case of nearly incompressible transient solid dynamics computations. Our method is based on a mixed formulation, in which the momentum equation is complemented by a rate equation for the evolution of the pressure field, approximated with piecewise linear, continuous finite element functions. The pressure equation is stabilized to prevent spurious pressure oscillations in computations. Incidentally, it is also shown that many stabilized methods previously developed for the static case do not generalize easily to transient dynamics. Extensive tests in the context of linear and nonlinear elasticity are used to corroborate the claim that the proposed method is robust, stable, and accurate. Copyright © 2015 John Wiley & Sons, Ltd.