A dynamic variational multiscale method for viscoelasticity using linear tetrahedral elements. (14th July 2017)

• Record Type: Journal Article
• Authors: Zeng, Xianyi; Scovazzi, Guglielmo; Abboud, Nabil; Colomés, Oriol; Rossi, Simone
• Is Part Of: International journal for numerical methods in engineering. Volume 112:Number 13(2017)
• Page Start: 1951
• Page End: 2003
• Publication Date: 2017-07-14
• Subjects: piece‐wise linear interpolation -- stabilized methods -- transient dynamics -- tetrahedral finite element -- viscoelasticity; Numerical analysis -- Periodicals; Engineering mathematics -- Periodicals; 620.001518
• DOI: 10.1002/nme.5591
• Languages: English
• ISSNs: 0029-5981

Abstract

Summary: In this article, we develop a dynamic version of the variational multiscale (D‐VMS) stabilization for nearly/fully incompressible solid dynamics simulations of viscoelastic materials. The constitutive models considered here are based on Prony series expansions, which are rather common in the practice of finite element simulations, especially in industrial/commercial applications. Our method is based on a mixed formulation, in which the momentum equation is complemented by a pressure equation in rate form. The unknown pressure, displacement, and velocity are approximated with piecewise linear, continuous finite element functions. To prevent spurious oscillations, the pressure equation is augmented with a stabilization operator specifically designed for viscoelastic problems, in that it depends on the viscoelastic dissipation. We demonstrate the robustness, stability, and accuracy properties of the proposed method with extensive numerical tests in the case of linear and finite deformations.