A simple, stable, and accurate linear tetrahedral finite element for transient, nearly, and fully incompressible solid dynamics: a dynamic variational multiscale approach

Abstract

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.

Document Details

Document Type
Pub Defense Publication
Publication Date
Nov 12, 2015
Source ID
10.1002/nme.5138

Entities

People

  • Brian Carnes
  • Guglielmo Scovazzi
  • Simone Rossi
  • Xianyi Zeng

Organizations

  • Duke University
  • Office of Naval Research
  • Sandia National Laboratories
  • United States Department of Energy

Tags

Fields of Study

  • Mathematics
  • Physics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)