A uniform deformation gradient hexahedron element with artificial hourglass control

30 August 1995

journal article
research article
Published by Wiley in International Journal for Numerical Methods in Engineering

Vol. 38 (16) , 2809-2828
https://doi.org/10.1002/nme.1620381608

Abstract

An 8‐noded linear hexahedron element for large strain hyperelastic analysis is presented in this paper. The element is based on a constant deformation gradient interpolation and is formulated using a mixed variational principle of the Hu–Washizu type. Volumetric and isochoric components of the deformation are treated independently to ensure the correct evaluation of the element volume. A simple procedure to control the propagation of spurious hourglass deformation modes is also discussed. This is based on the addition of artificial hourglass forces which vanish under constant deformation gradient conditions, thereby ensuring that the element passes a non‐linear version of the patch test. Applications in the field of neo‐Hookean materials and superplastic forming processes are also considered.

Keywords

This publication has 18 references indexed in Scilit:

Assumed strain stabilization of the eight node hexahedral element
Computer Methods in Applied Mechanics and Engineering, 1993
Assumed strain stabilization of the 4-node quadrilateral with 1-point quadrature for nonlinear problems
Computer Methods in Applied Mechanics and Engineering, 1991
New improved hourglass control for bilinear and trilinear elements in anisotropic linear elasticity
Computer Methods in Applied Mechanics and Engineering, 1987
Global mode hourglassing control
Computer Methods in Applied Mechanics and Engineering, 1987
Use of stabilization matrices in non‐linear analysis
Engineering Computations, 1985
Analysis of hourglass instabilities and control in underintegrated finite element methods
Computer Methods in Applied Mechanics and Engineering, 1984
Hourglass control in linear and nonlinear problems
Computer Methods in Applied Mechanics and Engineering, 1984
On the suppression of zero energy deformation modes
International Journal for Numerical Methods in Engineering, 1983
A uniform strain hexahedron and quadrilateral with orthogonal hourglass control
International Journal for Numerical Methods in Engineering, 1981
Treatment of hourglass patterns in low order finite element codes
International Journal for Numerical and Analytical Methods in Geomechanics, 1978