A finite strain Eulerian formulation for compressible and nearly incompressible hyperelasticity using high-order B-spline finite elements

Ravindra Duddu, Luc L. Lavier, Thomas Jr R Hughes, Victor M. Calo

Research output: Contribution to journalArticlepeer-review

35 Scopus citations

Abstract

We present a numerical formulation aimed at modeling the nonlinear response of elastic materials using large deformation continuum mechanics in three dimensions. This finite element formulation is based on the Eulerian description of motion and the transport of the deformation gradient. When modeling a nearly incompressible solid, the transport of the deformation gradient is decomposed into its isochoric part and the Jacobian determinant as independent fields. A homogeneous isotropic hyperelastic solid is assumed and B-splines-based finite elements are used for the spatial discretization. A variational multiscale residual-based approach is employed to stabilize the transport equations. The performance of the scheme is explored for both compressible and nearly incompressible applications. The numerical results are in good agreement with theory illustrating the viability of the computational scheme. © 2011 John Wiley & Sons, Ltd.
Original languageEnglish (US)
Pages (from-to)762-785
Number of pages24
JournalInternational Journal for Numerical Methods in Engineering
Volume89
Issue number6
DOIs
StatePublished - Oct 5 2011

ASJC Scopus subject areas

  • Applied Mathematics
  • Engineering(all)
  • Numerical Analysis

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