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 language||English (US)|
|Number of pages||24|
|Journal||International Journal for Numerical Methods in Engineering|
|State||Published - Oct 5 2011|
Bibliographical noteKAUST Repository Item: Exported on 2020-10-01
Acknowledgements: This work was supported by a Collaborative Research Grant from King Abdullah University of Science and Technology (KAUST) and we are grateful for its support. We also thank John Evans for his helpful input on NURBS and isogeometric analysis. T. J. R. Hughes was partially supported by the Office of Naval Research contract N00014-08-1-0992.
ASJC Scopus subject areas
- Applied Mathematics
- Numerical Analysis