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

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

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

Type

Article

Authors

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

KAUST Department

Applied Mathematics and Computational Science Program
Earth Science and Engineering Program
Environmental Science and Engineering Program
Numerical Porous Media SRI Center (NumPor)
Physical Science and Engineering (PSE) Division

Online Publication Date

2011-10-05

Print Publication Date

2012-02-10

Date

2011-10-05

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.

Citation

Duddu, R., Lavier, L. L., Hughes, T. J. R., & Calo, V. M. (2011). A finite strain Eulerian formulation for compressible and nearly incompressible hyperelasticity using high-order B-spline finite elements. International Journal for Numerical Methods in Engineering, 89(6), 762–785. doi:10.1002/nme.3262

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.