A finite strain Eulerian formulation for compressible and nearly incompressible hyperelasticity using high-order B-spline finite elements
KAUST DepartmentApplied Mathematics and Computational Science Program
Earth Science and Engineering Program
Physical Sciences and Engineering (PSE) Division
Environmental Science and Engineering Program
Numerical Porous Media SRI Center (NumPor)
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AbstractWe 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.
SponsorsThis 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.