A finite strain Eulerian formulation for compressible and nearly incompressible hyperelasticity using high-order B-spline finite elements
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 modelin...
| Main Authors: | , , , |
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| Format: | Journal Article |
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Wiley InterScience
2012
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| Online Access: | http://hdl.handle.net/20.500.11937/51419 |
| _version_ | 1848758694244777984 |
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| author | Duddu, R. Lavier, L. Hughes, T. Calo, Victor |
| author_facet | Duddu, R. Lavier, L. Hughes, T. Calo, Victor |
| author_sort | Duddu, R. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T09:48:03Z |
| format | Journal Article |
| id | curtin-20.500.11937-51419 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T09:48:03Z |
| publishDate | 2012 |
| publisher | Wiley InterScience |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-514192017-09-13T15:35:35Z A finite strain Eulerian formulation for compressible and nearly incompressible hyperelasticity using high-order B-spline finite elements Duddu, R. Lavier, L. Hughes, T. Calo, Victor 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. 2012 Journal Article http://hdl.handle.net/20.500.11937/51419 10.1002/nme.3262 Wiley InterScience restricted |
| spellingShingle | Duddu, R. Lavier, L. Hughes, T. Calo, Victor A finite strain Eulerian formulation for compressible and nearly incompressible hyperelasticity using high-order B-spline finite elements |
| title | A finite strain Eulerian formulation for compressible and nearly incompressible hyperelasticity using high-order B-spline finite elements |
| title_full | A finite strain Eulerian formulation for compressible and nearly incompressible hyperelasticity using high-order B-spline finite elements |
| title_fullStr | A finite strain Eulerian formulation for compressible and nearly incompressible hyperelasticity using high-order B-spline finite elements |
| title_full_unstemmed | A finite strain Eulerian formulation for compressible and nearly incompressible hyperelasticity using high-order B-spline finite elements |
| title_short | A finite strain Eulerian formulation for compressible and nearly incompressible hyperelasticity using high-order B-spline finite elements |
| title_sort | finite strain eulerian formulation for compressible and nearly incompressible hyperelasticity using high-order b-spline finite elements |
| url | http://hdl.handle.net/20.500.11937/51419 |