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

Handle URI:
http://hdl.handle.net/10754/561898
Title:
A finite strain Eulerian formulation for compressible and nearly incompressible hyperelasticity using high-order B-spline finite elements
Authors:
Duddu, Ravindra; Lavier, Luc L.; Hughes, Thomas Jr R; Calo, Victor M. ( 0000-0002-1805-4045 )
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.
KAUST Department:
Applied 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)
Publisher:
Wiley
Journal:
International Journal for Numerical Methods in Engineering
Issue Date:
5-Oct-2011
DOI:
10.1002/nme.3262
Type:
Article
ISSN:
00295981
Sponsors:
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.
Appears in Collections:
Articles; Environmental Science and Engineering Program; Applied Mathematics and Computational Science Program; Physical Sciences and Engineering (PSE) Division; Earth Science and Engineering Program

Full metadata record

DC FieldValue Language
dc.contributor.authorDuddu, Ravindraen
dc.contributor.authorLavier, Luc L.en
dc.contributor.authorHughes, Thomas Jr Ren
dc.contributor.authorCalo, Victor M.en
dc.date.accessioned2015-08-03T09:33:36Zen
dc.date.available2015-08-03T09:33:36Zen
dc.date.issued2011-10-05en
dc.identifier.issn00295981en
dc.identifier.doi10.1002/nme.3262en
dc.identifier.urihttp://hdl.handle.net/10754/561898en
dc.description.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.en
dc.description.sponsorshipThis 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.en
dc.publisherWileyen
dc.subjectEulerian formulationen
dc.subjectIncompressibilityen
dc.subjectIsogeometric analysisen
dc.subjectLarge deformationen
dc.subjectNonlinear elasticityen
dc.subjectNURBSen
dc.subjectVariational multiscale methodsen
dc.titleA finite strain Eulerian formulation for compressible and nearly incompressible hyperelasticity using high-order B-spline finite elementsen
dc.typeArticleen
dc.contributor.departmentApplied Mathematics and Computational Science Programen
dc.contributor.departmentEarth Science and Engineering Programen
dc.contributor.departmentPhysical Sciences and Engineering (PSE) Divisionen
dc.contributor.departmentEnvironmental Science and Engineering Programen
dc.contributor.departmentNumerical Porous Media SRI Center (NumPor)en
dc.identifier.journalInternational Journal for Numerical Methods in Engineeringen
dc.contributor.institutionInstitute for Geophysics, University of Texas at Austin, Austin, TX 78712, United Statesen
dc.contributor.institutionInstitute for Computational Engineering and Sciences, University of Texas at Austin, Austin, TX, 78712, United Statesen
kaust.authorCalo, Victor M.en
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