Error estimation and adaptivity for incompressible hyperelasticity

Handle URI:
http://hdl.handle.net/10754/597968
Title:
Error estimation and adaptivity for incompressible hyperelasticity
Authors:
Whiteley, J.P.; Tavener, S.J.
Abstract:
SUMMARY: A Galerkin FEM is developed for nonlinear, incompressible (hyper) elasticity that takes account of nonlinearities in both the strain tensor and the relationship between the strain tensor and the stress tensor. By using suitably defined linearised dual problems with appropriate boundary conditions, a posteriori error estimates are then derived for both linear functionals of the solution and linear functionals of the stress on a boundary, where Dirichlet boundary conditions are applied. A second, higher order method for calculating a linear functional of the stress on a Dirichlet boundary is also presented together with an a posteriori error estimator for this approach. An implementation for a 2D model problem with known solution, where the entries of the strain tensor exhibit large, rapid variations, demonstrates the accuracy and sharpness of the error estimators. Finally, using a selection of model problems, the a posteriori error estimate is shown to provide a basis for effective mesh adaptivity. © 2014 John Wiley & Sons, Ltd.
Citation:
Whiteley JP, Tavener SJ (2014) Error estimation and adaptivity for incompressible hyperelasticity. Int J Numer Meth Engng 99: 313–332. Available: http://dx.doi.org/10.1002/nme.4677.
Publisher:
Wiley-Blackwell
Journal:
International Journal for Numerical Methods in Engineering
KAUST Grant Number:
KUK-C1-013-04
Issue Date:
30-Apr-2014
DOI:
10.1002/nme.4677
Type:
Article
ISSN:
0029-5981
Sponsors:
This research was supported in part by award no. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST). Both authors would also like to acknowledge financial support through the Colorado State University, College of Natural Sciences International Scholars program.
Appears in Collections:
Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorWhiteley, J.P.en
dc.contributor.authorTavener, S.J.en
dc.date.accessioned2016-02-25T13:17:00Zen
dc.date.available2016-02-25T13:17:00Zen
dc.date.issued2014-04-30en
dc.identifier.citationWhiteley JP, Tavener SJ (2014) Error estimation and adaptivity for incompressible hyperelasticity. Int J Numer Meth Engng 99: 313–332. Available: http://dx.doi.org/10.1002/nme.4677.en
dc.identifier.issn0029-5981en
dc.identifier.doi10.1002/nme.4677en
dc.identifier.urihttp://hdl.handle.net/10754/597968en
dc.description.abstractSUMMARY: A Galerkin FEM is developed for nonlinear, incompressible (hyper) elasticity that takes account of nonlinearities in both the strain tensor and the relationship between the strain tensor and the stress tensor. By using suitably defined linearised dual problems with appropriate boundary conditions, a posteriori error estimates are then derived for both linear functionals of the solution and linear functionals of the stress on a boundary, where Dirichlet boundary conditions are applied. A second, higher order method for calculating a linear functional of the stress on a Dirichlet boundary is also presented together with an a posteriori error estimator for this approach. An implementation for a 2D model problem with known solution, where the entries of the strain tensor exhibit large, rapid variations, demonstrates the accuracy and sharpness of the error estimators. Finally, using a selection of model problems, the a posteriori error estimate is shown to provide a basis for effective mesh adaptivity. © 2014 John Wiley & Sons, Ltd.en
dc.description.sponsorshipThis research was supported in part by award no. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST). Both authors would also like to acknowledge financial support through the Colorado State University, College of Natural Sciences International Scholars program.en
dc.publisherWiley-Blackwellen
dc.subjectError estimationen
dc.subjectFinite elementen
dc.subjectNonlinear elasticityen
dc.titleError estimation and adaptivity for incompressible hyperelasticityen
dc.typeArticleen
dc.identifier.journalInternational Journal for Numerical Methods in Engineeringen
dc.contributor.institutionDepartment of Computer Science; University of Oxford; Wolfson Building, Parks Road UKen
dc.contributor.institutionDepartment of Mathematics; Colorado State University; 105 Weber Building Fort Collins, CO 80523 USAen
kaust.grant.numberKUK-C1-013-04en
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