Numerical simulation of shear and the Poynting effects by the finite element method: An application of the generalised empirical inequalities in non-linear elasticity

Handle URI:
http://hdl.handle.net/10754/599019
Title:
Numerical simulation of shear and the Poynting effects by the finite element method: An application of the generalised empirical inequalities in non-linear elasticity
Authors:
Angela Mihai, L.; Goriely, Alain
Abstract:
Finite element simulations of different shear deformations in non-linear elasticity are presented. We pay particular attention to the Poynting effects in hyperelastic materials, complementing recent theoretical findings by showing these effects manifested by specific models. As the finite element method computes uniform deformations exactly, for simple shear deformation and pure shear stress, the Poynting effect is represented exactly, while for the generalised shear and simple torsion, where the deformation is non-uniform, the solution is approximated efficiently and guaranteed computational bounds on the magnitude of the Poynting effect are obtained. The numerical results further indicate that, for a given elastic material, the same sign effect occurs under different shearing mechanisms, showing the genericity of the Poynting effect under a variety of shearing loads. In order to derive numerical models that exhibit either the positive or the negative Poynting effect, the so-called generalised empirical inequalities, which are less restrictive than the usual empirical inequalities involving material parameters, are assumed. © 2012 Elsevier Ltd.
Citation:
Angela Mihai L, Goriely A (2013) Numerical simulation of shear and the Poynting effects by the finite element method: An application of the generalised empirical inequalities in non-linear elasticity. International Journal of Non-Linear Mechanics 49: 1–14. Available: http://dx.doi.org/10.1016/j.ijnonlinmec.2012.09.001.
Publisher:
Elsevier BV
Journal:
International Journal of Non-Linear Mechanics
KAUST Grant Number:
KUK-C1-013-04
Issue Date:
Mar-2013
DOI:
10.1016/j.ijnonlinmec.2012.09.001
Type:
Article
ISSN:
0020-7462
Sponsors:
This publication is based on work supported in part by Award no. KUK-C1-013-04 made by King Abdullah University of Science and Technology (KAUST). A.G. is a Wolfson/Royal Society Merit Award Holder and acknowledges support also from a FP7 Marie Curie Reintegration Grant no. BKRVRG0. The support for L.A.M. by the Engineering and Physical Sciences Research Council of Great Britain under Research Programme EP/D048400/1 is gratefully acknowledged as well. The authors would further like to thank Professor J.T. Oden for providing them with a reprint of the article [15], which was very useful in their study of the finite element method for non-linear elastic materials.
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Full metadata record

DC FieldValue Language
dc.contributor.authorAngela Mihai, L.en
dc.contributor.authorGoriely, Alainen
dc.date.accessioned2016-02-25T13:51:18Zen
dc.date.available2016-02-25T13:51:18Zen
dc.date.issued2013-03en
dc.identifier.citationAngela Mihai L, Goriely A (2013) Numerical simulation of shear and the Poynting effects by the finite element method: An application of the generalised empirical inequalities in non-linear elasticity. International Journal of Non-Linear Mechanics 49: 1–14. Available: http://dx.doi.org/10.1016/j.ijnonlinmec.2012.09.001.en
dc.identifier.issn0020-7462en
dc.identifier.doi10.1016/j.ijnonlinmec.2012.09.001en
dc.identifier.urihttp://hdl.handle.net/10754/599019en
dc.description.abstractFinite element simulations of different shear deformations in non-linear elasticity are presented. We pay particular attention to the Poynting effects in hyperelastic materials, complementing recent theoretical findings by showing these effects manifested by specific models. As the finite element method computes uniform deformations exactly, for simple shear deformation and pure shear stress, the Poynting effect is represented exactly, while for the generalised shear and simple torsion, where the deformation is non-uniform, the solution is approximated efficiently and guaranteed computational bounds on the magnitude of the Poynting effect are obtained. The numerical results further indicate that, for a given elastic material, the same sign effect occurs under different shearing mechanisms, showing the genericity of the Poynting effect under a variety of shearing loads. In order to derive numerical models that exhibit either the positive or the negative Poynting effect, the so-called generalised empirical inequalities, which are less restrictive than the usual empirical inequalities involving material parameters, are assumed. © 2012 Elsevier Ltd.en
dc.description.sponsorshipThis publication is based on work supported in part by Award no. KUK-C1-013-04 made by King Abdullah University of Science and Technology (KAUST). A.G. is a Wolfson/Royal Society Merit Award Holder and acknowledges support also from a FP7 Marie Curie Reintegration Grant no. BKRVRG0. The support for L.A.M. by the Engineering and Physical Sciences Research Council of Great Britain under Research Programme EP/D048400/1 is gratefully acknowledged as well. The authors would further like to thank Professor J.T. Oden for providing them with a reprint of the article [15], which was very useful in their study of the finite element method for non-linear elastic materials.en
dc.publisherElsevier BVen
dc.subjectFinite element simulationen
dc.subjectGeneralised empirical inequalitiesen
dc.subjectNon-linear elasticityen
dc.subjectNumerical analysisen
dc.subjectPoynting effecten
dc.subjectShear deformationen
dc.titleNumerical simulation of shear and the Poynting effects by the finite element method: An application of the generalised empirical inequalities in non-linear elasticityen
dc.typeArticleen
dc.identifier.journalInternational Journal of Non-Linear Mechanicsen
dc.contributor.institutionCardiff University, Cardiff, United Kingdomen
dc.contributor.institutionUniversity of Oxford, Oxford, United Kingdomen
kaust.grant.numberKUK-C1-013-04en
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