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dc.contributor.authorFoster, Craig D.
dc.contributor.authorNejad, Talisa Mohammad
dc.date.accessioned2016-09-14T19:22:25Z
dc.date.available2016-09-14T19:22:25Z
dc.date.issued2015-11
dc.identifier.bibliographicCitationFoster, Craig D., and Talisa Mohammad Nejad. "Trilinear Hexahedra with Integral-Averaged Volumes for Nearly Incompressible Nonlinear Deformation." Engineering 7, no. 11 (2015): 765. DOI: 10.4236/eng.2015.711067en_US
dc.identifier.issn1947-3931
dc.identifier.urihttp://hdl.handle.net/10027/21154
dc.descriptionThis is a copy of an article published in the Engineering. © 2015 by authors and Scientific Research Publishing Inc. http://dx.doi.org/10.4236/eng.2015.711067en_US
dc.description.abstractMany materials such as biological tissues, polymers, and metals in plasticity can undergo large deformations with very little change in volume. Low-order finite elements are also preferred for certain applications, but are well known to behave poorly for such nearly incompressible materials. Of the several methods to relieve this volumetric locking, the B method remains popular as no extra variables or nodes need to be added, making the implementation relatively straightforward and efficient. In the large deformation regime, the incompressibility is often treated by using a reduced order or averaged value of the volumetric part of the deformation gradient, and hence this technique is often termed an F approach. However, there is little in the literature detailing the relationship between the choice of F and the resulting B and stiffness matrices. In this article, we develop a framework for relating the choice of F to the resulting B and stiffness matrices. We examine two volume-averaged choices for F , one in the reference and one in the current configuration. Volume-averaged F formulation has the advantage that no integration points are added. Therefore, there is a modest savings in memory and no integration point quantities needed to be interpolated between different sets of points. Numerical results show that the two formulations developed give similar results to existing methods.en_US
dc.language.isoen_USen_US
dc.publisherScientific Research Publishingen_US
dc.subjectIncompressibilityen_US
dc.subjectVolumetric Lockingen_US
dc.subjectStrain Projectionen_US
dc.subjectB-Baren_US
dc.subjectF-Baren_US
dc.subjectFinite Elementen_US
dc.titleTrilinear Hexahedra with Integral-Averaged Volumes for Nearly Incompressible Nonlinear Deformationen_US
dc.typeArticleen_US


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