Deficiencies in numerical models of anisotropic nonlinearly elastic materials

Files in This Item:
File Description SizeFormat 
deficiencies in numerical models of anisotropic nonlinearly elastic materials_manuscript.pdf269.37 kBAdobe PDFDownload
Title: Deficiencies in numerical models of anisotropic nonlinearly elastic materials
Authors: Ní Annaidh, Aisling
Destrade, Michel
Gilchrist, M. D.
et al.
Permanent link:
Date: 26-Sep-2012
Online since: 2014-09-29T11:13:11Z
Abstract: Incompressible nonlinearly hyperelastic materials are rarely simulated in finite element numerical experiments as being perfectly incompressible because of the numerical difficulties associated with globally satisfying this constraint. Most commercial finite element packages therefore assume that the material is slightly compressible. It is then further assumed that the corresponding strain-energy function can be decomposed additively into volumetric and deviatoric parts. We show that this decomposition is not physically realistic, especially for anisotropic materials, which are of particular interest for simulating the mechanical response of biological soft tissue. The most striking illustration of the shortcoming is that with this decomposition, an anisotropic cube under hydrostatic tension deforms into another cube instead of a hexahedron with non-parallel faces. Furthermore, commercial numerical codes require the specification of a 'compressibility parameter' (or 'penalty factor'), which arises naturally from the flawed additive decomposition of the strain-energy function. This parameter is often linked to a 'bulk modulus', although this notion makes no sense for anisotropic solids; we show that it is essentially an arbitrary parameter and that infinitesimal changes to it result in significant changes in the predicted stress response. This is illustrated with numerical simulations for biaxial tension experiments of arteries, where the magnitude of the stress response is found to change by several orders of magnitude when infinitesimal changes in 'Poisson’s ratio' close to the perfect incompressibility limit of 1/2 are made.
Type of material: Journal Article
Publisher: Springer-Verlag
Journal: Biomechanics and Modeling in Mechanobiology
Volume: 12
Issue: 4
Start page: 781
End page: 791
Copyright (published version): 2012 Springer-Verlag
Keywords: Nonlinear soft tissuesAnisotropyAdditive decompositionFinite elements simulations
DOI: 10.1007/s10237-012-0442-3
Language: en
Status of Item: Peer reviewed
Appears in Collections:Mechanical & Materials Engineering Research Collection

Show full item record

Citations 10

Last Week
Last month
checked on Feb 12, 2019

Google ScholarTM



This item is available under the Attribution-NonCommercial-NoDerivs 3.0 Ireland. No item may be reproduced for commercial purposes. For other possible restrictions on use please refer to the publisher's URL where this is made available, or to notes contained in the item itself. Other terms may apply.