Journal Article


M. D. Gilchrist
Michel Destrade
Aisling Ní Annaidh
J G Murphy



anisotropic numerical numerical simulations computer simulation elasticity finite element analysis anisotropy models theoretical soft tissue stress response nonlinear dynamics poisson s ratio finite element physiology incompressible materials elastic materials finite elements simulations additive decomposition arteries nonlinear soft tissues

Deficiencies in numerical models of anisotropic nonlinearly elastic materials (2012)

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.
Collections Ireland -> University College Dublin -> Mechanical & Materials Engineering Research Collection
Ireland -> University College Dublin -> College of Engineering & Architecture
Ireland -> University College Dublin -> School of Mechanical and Materials Engineering

Full list of authors on original publication

M. D. Gilchrist, Michel Destrade, Aisling Ní Annaidh, J G Murphy

Experts in our system

M. D. Gilchrist
University College Dublin
Total Publications: 172
Michel Destrade
National University of Ireland Galway
Total Publications: 106
Aisling Ní Annaidh
University College Dublin
Total Publications: 17
Jeremiah G Murphy
Dublin City University
Total Publications: 16