Journal Article


W. Parnell
Jeremiah G. Murphy
M. D. Gilchrist



physics behaviour slight compressibility anisotropic materials energy finite element method modelling soft tissue

Modelling the slight compressibility of anisotropic soft tissue (2014)

Abstract In order to avoid the numerical difficulties in locally enforcing the incompressibility constraint using the displacement formulation of the Finite Element Method, slight compressibility is typically assumed when simulating transversely isotropic, soft tissue. The current standard method of accounting for slight compressibility of hyperelastic soft tissue assumes an additive decomposition of the strain-energy function into a volumetric and a deviatoric part. This has been shown, however, to be inconsistent with the linear theory for anisotropic materials. It is further shown here that, under hydrostatic tension or compression, a transversely isotropic cube modelled using this additive split is simply deformed into another cube regardless of the size of the deformation, in contravention of the physics of the problem. A remedy for these defects is proposed here: the trace of the Cauchy stress is assumed linear in both volume change and fibre stretch. The general form of the strain-energy function consistent with this model is obtained and is shown to be a generalisation of the current standard model. A specific example is used to clearly demonstrate the differences in behaviour between the two models in hydrostatic tension and compression.
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

W. Parnell, Jeremiah G. Murphy, M. D. Gilchrist

Experts in our system

Jeremiah G Murphy
Dublin City University
Total Publications: 16
M. D. Gilchrist
University College Dublin
Total Publications: 172