Soft tissue deformation is often modelled using incompressible non-linear elasticity, with solutions computed using the finite element method. There are a range of options available when using the finite element method, in particular the polynomial degree of the basis functions used for interpolating position and pressure, and the type of element making up the mesh. The effect of these choices on the accuracy of the computed solution is investigated, using a selection of model problems motivated by typical deformations seen in soft tissue modelling. Model problems are set up with discontinuous material properties (as is the case for the breast), steeply changing gradients in the body force (as found in contracting cardiac tissue), and discontinuous first derivatives in the solution at the boundary, caused by a discontinuous applied force (as in the breast during mammography). It was found that the choice of pressure basis functions is vital in the presence of a material interface, higher-order schemes do not perform as well as may be expected when there are sharp gradients, and in general it is important to take the expected regularity of the solution into account when choosing a numerical scheme. © IMechE 2009.
|Original language||English (US)|
|Number of pages||16|
|Journal||The Journal of Strain Analysis for Engineering Design|
|State||Published - May 2009|
Bibliographical noteKAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUK-CI-013-04
Acknowledgements: PP is supported through the EPSRC-funded OXMOS project New frontiers in the mathematics of solids (Grant EP/D048400/1). JPW is partially funded by the EPSRC under Grant EP/D503035/1. This publication is based on work supported by Award KUK-CI-013-04, made by King Abdullah University of Science and Technology (KAUST).
This publication acknowledges KAUST support, but has no KAUST affiliated authors.