A comparison of numerical methods used for finite element modelling of soft tissue deformation
A comparison of numerical methods used for finite element modelling of soft tissue deformation
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DOI：
10.1243/03093247jsa482
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发表时间：
2009-07-01
影响因子：
1.6
通讯作者：
Whiteley, J.
中科院分区：
文献类型：
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作者：
Pathmanathan, P.;Gavaghan, D.;Whiteley, J.
软组织变形通常使用不可压缩非线性弹性进行建模，并使用有限元方法计算解。使用有限元方法时有一系列可用选项，特别是用于插值位置和压力的基函数的多项式次数，以及使 LIP 成为网格的元素类型。使用由软组织建模中常见变形驱动的一系列模型问题来研究这些选择对计算解决方案准确性的影响。模型问题包括具有不连续材料属性的 Set LIP（如乳房的情况）、急剧变化的体力梯度（如在收缩的心脏组织中发现的）以及由不连续施加的力引起的边界处解的不连续一阶导数（如乳房 X 光检查期间的乳房）。研究发现，在存在材料界面的情况下，压力基函数的选择至关重要，当存在尖锐梯度时，高阶方案的表现不如预期，而且一般情况下，在选择数值方案时考虑解的预期规律性非常重要。
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 LIP the mesh. The effect of these choices oil 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 LIP 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 ill 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 ill general it is important to take the expected regularity of the Solution into account when choosing a numerical scheme.