Transversely isotropic biological, soft tissue must be modelled using both anisotropic invariants
Transversely isotropic biological, soft tissue must be modelled using both anisotropic invariants
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DOI：
10.1016/j.euromechsol.2013.04.003
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发表时间：
2013-11-01
影响因子：
4.1
通讯作者：
Murphy, J. G.
中科院分区：
文献类型：
--
作者：
Murphy, J. G.
骨骼肌、韧带和肌腱通常被认为是不可压缩的、横向各向同性的、非线性超弹性材料。如果采用现象学方法进行建模，则相应的应变能量函数可以表示为柯西-格林应变张量的两个不变量（代表各向同性贡献）和两个伪不变量（代表各向异性贡献）的任意函数。为了数学上的方便，通常会放弃对这些伪不变量之一的依赖。这里将表明，应变能量函数的这种简化形式的必然结果是无穷小剪切模量是相同的，但实验数据不支持这一假设。还将表明，进一步的结果是三种剪切模式中的两种在整个变形范围内是相同的。结论是必须使用两个各向异性不变量对横向各向同性生物软组织进行建模。 (C) 2013 Elsevier Masson SAS。版权所有。
Skeletal muscles, ligaments and tendons are typically assumed to be incompressible, transversely isotropic, non-linearly hyperelastic materials. If one adopts the phenomenological approach to modelling, then the corresponding strain-energy function can be represented as an arbitrary function of two invariants of the Cauchy-Green strain tensors, representing the isotropic contribution, and two pseudo-invariants, representing the anisotropic contribution. For mathematical convenience, dependence on one of these pseudo-invariants is usually dropped. It will be shown here that a necessary consequence of this reduced form of the strain-energy function is that the infinitesimal shear moduli are identical, an assumption that is not supported by experimental data. It will also be shown that a further consequence is that two out of the three shearing modes are identical over the full range of deformation. The conclusion is that transversely isotropic biological, soft tissue must be modelled using both anisotropic invariants. (C) 2013 Elsevier Masson SAS. All rights reserved.